Recent zbMATH articles in MSC 74https://zbmath.org/atom/cc/742022-07-25T18:03:43.254055ZUnknown authorWerkzeugHomogenization theory: periodic and beyond. Abstracts from the workshop held March 14--20, 2021 (online meeting)https://zbmath.org/1487.000362022-07-25T18:03:43.254055ZSummary: The objective of the workshop has been to review the latest developments in homogenization theory for a large category of equations and settings arising in the modeling of solid, fluids, wave propagation, heterogeneous media, etc. The topics approached have covered periodic and non-periodic deterministic homogenization, stochastic homogenization, regularity theory, derivation of wall laws and detailed study of boundary layers, ...Existence results for Sobolev type fuzzy integrodifferential evolution equationhttps://zbmath.org/1487.340592022-07-25T18:03:43.254055Z"Nagarajan, M."https://zbmath.org/authors/?q=ai:nagarajan.murugesan"Radhakrishnan, B."https://zbmath.org/authors/?q=ai:radhakrishnan.bheeman"Anukokila, P."https://zbmath.org/authors/?q=ai:anukokila.paramanSummary: This paper deals with the existence and uniqueness results for Sobolev-type fuzzy integrodifferential evolution equation with non-local condition. The invented outputs are derived by contraction principle and fuzzy number. Also fuzzy number values are normal, upper semi-continuous, convex and compactly supported interval in \(\mathcal{E}_n\). Finally, an example is provided.Positive solutions of beam equations under nonlocal boundary value conditionshttps://zbmath.org/1487.340822022-07-25T18:03:43.254055Z"Wang, Shenglin"https://zbmath.org/authors/?q=ai:wang.shenglin"Chai, Jialong"https://zbmath.org/authors/?q=ai:chai.jialong"Zhang, Guowei"https://zbmath.org/authors/?q=ai:zhang.guowei.1|zhang.guowei(no abstract)The thin obstacle problem: a surveyhttps://zbmath.org/1487.350022022-07-25T18:03:43.254055Z"Fernández-Real, Xavier"https://zbmath.org/authors/?q=ai:fernandez-real.xavierIn this paper under review, the author gives a self-contained survey on the main currently known results about the thin obstacle problem (Signorini problem). The author presents the regularity theory for the thin obstacle problem together with some proofs, some of which are different from the current literature: for instance the classification result for free boundary points with frequency less than two, the dimension estimates for the non-regular non-singular set.
This survey provides a detailed introduction on the original Signorini problem in elasticity as well as several related problems, like the obstacle problem for the fractional Laplacian. It also covers some very recent results on the singular set, non-regular non-singular set and generic regularity. It thus serves a very good resource for those who want to learn the topic and get to know the recent development of the field.
Reviewer: Wenhui Shi (Clayton)\(\Gamma\)-convergence of quadratic functionals with non uniformly elliptic conductivity matriceshttps://zbmath.org/1487.350402022-07-25T18:03:43.254055Z"D'Elia, Lorenza"https://zbmath.org/authors/?q=ai:delia.lorenzaSummary: We investigate the homogenization through \(\Gamma\)-convergence for the \(L^2({\Omega})\)-weak topology of the conductivity functional with a zero-order term where the matrix-valued conductivity is assumed to be non strongly elliptic. Under proper assumptions, we show that the homogenized matrix \(A^\ast\) is provided by the classical homogenization formula. We also give algebraic conditions for two and three dimensional 1-periodic rank-one laminates such that the homogenization result holds. For this class of laminates, an explicit expression of \(A^\ast\) is provided which is a generalization of the classical laminate formula. We construct a two-dimensional counter-example which shows an anomalous asymptotic behaviour of the conductivity functional.Stability result of a viscoelastic plate equation with past history and a logarithmic nonlinearityhttps://zbmath.org/1487.350552022-07-25T18:03:43.254055Z"Al-Mahdi, Adel M."https://zbmath.org/authors/?q=ai:al-mahdi.adel-mSummary: In this paper, we are concerned with the decay rate of the solution of a viscoelastic plate equation with infinite memory and logarithmic nonlinearity. We establish an explicit and general decay rate results with imposing a minimal condition on the relaxation function. In fact, we assume that the relaxation function \(h\) satisfies
\[
h^{\prime}(t)\le-\xi(t) H\bigl(h(t)\bigr),\quad t\geq0,
\] where the functions \(\xi\) and \(H\) satisfy some conditions. Our proof is based on the multiplier method, convex properties, logarithmic inequalities, and some properties of integro-differential equations. Moreover, we drop the boundedness assumption on the history data, usually made in the literature. In fact, our results generalize, extend, and improve earlier results in the literature.General decay of Bresse system by modified thermoelasticity of type IIIhttps://zbmath.org/1487.350582022-07-25T18:03:43.254055Z"Dridi, Hanni"https://zbmath.org/authors/?q=ai:dridi.hanni"Saci, Marwa"https://zbmath.org/authors/?q=ai:saci.marwa"Djebabla, Abdelhak"https://zbmath.org/authors/?q=ai:djebabla.abdelhakSummary: In this paper we have studied the model for arched beams problem
\[
\begin{aligned}
&\rho_1\varphi_{tt}-k(\varphi_x+\psi +l\omega)_x-k_0l(\omega_x-l\varphi)=0,\\
&\rho_2\psi_{tt}-b\psi_{xx}+k(\varphi_x+\psi +l\omega)+\gamma \theta_{tx}=0,\\
&\rho_1\omega_{tt}-k_0(\omega_x-l\varphi)_x+kl(\varphi_x +\psi +l\omega)=0,\\
&\rho_3\theta_{tt}-\kappa \theta_{xx}+\beta (g*\theta_{xx})+\gamma \psi_{tx}=0,
\end{aligned}
\] which reduces to the classical Timoshenko system when the arch curvature \(l=0\), the asymptotic stability of one-dimensional Timoshenko system by thermoelasticity of type III was proved by \textit{A. Djebabla} and \textit{N. Tatar} [J. Dyn. Control Syst. 16, No. 2, 189--210 (2010; Zbl 1203.93173)]. The subject of this paper is to supplement these previous results by proving that the Bresse system which is considered a generalization of the Timoshenko system, is also subjected to the same sufficient condition that controls the stability of the Timoshenko system and we have shown that (exponential / polynomial) energy stability is achieved in an (exponential and polynomial) kernel function state.Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory termhttps://zbmath.org/1487.350692022-07-25T18:03:43.254055Z"Boulaaras, Salah"https://zbmath.org/authors/?q=ai:boulaaras.salah-mahmoud"Doudi, Nadjat"https://zbmath.org/authors/?q=ai:doudi.nadjatSummary: In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo-Galerkin method. In addition, an appropriate Lyapunov functional, more general relaxation functions, and some properties of convex functions are considered.Exponential and polynomial stability results for networks of elastic and thermo-elastic rodshttps://zbmath.org/1487.350802022-07-25T18:03:43.254055Z"Hayek, Alaa"https://zbmath.org/authors/?q=ai:hayek.alaa"Nicaise, Serge"https://zbmath.org/authors/?q=ai:nicaise.serge"Salloum, Zaynab"https://zbmath.org/authors/?q=ai:salloum.zaynab"Wehbe, Ali"https://zbmath.org/authors/?q=ai:wehbe.aliSummary: In this paper, we investigate a network of elastic and thermo-elastic materials. On each thermo-elastic edge, we consider two coupled wave equations such that one of them is damped via a coupling with a heat equation. On each elastic edge (undamped), we consider two coupled conservative wave equations. Under some conditions, we prove that the thermal damping is enough to stabilize the whole system. If the two waves propagate with the same speed on each thermo-elastic edge, we show that the energy of the system decays exponentially. Otherwise, a polynomial energy decay is attained. Finally, we present some other boundary conditions and show that under sufficient conditions on the lengths of some elastic edges, the energy of the system decays exponentially on some particular networks similar to the ones considered in [\textit{F. Shel}, Math. Methods Appl. Sci. 36, No. 8, 869--879 (2013; Zbl 1267.35241)].Global existence and exponential decay of solutions for generalized coupled non-degenerate Kirchhoff system with a time varying delay termhttps://zbmath.org/1487.350892022-07-25T18:03:43.254055Z"Mezouar, Nadia"https://zbmath.org/authors/?q=ai:mezouar.nadia"Boulaaras, Salah"https://zbmath.org/authors/?q=ai:boulaaras.salah-mahmoudSummary: The paper studies a system of nonlinear viscoelastic Kirchhoff system with a time varying delay and general coupling terms. We prove the global existence of solutions in a bounded domain using the energy and Faedo-Galerkin methods with respect to the condition on the parameters in the coupling terms together with the weight condition as regards the delay terms in the feedback and the delay speed. Furthermore, we construct some convex function properties, and we prove the uniform stability estimate.Random attractors for stochastic plate equations with memory in unbounded domainshttps://zbmath.org/1487.351082022-07-25T18:03:43.254055Z"Yao, Xiao Bin"https://zbmath.org/authors/?q=ai:yao.xiaobin(no abstract)Constrained optimization problems governed by PDE models of grain boundary motionshttps://zbmath.org/1487.352182022-07-25T18:03:43.254055Z"Antil, Harbir"https://zbmath.org/authors/?q=ai:antil.harbir"Kubota, Shodai"https://zbmath.org/authors/?q=ai:kubota.shodai"Shirakawa, Ken"https://zbmath.org/authors/?q=ai:shirakawa.ken"Yamazaki, Noriaki"https://zbmath.org/authors/?q=ai:yamazaki.noriakiSummary: In this article, we consider a class of optimal control problems governed by state equations of Kobayashi-Warren-Carter-type. The control is given by physical temperature. The focus is on problems in dimensions less than or equal to 4. The results are divided into four Main Theorems, concerned with: solvability and parameter dependence of state equations and optimal control problems; the first-order necessary optimality conditions for these regularized optimal control problems. Subsequently, we derive the limiting systems and optimality conditions and study their well-posedness.Solutions to a multi-phase model of sea ice growthhttps://zbmath.org/1487.352192022-07-25T18:03:43.254055Z"Tang, Yangxin"https://zbmath.org/authors/?q=ai:tang.yangxin"Zheng, Lin"https://zbmath.org/authors/?q=ai:zheng.lin"Luan, Liping"https://zbmath.org/authors/?q=ai:luan.liping(no abstract)On the obstacle problem for the 1D wave equationhttps://zbmath.org/1487.352542022-07-25T18:03:43.254055Z"Fernández-Real, Xavier"https://zbmath.org/authors/?q=ai:fernandez-real.xavier"Figalli, Alessio"https://zbmath.org/authors/?q=ai:figalli.alessioSummary: Our goal is to review the known theory on the one-dimensional obstacle problem for the wave equation, and to discuss some extensions. We introduce the setting established by Schatzman within which existence and uniqueness of solutions can be proved, and we prove that (in some suitable systems of coordinates) the Lipschitz norm is preserved after collision. As a consequence, we deduce that solutions to the obstacle problem (both simple and double) for the wave equation have bounded Lipschitz norm at all times. Finally, we discuss the validity of an explicit formula for the solution that was found by Bamberger and Schatzman.Navier-Stokes equation and elastic collisionshttps://zbmath.org/1487.352992022-07-25T18:03:43.254055Z"Likar, Andrej"https://zbmath.org/authors/?q=ai:likar.andrejSummary: We show that one can quite well solve the Navier-Stokes equation in two dimensions by following discs which slide on a smooth plate and colide elastically. This approach is so simple that it can be easily used by high-school students with some programming skills. Beside laminar flows without eddies we deal with eddies in rivers and bathtub vortex.Rigorous derivation of a linear sixth-order thin-film equation as a reduced model for thin fluid-thin structure interaction problemshttps://zbmath.org/1487.353142022-07-25T18:03:43.254055Z"Bukal, Mario"https://zbmath.org/authors/?q=ai:bukal.mario"Muha, Boris"https://zbmath.org/authors/?q=ai:muha.borisSummary: We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation inequalities quantified in terms of two small parameters, thickness of the fluid layer and thickness of the elastic structure, we identify the right relation between the system coefficients and small parameters which eventually provide a reduced model on the vanishing limit. The reduced model is a linear sixth-order thin-film equation describing the out-of-plane displacement of the structure, which is justified in terms of weak convergence results relating its solution to the solutions of the original fluid-structure interaction problem. Furthermore, approximate solutions to the fluid-structure interaction problem are reconstructed from the reduced model and quantitative error estimates are obtained, which provide even strong convergence results.Thermal flows in fractured porous mediahttps://zbmath.org/1487.353172022-07-25T18:03:43.254055Z"Gruais, Isabelle"https://zbmath.org/authors/?q=ai:gruais.isabelle"Poliševski, Dan"https://zbmath.org/authors/?q=ai:polisevski.dan-aSummary: We consider the thermal flow problem occuring in a fractured porous medium. The incompressible filtration flow in the porous matrix and the viscous flow in the fractures obey the Boussinesq approximation of Darcy-Forchheimer law and respectively, the Stokes system. They are coupled by the Saffman's variant of the Beavers-Joseph condition. Existence and uniqueness properties are presented. The use of the energy norm in describing the Darcy-Forchheimer law proves to be appropriate. In the \(\varepsilon\)-periodic framework, we find the two-scale homogenized system which governs their asymptotic behaviours when \(\varepsilon \rightarrow 0\) and the Forchheimer effect vanishes. The limit problem is mainly a model of two coupled thermal flows, neither of them being incompressible.The tangential cone condition for some coefficient identification model problems in parabolic PDEshttps://zbmath.org/1487.353432022-07-25T18:03:43.254055Z"Kaltenbacher, Barbara"https://zbmath.org/authors/?q=ai:kaltenbacher.barbara"Nguyen, Tram Thi Ngoc"https://zbmath.org/authors/?q=ai:nguyen.tram-thi-ngoc"Scherzer, Otmar"https://zbmath.org/authors/?q=ai:scherzer.otmarSummary: The tangential condition was introduced in [\textit{M. Hanke} et al., Numer. Math. 72, No. 1, 21--37 (1995; Zbl 0840.65049)] as a sufficient condition for convergence of the Landweber iteration for solving ill-posed problems.
In this paper we present a series of time dependent benchmark inverse problems for which we can verify this condition.
For the entire collection see [Zbl 1471.65006].Study of the dielectric gradient values of reinforced concrete sample by considering radar measurements in an inverse problemhttps://zbmath.org/1487.353572022-07-25T18:03:43.254055Z"Ferrieres, X."https://zbmath.org/authors/?q=ai:ferrieres.xavier"Klysz, G."https://zbmath.org/authors/?q=ai:klysz.g"Guihard, V."https://zbmath.org/authors/?q=ai:guihard.vincent"Albrand, M."https://zbmath.org/authors/?q=ai:albrand.mSummary: The goal of this study is to develop a tool that will evaluate the moisture content gradient in the depth of reinforced concretes in the context of building safety. The monitoring of ageing phenomena, such as the corrosion of steel reinforcements, depends on the amount of water and on its gradient as they are directly related to the dielectric values of the concrete. In this paper, to obtain these values, we propose to solve an inverse problem for reinforced concrete. First, an experimental device based on radar measurements is proposed with its 3D numerical model. Next, we describe an inverse process to determine a dielectric profile according to the depth and validate it on measured data obtained for control samples.Holmgren-John unique continuation theorem for viscoelastic systemshttps://zbmath.org/1487.353612022-07-25T18:03:43.254055Z"de Hoop, Maarten V."https://zbmath.org/authors/?q=ai:de-hoop.maarten-v"Lin, Ching-Lung"https://zbmath.org/authors/?q=ai:lin.ching-lung"Nakamura, Gen"https://zbmath.org/authors/?q=ai:nakamura.genSummary: We consider Holmgren-John's uniqueness theorem for a partial differential equation with a memory term when the coefficients of the equation are analytic. This is a special case of the general unique continuation property (UCP) for the equation if its coefficients are analytic. As in the case in the absence of a memory term, the Cauchy-Kowalevski theorem is the key to prove this. The UCP is an important tool in the analysis of related inverse problems. A typical partial differential equation with memory term is the equation describing viscoelastic behavior. Here, we prove the UCP for the viscoelastic equation when the relaxation tensor is analytic and allowed to be fully anisotropic.
For the entire collection see [Zbl 1471.65006].Continuum model and numerical method for dislocation structure and energy of grain boundarieshttps://zbmath.org/1487.353632022-07-25T18:03:43.254055Z"Qin, Xiaoxue"https://zbmath.org/authors/?q=ai:qin.xiaoxue"Gu, Yejun"https://zbmath.org/authors/?q=ai:gu.yejun"Zhang, Luchan"https://zbmath.org/authors/?q=ai:zhang.luchan"Xiang, Yang"https://zbmath.org/authors/?q=ai:xiang.yangUnique identification of a multi-layered fluid-solid mediumhttps://zbmath.org/1487.354412022-07-25T18:03:43.254055Z"Cui, Yanli"https://zbmath.org/authors/?q=ai:cui.yanli"Li, Xiliang"https://zbmath.org/authors/?q=ai:li.xiliang"Qu, Fenglong"https://zbmath.org/authors/?q=ai:qu.fenglongSummary: This paper is concerned with the inverse scattering of time-harmonic acoustic plane waves by a multi-layered fluid-solid medium in the three dimensional space. We establish the global uniqueness in identifying the embedded penetrable solid obstacle, the surrounding fluid medium and its wave number from the acoustic far-field pattern for all incident plane waves at a fixed frequency. The proof depends on constructing different kinds of interior transmission problems in appropriate small domains and the a priori estimates derived for both the elastic wave fields in the embedded solid obstacle and the acoustic wave fields in the surrounding fluid medium.Monotonicity-based regularization for shape reconstruction in linear elasticityhttps://zbmath.org/1487.354452022-07-25T18:03:43.254055Z"Eberle, Sarah"https://zbmath.org/authors/?q=ai:eberle.sarah"Harrach, Bastian"https://zbmath.org/authors/?q=ai:harrach.bastianSummary: We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from Eberle and Harrach (Inverse Probl 37(4):045006, 2021), but have no rigorously proven convergence theory. Therefore we show how the monotonicity methods can be converted into a regularization method for a data-fitting functional without losing the convergence properties of the monotonicity methods. This is a great advantage and a significant improvement over standard regularization techniques. In more detail, we introduce constraints on the minimization problem of the residual based on the monotonicity methods and prove the existence and uniqueness of a minimizer as well as the convergence of the method for noisy data. In addition, we compare numerical reconstructions of inclusions based on the monotonicity-based regularization with a standard approach (one-step linearization with Tikhonov-like regularization), which also shows the robustness of our method regarding noise in practice.Recovering density for the Mindlin-Timoshenko system by means of a single boundary measurementhttps://zbmath.org/1487.354482022-07-25T18:03:43.254055Z"Kurz, Jason"https://zbmath.org/authors/?q=ai:kurz.jason"Liu, Shitao"https://zbmath.org/authors/?q=ai:liu.shitao"Pei, Pei"https://zbmath.org/authors/?q=ai:pei.peiSummary: In this paper, we consider an inverse problem for the Mindlin-Timoshenko plate system, which is a strongly coupled two-dimensional system consisting of a wave equation and a system of isotropic elasticity, that arises in modeling plate vibrations especially at high frequencies and thicker plates. More precisely, we prove the global uniqueness of recovering the plate density from a single boundary measurement under appropriate geometrical assumptions. Our approach relies on diagonalizing the principal part of the system and making it a system of wave-like equations.Random attractors for the stochastic coupled suspension bridge equations of Kirchhoff typehttps://zbmath.org/1487.354662022-07-25T18:03:43.254055Z"Xu, Ling"https://zbmath.org/authors/?q=ai:xu.ling"Huang, Jianhua"https://zbmath.org/authors/?q=ai:huang.jianhua"Ma, Qiaozhen"https://zbmath.org/authors/?q=ai:ma.qiaozhen(no abstract)Spectral analysis of integro-differential equations arising in thermal physicshttps://zbmath.org/1487.450132022-07-25T18:03:43.254055Z"Pankratova, E. V."https://zbmath.org/authors/?q=ai:pankratova.ekaterina-v|pankratova.evgeniya-vThis paper is devoted to the spectrum of an operator function arising in the study of the following abstract second-order integro-differential equation in a separable Hilbert space \(H\):
\[
\frac{d^2u(t)}{dt^2} + \int \limits ^t_0 Q(t - s)\frac{du(s)}{ds} ds + A^2u(t) - \int \limits ^t_0 K(t - s)A^2 2u(s) ds = f(t), \tag{1}
\]
with \(t \in \mathbb{R}_+\) and initial conditions \(u(+0) = \varphi_0\), \(u^{\prime}(+0) = \varphi_1\). Here, \(A \) is a linear operator on \( H\) and \(A: \operatorname{Dom}(A) \to H\) is a self-adjoint positive definite operator with compact inverse.
The author is mainly interested in the spectral analysis of the operator function resulting from applying the Laplace transform to the left-hand side of Equation~(1). In particular, the localization of the spectrum of this operator function is obtained. The asymptotics of the non-real part of the spectrum is constructed.
Reviewer: Anar Assanova (Almaty)Strong dissipative hydrodynamical systems and the operator pencil of S. Kreinhttps://zbmath.org/1487.470262022-07-25T18:03:43.254055Z"Voytitsky, V. I."https://zbmath.org/authors/?q=ai:voytitsky.victor-ivanovichThis review article is devoted to the linear operator differential equation \(u''(t)+(A+iG)u'(t)+Bu(t)=f(t)\) provided strong dissipativeness and to spectral properties of the related operator pencil of the form \(L(\lambda)=I-\lambda S-\lambda^{-1}T\) in a Hilbert space. The paper deals with factorization problems and asymptotics for eigenvalues of the pencil. Such type of equations and pencils arise in hydrodynamics. The author considers applications to the following problems:
\begin{itemize}
\item normal oscillations of viscous liquid in an open vessel,
\item normal oscillations of heavy rotating liquid in an open vessel,
\item normal convective movements of heavy liquid in an open vessel,
\item normal oscillations of joined pendulums with cavities filled with viscous liquids.
\end{itemize}
Reviewer: Nikita V. Artamonov (Moskva)Anisotropic surface tensions for phase transitions in periodic mediahttps://zbmath.org/1487.490182022-07-25T18:03:43.254055Z"Choksi, Rustum"https://zbmath.org/authors/?q=ai:choksi.rustum"Fonseca, Irene"https://zbmath.org/authors/?q=ai:fonseca.irene"Lin, Jessica"https://zbmath.org/authors/?q=ai:lin.jessica"Venkatraman, Raghavendra"https://zbmath.org/authors/?q=ai:venkatraman.raghavendraThe authors consider the Allen-Cahn energy functional \(\mathcal{F} _{\varepsilon }:H^{1}(\Omega )\rightarrow \lbrack 0,\infty ]\) defined as \( \mathcal{F}_{\varepsilon }(u)=\int_{\Omega }[\frac{1}{\varepsilon }a(\frac{x }{\varepsilon })W(u)+\frac{\varepsilon }{2}\left\vert \nabla u\right\vert ^{2}]dx\), where \(\Omega \sqsubseteq \mathbb{R}^{N}\), \(N\geq 2\), is a Lipschitz domain, \(a:\mathbb{R}^{N}\rightarrow \mathbb{R}\) is a continuous, strictly positive and \(\mathbb{T}^{N}\)-periodic function, \(\mathbb{T}^{N}\) being the standard \(N\)-dimensional torus, which satisfies \(0<\theta \leq a(x)\leq \Theta \), for all \(x\in \mathbb{R}^{N}\), and \(W\) is the double-well potential \(W(u)=(1-u^{2})^{2}\). The authors recall some homogenization results concerning this functional. They introduce the anisotropic surface energy \(\sigma :\mathbb{S}^{N-1}\rightarrow \lbrack 0,\infty )\) through the cell formula \(\sigma (\nu )=\lim_{T\rightarrow \infty }\frac{1}{T^{N-1}}\inf \{\int_{TQ_{\nu }}[a(y)W(u)+\frac{1}{2}\left\vert \nabla u\right\vert ^{2}]dy:u\in C(TQ_{\nu })\}\), where \(C(TQ_{\nu })=u\in \{H^{1}(TQ_{\nu }):u=\rho \ast u_{0,\nu }\) on \(\partial (TQ_{\nu })\}\), with \(u_{0,\nu }(y)=-1\) if \(x\cdot \nu \leq 0\), and \(u_{0,\nu }(y)=1\) if \(x\cdot \nu >0\), and \(\rho \in C_{c}^{\infty }(B(0,1))\), with \(0\leq \rho \leq 1\), and \(\int_{ \mathbb{R}^{N}}\rho (x)dx=1\). They also introduce the function \(q:\mathbb{R} \rightarrow \mathbb{R}\) defined by \(q(z)=\tanh (\sqrt{2}z)\), \(z\in \mathbb{R} \), and for \(\nu \in \mathbb{S}^{N-1}\), they define \underline{\(\lambda \)}\( (\nu )=\lim \inf_{T\rightarrow \infty }\frac{1}{T^{N}}\int_{TQ_{\nu }}[a(y)W(q\circ h_{\nu })+\frac{1}{2}2\left\vert \nabla (q\circ h_{\nu })\right\vert ^{2}]dy\) and \(\overline{\lambda }(\nu )=\lim \sup_{T\rightarrow \infty }\frac{1}{T^{N}}\int_{TQ_{\nu }}[a(y)W(q\circ h_{\nu })+\frac{1}{2}2\left\vert \nabla (q\circ h_{\nu }\right\vert ^{2}]dy\) , where \(h_{\nu }(y)=sign(y\cdot \nu )\inf_{z\in \Sigma _{\nu }}d_{\sqrt{a} }(y,z)\), \(\Sigma _{\nu }=\{x\in \mathbb{R}^{N}:x\cdot \nu =0\}\). The first main result proves the existence of a universal constant \(\Lambda _{0}>0\) and of \(\lambda _{0}:\mathbb{S}^{N-1}\rightarrow \lbrack 0,\Lambda _{0}]\) such that \(\overline{\lambda }(\nu )-\lambda _{0}(\nu )\leq \sigma (\nu )\leq \underline{\lambda }(\nu )\). The second main result proves that for each \(\nu \in \mathbb{S}^{N-1}\), there exists a unique \(c(\nu )\in \lbrack \sqrt{\theta },\sqrt{\Theta }]\) such that for every compact \(K\sqsubseteq \mathbb{R}^{N}\), \(\lim_{T\rightarrow \infty }\sup_{x\in K}\left\vert \frac{1}{T}h_{\nu }(Tx)-c(\nu )(x\cdot \nu )\right\vert =0\), and \(c(\nu )=c(-\nu )\). The authors finally also prove a similar result if \(a:\mathbb{R} ^{N}\rightarrow \mathbb{R}\) is a Bohr almost periodic function. For the proof of the first main result, the authors use the standard De Giorgi slicing technique that they recall in an Appendix to prove the upper bound. For the proof of the lower bound, they choose \(\phi =\sqrt{2}\int_{0}^{z} \sqrt{W(s)}ds\) and they prove properties of the function \(h_{\nu }\) in connection with the signed distance \(d_{\sqrt{a}}(y_{1},y_{2})=\inf_{\gamma (0)=y_{1},\gamma (1)=y_{2}}\int_{0}^{1}\sqrt{a(\gamma (t))}\left\vert \overset{.}{\gamma }(t)\right\vert dt\), where \(\gamma \) is a Lipschitz curve \([0,1]\rightarrow \mathbb{R}^{N}\). For the proof of the second and third main results, the authors prove further properties of the function \(h_{\nu }\) and of Bohr almost periodic functions for the third result.
Reviewer: Alain Brillard (Riedisheim)Optimal control of longitudinal motion of an elastic rod using boundary forceshttps://zbmath.org/1487.490572022-07-25T18:03:43.254055Z"Gavrikov, A. A."https://zbmath.org/authors/?q=ai:gavrikov.a-a"Kostin, G. V."https://zbmath.org/authors/?q=ai:kostin.georgy-viktorovichSummary: This study is devoted to the issues of controllability and optimization of oscillatory motions of dynamic systems with distributed parameters. The longitudinal displacements of a thin rectilinear elastic rod are considered. Based on the method of integrodifferential relations proposed by the authors, a generalized formulation of the initial-boundary value problem is given, the solution of which is sought with respect to the kinematic and dynamic variables in a Sobolev energy space. For the case of a uniform rod controlled by external forces applied at both ends, the critical time for which the system can be brought to the rest is determined and the impossibility for arbitrary initial conditions of bringing the points of the rod to the zero state is shown. For fixed time intervals longer than the critical one, the problem is posed to optimally bring the system to the zero state. In this case, the minimized functional is the mean mechanical energy stored in the rod during motion. It is shown that using the d'Alembert representation (in the form of traveling waves), taking into account the properties of the generalized solution, the two-dimensional in space and time control problem is reduced to the classical one-dimensional quadratic variational problem with fixed ends, which is specified with respect to two unknown d'Alembert functions. Using the methods of the calculus of variations, the optimal control and the corresponding motion of the rod are found explicitly. The dependence of the mean energy stored in the system on the control time is analyzed.Computable constants for Korn's inequalities on Riemannian manifoldshttps://zbmath.org/1487.530572022-07-25T18:03:43.254055Z"Knops, R. J."https://zbmath.org/authors/?q=ai:knops.robin-jSummary: A method is presented for the explicit construction of the non-dimensional constant occurring in Korn's inequalities for a bounded two-dimensional Riemannian differentiable simply connected manifold subject to Dirichlet boundary conditions. The method is illustrated by application to the spherical cap and minimal surface.Material distributionshttps://zbmath.org/1487.531232022-07-25T18:03:43.254055Z"Jiménez, Víctor Manuel"https://zbmath.org/authors/?q=ai:jimenez.victor-manuel"de León, Manuel"https://zbmath.org/authors/?q=ai:de-leon.manuel"Epstein, Marcelo"https://zbmath.org/authors/?q=ai:epstein.marceloSummary: The concept of material distribution is introduced as describing the geometric material structure of a general non-uniform body. Any smooth constitutive law is shown to give rise to a unique smooth integrable singular distribution. Ultimately, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform components. Thus, the constitutive law induces a unique partition of the body into smoothly uniform sub-bodies, laminates, filaments and isolated points.Computation of the interior transmission eigenvalues for elastic scattering in an inhomogeneous medium containing an obstaclehttps://zbmath.org/1487.650412022-07-25T18:03:43.254055Z"Chang, Wei-Chen"https://zbmath.org/authors/?q=ai:chang.wei-chen"Li, Tiexiang"https://zbmath.org/authors/?q=ai:li.tiexiang"Lin, Wen-Wei"https://zbmath.org/authors/?q=ai:lin.wen-wei"Wang, Jenn-Nan"https://zbmath.org/authors/?q=ai:wang.jenn-nanSummary: In this work, we study the interior transmission eigenvalues for elastic scattering in an inhomogeneous medium containing an obstacle. This problem is related to the reconstruction of the support of the inhomogeneity without the knowledge of the embedded obstacle by the far-field data or the invisibility cloaking of an obstacle. Our goal is to provide an efficient numerical algorithm to compute as many positive interior transmission eigenvalues as possible. We consider two cases of medium jumps: Case 1, where \(\mathbf{C}_0=\mathbf{C}_1\), \(\rho_0\neq\rho_1\), and Case 2, where \(\mathbf{C}_0\neq\mathbf{C}_1\), \(\rho_0=\rho_1\) with either Dirichlet or Neumann boundary conditions on the boundary of the embedded obstacle. The partial differential equation problem is reduced to a generalized eigenvalue problem (GEP) for matrices by the finite element method. We will apply the Jacobi-Davidson (JD) algorithm to solve the GEP. Case 1 requires special attention because of the large number of zero eigenvalues, which depends on the discretization size. To compute the positive eigenvalues effectively, it is necessary to deflate the zeros to infinity at the beginning of the algorithm.Sequential subspace optimization for recovering stored energy functions in hyperelastic materials from time-dependent datahttps://zbmath.org/1487.651392022-07-25T18:03:43.254055Z"Klein, Rebecca"https://zbmath.org/authors/?q=ai:klein.rebecca"Schuster, Thomas"https://zbmath.org/authors/?q=ai:schuster.thomas"Wald, Anne"https://zbmath.org/authors/?q=ai:wald.anneSummary: Monitoring structures of elastic materials for defect detection by means of ultrasound waves (Structural Health Monitoring, SHM) demands for an efficient computation of parameters which characterize their mechanical behavior. Hyperelasticity describes a nonlinear elastic behavior where the second Piola-Kirchhoff stress tensor is given as a derivative of a scalar function representing the stored (strain) energy. Since the stored energy encodes all mechanical properties of the underlying material, the inverse problem of computing this energy from measurements of the displacement field is very important regarding SHM. The mathematical model is represented by a high-dimensional parameter identification problem for a nonlinear, hyperbolic system with given initial and boundary values. Iterative methods for solving this problem, such as the Landweber iteration, are very time-consuming. The reason is the fact that such methods demand for several numerical solutions of the hyperbolic system in each iteration step. In this contribution we present an iterative method based on sequential subspace optimization (SESOP) which in general uses more than only one search direction per iteration and explicitly determines the step size. This leads to a significant acceleration compared to the Landweber method, even with only one search direction and an optimized step size. This is demonstrated by means of several numerical tests.
For the entire collection see [Zbl 1471.65006].Numerical approximation of some poro-elastic problems with MGT-type dissipation mechanismshttps://zbmath.org/1487.651462022-07-25T18:03:43.254055Z"Bazarra, N."https://zbmath.org/authors/?q=ai:bazarra.noelia"Fernández, J. R."https://zbmath.org/authors/?q=ai:fernandez.jose-ramon"Quintanilla, R."https://zbmath.org/authors/?q=ai:quintanilla.ramonSummary: In this work, we numerically analyze a porous elastic problem including several dissipation mechanisms of MGT type. The resulting variational problem is written in terms of the acceleration and the porosity speed. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved from which the linear convergence of the approximation is derived. Finally, some numerical simulations are presented to show the accuracy of the approximation, the discrete energy decay and the behavior of the solution.Numerical analysis of a porous-elastic model for convection enhanced drug deliveryhttps://zbmath.org/1487.651482022-07-25T18:03:43.254055Z"Ferreira, J. A."https://zbmath.org/authors/?q=ai:ferreira.jose-augusto"Pinto, L."https://zbmath.org/authors/?q=ai:pinto.linu"Santos, R. F."https://zbmath.org/authors/?q=ai:santos.rita-filomena|santos.rui-filipe|santos.rafael-fThe authors of this work studied a coupled system of partial differential equations stemming from modeling of the technique of convection-enhanced drug delivery in an elastic medium. The main contribution of the work is the numerical analysis of a piecewise linear finite element method used for the numerical solution of the system. The authors derived energy and stability estimates for the continuous and discrete pressure, displacement, and concentration variables, and conducted a convergence analysis. Second-order convergence for the three discrete quantities in suitable norms was proven. These estimates were verified by a one-dimensional numerical example. Additional one-dimensional numerical examples with varying elastic properties of tissues were presented.
Reviewer: Baasansuren Jadamba (Rochester)Theoretical and computational structures on solitary wave solutions of Benjamin Bona Mahony-Burgers equationhttps://zbmath.org/1487.651802022-07-25T18:03:43.254055Z"Karakoc, Seydi Battal Gazi"https://zbmath.org/authors/?q=ai:karakoc.seydi-battal-gazi"Ali, Khalid Karam"https://zbmath.org/authors/?q=ai:ali.khalid-karamSummary: This paper aims to obtain exact and numerical solutions of the nonlinear Benjamin Bona Mahony-Burgers (BBM-Burgers) equation. Here, we propose the modified Kudryashov method for getting the exact traveling wave solutions of BBM-Burgers equation and a septic B-spline collocation finite element method for numerical investigations. The numerical method is validated by studying solitary wave motion. Linear stability analysis of the numerical scheme is done with Fourier method based on von-Neumann theory. To show suitability and robustness of the new numerical algorithm, error norms \(L_2, L_{\infty }\) and three invariants \(I_1,I_2\) and \(I_3\) are calculated and obtained results are given both numerically and graphically. The obtained results state that our exact and numerical schemes ensure evident and they are penetrative mathematical instruments for solving nonlinear evolution equation.An element-based preconditioner for mixed finite element problemshttps://zbmath.org/1487.651852022-07-25T18:03:43.254055Z"Rees, Tyrone"https://zbmath.org/authors/?q=ai:rees.tyrone"Wathen, Michael"https://zbmath.org/authors/?q=ai:wathen.michaelStability of nontrivial relative equilibria of a gyrostat with an elastic rod with a mass at the endhttps://zbmath.org/1487.700052022-07-25T18:03:43.254055Z"Chaĭkin, S. V."https://zbmath.org/authors/?q=ai:chaikin.s-vTranslation from the Russian: In a restricted formulation, the motion of a complex mechanical system in a circular Kepler orbit in a central Newtonian force field is considered. The mechanical system consists of a gyrostat and an elastic rod with mass at the free end. The gyrostat is regarded as a rigid object, and a dynamically and statically balanced flywheel is situated in the gyrostat. The homogeneous elastic rod, which is rectilinear in the undeformed state, is rigidly clamped at one end to the gyrostat body. The axis of the undeformed rod is arbitrarily located in the principal central plane of inertia of the gyrostat. The relative displacements of the points of the system as a result of a small deformation of its elastic link are represented as infinite series expansions (without a priori truncation) in a given system of functions that depend on the spatial coordinates, with unknown time-dependent coefficients. The orientation of the system toward the center of attraction is determined by specifying the position with respect to the associated coordinate system of the unit vectors of the normal to the orbital plane and the position vector at the center of mass of the system. This pair of unit vectors is located in the principal central plane of inertia of the gyrostat containing the axis of the undeformed rod. For the one-parameter family of uniaxial orientations of the system toward the center of attraction singled-out in this manner, the author analytically determines the deformations of the rod, which naturally depend on the orientation and the gyrostatic moment, which ensures equilibrium of the chosen orientation (nontrivial equilibrium since, in this case, the rod is, in general, deformed) and conditions for the Lyapunov stability of equilibria.Bifurcation of stationary solutions of a system of Euler-Kirchhoff equations in the case of symmetryhttps://zbmath.org/1487.700252022-07-25T18:03:43.254055Z"Ilyukhin, A. A."https://zbmath.org/authors/?q=ai:ilyukhin.aleksandr-alekseevich"Kolesnikov, S. A."https://zbmath.org/authors/?q=ai:kolesnikov.s-a(no abstract)On the description of deceleration of a body in a medium flowhttps://zbmath.org/1487.700302022-07-25T18:03:43.254055Z"Samsonov, V. A."https://zbmath.org/authors/?q=ai:samsonov.vitaly-a"Selyutskiĭ, Yu. D."https://zbmath.org/authors/?q=ai:selyutskii.yu-d(no abstract)Damping of the forced oscillations of a manipulator with elastic linkshttps://zbmath.org/1487.700322022-07-25T18:03:43.254055Z"Bolgrabskaya, I. A."https://zbmath.org/authors/?q=ai:bolgrabskaya.irina-aTranslation from the Russian: We study the plane motion of a two-link manipulator, consisting of an elastic link and a gripper, under the action of a variable external force. The elastic link of the manipulator is connected to an immovable base by a cylindrical hinge. A gripper is attached to the elastic link by means of a telescopic hinge. We present a finite-dimensional model of this mechanical system, which is a system of \((n+1)\) rigid bodies, the first \(n\) of which are connected by elastic cylindrical hinges, while the \((n+1)\)-th body is attached to the \(n\)-th body by a telescopic hinge. Two additional bodies (oscillation dampers) are attached to the manipulator. We determine conditions under which a controlled motion of the additional bodies can produce a regime in the manipulator in which the links of the manipulator are immovable. We establish that such a regime is possible only when another additional intermediate rigid body is attached to the elastic link by a cylindrical hinge, and the gripper is attached to the additional body by means of a telescope.Closed systems of connected rigid bodieshttps://zbmath.org/1487.700652022-07-25T18:03:43.254055Z"Bolgrabskaya, I. A."https://zbmath.org/authors/?q=ai:bolgrabskaya.irina-a"Savchenko, A. Ya."https://zbmath.org/authors/?q=ai:savchenko.a-ya"Shchepin, N. N."https://zbmath.org/authors/?q=ai:shchepin.n-nTranslation from the Russian: We consider a finite-dimensional model of a closed elastic rod, which enables us to study systems with large deflection. We use a general approach to the representation of the equations of motion of a closed system of \(n\) bodies \(S_1,\ldots,S_n\), starting from the laws of the change in momentum and angular momentum of an individual body \(S_k\). We obtain an expression for the elastic moment, which coincides with the moment introduced in the theory of elastic rods as \(n\to\infty\). We study the equilibrium positions of the system investigated, and consider in detail the case when the axial line of the rod lies in a plane. In explicit form, we find two solutions, in one of which the rod axis being modeled is an annulus, and in the other one, a figure eight.Stabilization of a flexible-link manipulator with passive hingeshttps://zbmath.org/1487.700682022-07-25T18:03:43.254055Z"Zuev, A. L."https://zbmath.org/authors/?q=ai:zuyev.alexander|zuev.a-lTranslation from the Russian: The author studies the dynamics of a manipulator with an arbitrary number of flexible links, based on the Euler-Bernoulli beam model. The first link of the system rotates about a fixed point under the action of a control moment. Neighboring links are connected by hinges, which produce elastic restoring moments directed at an arrangement of central lines of the links. A load is attached to the last link of the system. He obtains a mathematical model of such a manipulator in the form of a boundary value problem with partial derivatives, and studies its eigenfunctions. For the boundary value problem considered, he constructs an approximate system in the sense of Galerkin. A feedback control is proposed that solves the problem of stabilizing the equilibrium position of the approximate system. He studies observability in a linear formulation and numerically models the controlled motion of a nonlinear finite-dimensional system.Asymptotic properties of the eigenvalues in the problem of the oscillation of a flexible manipulatorhttps://zbmath.org/1487.700692022-07-25T18:03:43.254055Z"Zuev, A. L."https://zbmath.org/authors/?q=ai:zuev.a-l|zuyev.alexanderTranslation from the Russian: We consider the Sturm-Liouville problem for a model of a flexible manipulator in the form of a Timoshenko beam to which a rigid body is attached. We prove statements on the distribution of the eigenvalues of this problem. Under additional assumptions about the mechanical parameters, we obtain an asymptotic representation of the natural frequencies.On the inertial motion about the center of mass of an absolutely rigid ellipsoidal shell with viscoelastic and fluid fillingshttps://zbmath.org/1487.700702022-07-25T18:03:43.254055Z"Sudakov, S. N."https://zbmath.org/authors/?q=ai:sudakov.s-nTranslation from the Russian: The problem of inertial motion about the center of mass of a mechanical system consisting of two similar coaxial ellipsoids rigidly connected to each other is considered. The space between the ellipsoids is completely filled with an incompressible viscoelastic Kelvin-Voigt medium. It is assumed that kinematic constraints that allow only uniform deformations are imposed on the medium. The interior ellipsoid is completely filled with an incompressible Newtonian fluid and undergoes uniform vortex motion. The motion of the system is described by nine ordinary differential equations. The authors derive stationary solutions of these equations, which describe uniform rotations of the system about the smallest axis of the ellipsoids. In a linear formulation, they study the behavior of the solutions of the equations of motion in a small neighborhood of the stationary solutions. They establish that if the geometric dimensions and the mass characteristics of the ellipsoids and their fillings are chosen to be those that the Earth has, one can indicate the value of the Young modulus of the viscoelastic medium for which the period of time for the angular velocity vector to go around the smallest axis of the ellipsoids will be equal to the Chandler period.Stability of elastic multi-link structureshttps://zbmath.org/1487.740012022-07-25T18:03:43.254055Z"Ammari, Kaïs"https://zbmath.org/authors/?q=ai:ammari.kais"Shel, Farhat"https://zbmath.org/authors/?q=ai:shel.farhatPublisher's description: This brief investigates the asymptotic behavior of some PDEs on networks. The structures considered consist of finitely interconnected flexible elements such as strings and beams (or combinations thereof), distributed along a planar network. Such study is motivated by the need for engineers to eliminate vibrations in some dynamical structures consisting of elastic bodies, coupled in the form of chain or graph such as pipelines and bridges.
There are other complicated examples in the automotive industry, aircraft and space vehicles, containing rather than strings and beams, plates and shells. These multi-body structures are often complicated, and the mathematical models describing their evolution are quite complex. For the sake of simplicity, this volume considers only 1-\textit{d }networks.Hamilton's principle in continuum mechanicshttps://zbmath.org/1487.740022022-07-25T18:03:43.254055Z"Bedford, Anthony"https://zbmath.org/authors/?q=ai:bedford.anthonyPublisher's description: This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton's principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton's principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.
\begin{itemize}
\item Presents a comprehensive, rigorous description of the application of Hamilton's principle to continuous media;
\item Includes recent applications of the principle to continua with microstructure, mixtures, and media with surfaces of discontinuity;
\item Discusses foundations of continuum mechanics and variational methods therein in the context of linear vector spaces.
\end{itemize}Classical continuum mechanicshttps://zbmath.org/1487.740032022-07-25T18:03:43.254055Z"Surana, Karan S."https://zbmath.org/authors/?q=ai:surana.karan-sPublisher's description: This book provides physical and mathematical foundation as well as complete derivation of the mathematical descriptions and constitutive theories for deformation of solid and fluent continua, both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contra-variant bases. Definitions of co- and contra-variant tensors and tensor calculus are introduced using curvilinear frame and then specialized for Cartesian frame. Both Galilean and non-Galilean coordinate transformations are presented and used in establishing objective tensors and objective rates. Convected time derivatives are derived using the conventional approach as well as non-Galilean transformation and their significance is illustrated in finite deformation of solid continua as well as in the case of fluent continua.
Constitutive theories are derived using entropy inequality and representation theorem. Decomposition of total deformation for solid and fluent continua into volumetric and distortional deformation is essential in providing a sound, general and rigorous framework for deriving constitutive theories. Energy methods and the principle of virtual work are demonstrated to be a small isolated subset of the calculus of variations. Differential form of the mathematical models and calculus of variations preclude energy methods and the principle of virtual work. The material in this book is developed from fundamental concepts at very basic level with gradual progression to advanced topics.
This book contains core scientific knowledge associated with mathematical concepts and theories for deforming continuous matter to prepare graduate students for fundamental and basic research in engineering and sciences. The book presents detailed and consistent derivations with clarity and is ideal for self-study.
See the review of the first edition in [Zbl 1326.74003].Bulk and surface acoustic waves. Fundamentals, devices, and applicationshttps://zbmath.org/1487.740042022-07-25T18:03:43.254055Z"Zhang, Guigen"https://zbmath.org/authors/?q=ai:zhang.guigenPublisher's description: This book introduces acoustic wave theories using a reader-friendly matrix-based linear algebra approach. It will enable the reader to take advantage of software tools such as MATLAB (commercial codes) and OCTAVE (open-source codes) to gain better and deeper understanding of the underlying physics quickly. In this aspect, this text can be regarded as a practical introduction of the acoustic wave theories in an easy-to-follow linear algebra format using matrix manipulations instead of an abstract approach relying on tensor manipulations. The book also uses case studies to demonstrate how the fundamentals on acoustic waves discussed throughout the book are applied in device designs and analyses such that the connections and interdependences between the underlying sciences and the observed behavior and performances can be better appreciated by the reader. To achieve this, all problems for illustrations, examples, case studies, and device analyses are developed and solved based on the mathematical foundations laid out in the book.Current trends and open problems in computational mechanicshttps://zbmath.org/1487.740052022-07-25T18:03:43.254055ZPublisher's description: This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his 70th birthday. Thanks to his high dedication to research, over the years Peter Wriggers has built an international network with renowned experts in the field of computational mechanics. This is proven by the large number of contributions from friends and collaborators as well as former PhD students from all over the world. The diversity of Peter Wriggers network is mirrored by the range of topics that are covered by this book. To name only a few, these include contact mechanics, finite \& virtual element technologies, micromechanics, multiscale approaches, fracture mechanics, isogeometric analysis, stochastic methods, meshfree and particle methods. Applications of numerical simulation to specific problems, e.g. Biomechanics and Additive Manufacturing is also covered. The volume intends to present an overview of the state of the art and current trends in computational mechanics for academia and industry.
The articles of this volume will be reviewed individually.Theoretical analyses, computations, and experiments of multiscale materials. A tribute to Francesco dell'Isolahttps://zbmath.org/1487.740062022-07-25T18:03:43.254055ZPublisher's description: This book is devoted to the 60th birthday of the Prof. Francesco dell'Isola, who is known for his long-term contribution in the field of multiscale materials. It contains several contributions from researchers in the field, covering theoretical analyses, computational aspects and experiments.
The articles of mathematical interest will be reviewed individually.Non-standard discretisation methods in solid mechanicshttps://zbmath.org/1487.740072022-07-25T18:03:43.254055ZPublisher's description: This edited volume summarizes research being pursued within the DFG Priority Programme 1748: ``Reliable Simulation Methods in Solid Mechanics. Development of non-standard discretisation methods, mechanical and mathematical analysis'', the aim of which was to develop novel discretisation methods based e.g. on mixed finite element methods, isogeometric approaches as well as discontinuous Galerkin formulations, including a sound mathematical analysis for geometrically as well as physically nonlinear problems. The Priority Programme has established an international framework for mechanical and applied mathematical research to pursue open challenges on an inter-disciplinary level. The compiled results can be understood as state of the art in the research field and show promising ways of further research in the respective areas. The book is intended for doctoral and post-doctoral students in civil engineering, mechanical engineering, applied mathematics and physics, as well as industrial researchers interested in the field.
The articles of mathematical interest will be reviewed individually.The effect of superheat on the nucleation undercooling of metallic meltshttps://zbmath.org/1487.740082022-07-25T18:03:43.254055Z"Xu, Junfeng"https://zbmath.org/authors/?q=ai:xu.junfeng"Fan, Dandan"https://zbmath.org/authors/?q=ai:fan.dandan"Zhang, Tao"https://zbmath.org/authors/?q=ai:zhang.tao.2|zhang.tao.1|zhang.tao.4|zhang.tao.6|zhang.tao.5Summary: The influences of the superheating temperature \((T_s)\) on the nucleation undercooling \((\Delta T)\) of metallic melts were investigated by using molecular dynamics simulations based on the embedded atom model (EAM) potential function. The results agree with the intuitive expectation that extremely high heating rates followed by short equilibration time lead to a superheating and partial melting of the solid phase. The fraction of the remained crystalline clusters in the superheated phase depends on the superheating temperature \(T_s\) and the equilibration time, as long as \(T_s\) is below the maximal superheating. A subsequent fast cooling facilitates a substantial undercooling of the molten phase. The achieved undercooling \(\Delta T\) below the steady-state melting temperature \(T_m\) depends on the size and the concentration of the crystalline clusters remained in the liquid phase, and thus on the initial superheating temperature \(T_s\). Based on the simulated results, a model was proposed for describing the relationship of \(\Delta T\) and \(T_s\), with which simulated data are well fitted and the maximal undercooling for metals can be predicted.Mathematical modeling of the stress-strain state in metallic media based on the concept of force lineshttps://zbmath.org/1487.740092022-07-25T18:03:43.254055Z"Chukanov, Aleksandr Nikolaevich"https://zbmath.org/authors/?q=ai:chukanov.aleksandr-nikolaevich"Terëshin, Valeriĭ Alekseevich"https://zbmath.org/authors/?q=ai:tereshin.valerii-alekseevich"Tsoĭ, Evgeniĭ Vladimirovich"https://zbmath.org/authors/?q=ai:tsoi.evgenii-vladimirovichSummary: In this article, based on the classical works of G. Kirsch, K. Inglis, G. V. Kolosov, and N. I. Muskhelishvili, we continue to develop a mathematical apparatus that allows us to obtain solutions to a number of three-dimensional problems of fracture mechanics in a hardened metal medium.
Based on the work of G. R. Irwin, G. I. Barenblatt, Westergaard, L. D. Landau, and E. M. Livshits, the authors performed mathematical modeling of the stress-strain state in the volume of a loaded steel sample in the vicinity of pores of various morphologies resulting from operational loads and aggressive environmental influences. An algorithm for determining the components of the stress tensor near concentrators in the form of pores of various shapes is proposed for understanding the force lines of the stress field in a metallic medium. A stationary case with a fixed ratio of external stress and yield strength was considered.Identifying processes governing damage evolution in quasi-static elasticity. I: Analysishttps://zbmath.org/1487.740102022-07-25T18:03:43.254055Z"Grützner, Simon"https://zbmath.org/authors/?q=ai:grutzner.simon"Muntean, Adrian"https://zbmath.org/authors/?q=ai:muntean.adrianThe authors consider a quasi-static elasticity model with damage written as \( \sigma =(1-d)\mathbb{E}\varepsilon (u)\), \(-div(\sigma )=f\), \( d^{\prime }=(1-d)^{-\alpha }g(\nabla u)\), and posed in \(S\times \Omega \), where \(S=(0,T)\) and \(\Omega \) is a bounded and Lipschitz domain in \(\mathbb{R }^{N}\), \(N=1,2,3\). The boundary \(\partial \Omega \) of \(\Omega \) may be decomposed as \(\Gamma _{0}\cup \Gamma _{1}\) where \(\Gamma _{0}\) and \(\Gamma _{1}\) are disjoint, closed, have positive surface measures and are the union of connected components of \(\partial \Omega \). The authors define the set \( \mathcal{G}\) of admissible damage process as \(\mathcal{G}=\{g\in L^{\infty }(S;L^{\infty }(\Omega ;C^{1,1}(\overline{Y})));\) \(\forall y\in \overline{Y} :0\leq g(\cdot ,\cdot ,y)\leq T^{-1}(\omega _{1}-\omega _{0})(1-\omega _{1})^{\alpha }\) a.e. in \(S\times \Omega \}\), where \(\overline{Y}=\overline{B }(0,\overline{y})\subset \mathbb{R}^{N^{2}}\). They prove that for every \( f\in L^{\infty }(S;L^{\infty }(\Omega ))^{N^{2}}\) an admissible damage process \(g\in \mathcal{G}\) generates a Lipschitz-continuous Nemytskii operator \(G:L^{\infty }(S;L^{\infty }(\Omega ))^{N^{2}}\rightarrow L^{\infty }(S;L^{\infty }(\Omega ))\) through \(G(f)(t,x)=g(t,x,f(t,x))\). They define the set of admissible tractions \(\tau \) as \(L^{\infty }(S;W^{\ast })\) and they introduce the function spaces \(V=\{v\in W^{1,2}(\Omega )^{N};\) \(v=0\) on \(\Gamma _{0}\}\), \(W=W^{1/2,2}(\Gamma _{1})^{N}\), their duals \(V^{\ast }\) and \(W^{\ast }\) and the family of operators \(A_{d}(t):V\rightarrow V^{\ast }\) for a.e. \(t\in S\) and its realization \(\mathcal{A}(d):L^{2}(S;V)\rightarrow L^{2}(S;V^{\ast })\) through \(\left\langle (\mathcal{A}(d)u)(t),v\right \rangle _{L^{2}(\Omega )}=\left\langle (A_{d}(t)u(t)),v\right\rangle _{L^{2}(\Omega )}=\int_{\Omega }(1-d(t))\mathbb{E}\varepsilon (u(t)):\varepsilon (v)dx\). They finally define the traction-driven problem as: For given \(f\in L^{\infty }(S;V^{\ast })\), \(\tau \in L^{\infty }(S;W^{\ast })\), \(d_{0}\in D_{0}=\{d_{0}\in L^{\infty }(\Omega );\) \(0\leq d_{0}(x)\leq \omega _{0}\) a.e. in \(\Omega \}\), and \(g\in \mathcal{G}\), find \( u\in L^{\infty }(S;V)\) such that \(\mathcal{A}(d)u=f+\tau \) in \(L^{\infty }(S;V^{\ast })\), \(d^{\prime }=(1-d)^{-\alpha }G(\nabla ^{\mu }u)\) in \( L^{\infty }(S;L^{\infty }(\Omega ))\), and \(d(0)=d_{0}\) in \(L^{\infty }(\Omega )\). They also define the forward operator \(\Phi :\mathcal{G} \rightarrow L^{\infty }(S\times \Omega )^{N}\) through \(\Phi =\pi _{1}\circ F\), where \(\pi _{1}\) is the projection on the first component of \(F\). The first result proves that the traction-driven problem has a unique solution which is Lipschitz continuous with respect to the data. The proof is obtained decoupling the momentum balance and the damage evolution equation. The solution to the coupled problem is obtained applying Banach's fixed point theorem. The authors also prove that the above-defined Nemytskii operator is Fréchet-differentiable and they compute its Fréchet-differential. They characterize the adjoint of the linearized forward operator. In the last part of their paper, the authors analyze the ill-posedness of the inverse problem: Find \(g\) such that \(\Phi (g)=u^{\delta }\in L^{2}(S\times \Omega )^{N}\), whose linearization is \(\partial \Phi (g)h=u^{\delta }\) in \(L^{2}(S\times \Omega )^{N}\). They prove that the inverse problem is locally and globally ill-posed. They use a tangential condition they establish.
Reviewer: Alain Brillard (Riedisheim)On the quasi-static approximation in the initial boundary value problem of linearised elastodynamicshttps://zbmath.org/1487.740112022-07-25T18:03:43.254055Z"Knops, R. J."https://zbmath.org/authors/?q=ai:knops.robin-j"Quintanilla, R."https://zbmath.org/authors/?q=ai:quintanilla.ramonSummary: Continuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial homogeneous boundary value problem in the theory of small elastic deformations superposed upon large elastic deformations. This theory imposes no sign-definite assumptions on the linearised elastic moduli and in consequence the requisite estimates are established using methods principally motivated by known Lagrange identity arguments.An intrinsic geometric formulation of hyper-elasticity, pressure potential and non-holonomic constraintshttps://zbmath.org/1487.740122022-07-25T18:03:43.254055Z"Kolev, B."https://zbmath.org/authors/?q=ai:kolev.boris"Desmorat, R."https://zbmath.org/authors/?q=ai:desmorat.rodrigueSummary: Isotropic hyper-elasticity, altogether with the equilibrium equations and the usual boundary conditions, are formulated directly on the body \(\mathcal{B}\), a three-dimensional compact and orientable manifold with boundary equipped with a mass measure. Pearson-Sewell-Beatty pressure potential on the boundary is recovered, using the Poincaré formula. The existence of such a potential requires conditions, which are formulated as non-holonomic constraints on the configuration space.On the incompressible behavior in weakly nonlinear elasticityhttps://zbmath.org/1487.740132022-07-25T18:03:43.254055Z"Kube, Christopher M."https://zbmath.org/authors/?q=ai:kube.christopher-mSummary: This article considers the influence of incompressibility on the compliance and stiffness constants that appear in the weakly nonlinear theory of elasticity. The formulation first considers the incompressibility constraint applied to compliances, which gives explicit finite limits for the second-, third-, and fourth-order compliance constants. The stiffness/compliance relationships for each order are derived and used to determine the incompressible behavior of the second-, third-, and fourth-order stiffness constants. Unlike the compressible case, the fourth-order compliances are not found to be dependent on the fourth-order stiffnesses.Applied questions of Il'yushin theory of elastoplastic processeshttps://zbmath.org/1487.740142022-07-25T18:03:43.254055Z"Molodtsov, I. N."https://zbmath.org/authors/?q=ai:molodtsov.i-n.1Summary: The experimental results of the processes of complex loading along helical strain trajectories are used to find out that the response to the helical strain trajectory following the simple loading after exhaustion of some trace takes a certain shape of the limit mode, that is, there is a correspondence between the deformation trajectory geometry and the form of response. A new variant of constitutive equations for describing complex loading processes with strain trajectories of arbitrary geometry and dimension is considered. The vector constitutive equations and the system of differential equations for the four angles from the Frenet decomposition are obtained. It is proved that the stress vector is represented in the form of sum of three terms: rapidly decaying plastic traces of elastic states, instantaneous responses to the deformation process, and irreversible stresses accumulated along the deformation trajectory. A new method for mathematical modeling of five-dimensional processes of complex loading is constructed and tested on two- and three-dimensional processes.Unified yield criterion and elastoplastic analysis of a rotating solid cylinderhttps://zbmath.org/1487.740152022-07-25T18:03:43.254055Z"Prokudin, A. N."https://zbmath.org/authors/?q=ai:prokudin.aleksandr-nikolaevich"Burenin, A. A."https://zbmath.org/authors/?q=ai:burenin.anatolii-aleksandrovichSummary: Results of the elastoplastic analysis of a rotating solid cylinder with fixed ends under monotonic loading by centrifugal forces are reported. The problem formulation is based on the theory of infinitesimal elastoplastic strains. The unified piecewise-linear yield condition and the associated flow law are used for calculating the plastic component of the strain. The adopted plasticity condition depends on a parameter that can be considered as a material characteristic. An exact solution of the governing system of equations is derived. Regular features of plastic flow development are found. It is demonstrated that six plastic domains are formed in the cylinder in the general case; these domains correspond to different edges and faces of the surface defined by the unified piecewise-linear condition. A dependence of the plastic limit velocity of cylinder rotation on the parameter included into the yield condition is derived.Dynamic deformation of a thin plastic layer between converging rigid cylindershttps://zbmath.org/1487.740162022-07-25T18:03:43.254055Z"Shabaykin, R. R."https://zbmath.org/authors/?q=ai:shabaykin.r-rSummary: Dynamic solutions of an analogue of the Prandtl problem in the case of a cylindrical layer, including terms with \(\alpha^{-1}\) and \(\alpha^0\), for various configurations of cylinders are obtained and analyzed on the basis of asymptotic analysis with a natural small geometric parameter \(\alpha\) without any static or kinematic hypotheses.Model-based estimation of the stress-strain curve of metal stripshttps://zbmath.org/1487.740172022-07-25T18:03:43.254055Z"Stadler, G."https://zbmath.org/authors/?q=ai:stadler.georg"Steinboeck, A."https://zbmath.org/authors/?q=ai:steinboeck.andreas"Baumgart, M."https://zbmath.org/authors/?q=ai:baumgart.michael"Ettl, A."https://zbmath.org/authors/?q=ai:ettl.a"Kugi, A."https://zbmath.org/authors/?q=ai:kugi.andreasSummary: The identification of the stress-strain curve of metal strips is a common task in the metals industry. As an alternative to commonly used tensile test machines, an inexpensive, model-based optical measurement method is presented. Particular importance was placed on the cost and usability of the method. The indirect approach computes the stress-strain curve based on a measured strip bending line. For the measurement, a metal strip is bent over a solid roll. A defined weight can be mounted at the end of the strip to control the local bending moment in the strip. The bending line of the strip is optically measured by a camera. The identification is carried out based on an optimization problem, where the quadratic error between the measured and the modelled strip bending line is minimized. Experimental results and measurements from a tensile test machine show a good agreement and thus verify the proposed identification method.A fractional derivative-based numerical approach to rate-dependent stress-strain relationship for viscoelastic materialshttps://zbmath.org/1487.740182022-07-25T18:03:43.254055Z"Su, Teng"https://zbmath.org/authors/?q=ai:su.teng"Zhou, Hongwei"https://zbmath.org/authors/?q=ai:zhou.hongwei"Zhao, Jiawei"https://zbmath.org/authors/?q=ai:zhao.jiawei"Liu, Zelin"https://zbmath.org/authors/?q=ai:liu.zelin"Dias, Daniel"https://zbmath.org/authors/?q=ai:dias.daniel-m|dias.daniel-a|dias.daniel-bSummary: Strain/stress-controlled loading, loading\textbf{-}unloading, loading-relaxation (or creep), and corresponding cyclic tests are essential for characterizing the viscoelastic materials' rate-dependent stress-strain relationship. A three-parameter model is proposed based on the basic definition of fractional derivative viscoelasticity and time-varying viscosity. This model is applied to many complex loading conditions. The solutions for three monocyclic loading conditions are given and then further generalized to arbitrary linear loading conditions, which are assumed to be first-order functions of time. The generalized solution for the arbitrary linear loading path is validated by modelling the mechanical response of cyclic loading-unloading and loading-relaxation (or creep) tests. Four sets of experimental data for polymer materials are employed to demonstrate the proposed fractional derivative model's efficiency. The results show that it can accurately model strain/ stress-controlled response under various loading conditions using only three parameters. The model is then implemented in numerical software to explore its capacity further, and the simulation results show that it also succeeds in simulating cyclic loading-unloading tests.Free energies for nonlinear materials with memoryhttps://zbmath.org/1487.740192022-07-25T18:03:43.254055Z"Golden, J. M."https://zbmath.org/authors/?q=ai:golden.john-murroughSummary: An exploration of representations of free energies and associated rates of dissipation for a broad class of nonlinear viscoelastic materials is presented in this work. Also included are expressions for the stress functions and work functions derivable from such free energies. For simplicity, only the scalar case is considered. Certain standard formulae are generalized to include higher power terms.
It is shown that the correct initial procedure in this context is to specify the rate of dissipation as a positive semi-definite functional and then to determine the free energy from this, rather than the other way around, which would be the traditional approach.
Particularly detailed versions of these formulae are given for the model with two memory contributions in the free energy, the first being the well-known quadratic functional leading to constitutive relations with linear history terms, while the second is a quartic functional yielding a cubic term for the stress function memory dependence. Also, the discrete spectrum model, for which each memory kernel is a sum of exponentials, is generalized from the quadratic functional representation for the free energy to that with the quartic functional included.
Finally, a model is considered, allowing functional power series with an infinite number of terms for the free energy, rate of dissipation and stress function.Prismatic dislocation loops in crystalline materials with empty and coated channelshttps://zbmath.org/1487.740202022-07-25T18:03:43.254055Z"Kolesnikova, Anna L."https://zbmath.org/authors/?q=ai:kolesnikova.anna-l"Chernakov, Anton P."https://zbmath.org/authors/?q=ai:chernakov.anton-p"Gutkin, Mikhail Yu."https://zbmath.org/authors/?q=ai:gutkin.mikhail-yu"Romanov, Alexey E."https://zbmath.org/authors/?q=ai:romanov.alexey-eSummary: This paper presents for the first time an analytical solution to the boundary-value problem in the theory of elasticity for a circular prismatic dislocation loop (PDL) coaxial to a hollow cylindrical channel in an elastically isotropic infinite matrix. The stress fields and energy of the PDL are calculated and analyzed in detail. Based on the solution, a theoretical model for the misfit stress relaxation through the formation of a misfit PDL around a misfitting nanotube embedded in an infinite matrix is suggested. The critical radii of the embedded nanotube are found and discussed. It is shown that, for thin nanotubes prepared by nanolayer growth on the initial channel surface, there are two critical inner radii of the nanotube, between which the formation of a misfit PDL is energetically favorable.Modeling the temperature, crystallization, and residual stress for selective laser sintering of polymeric powderhttps://zbmath.org/1487.740212022-07-25T18:03:43.254055Z"Shen, Fei"https://zbmath.org/authors/?q=ai:shen.fei"Zhu, Wei"https://zbmath.org/authors/?q=ai:zhu.wei"Zhou, Kun"https://zbmath.org/authors/?q=ai:zhou.kun"Ke, Liao-Liang"https://zbmath.org/authors/?q=ai:ke.liaoliangSummary: A thermomechanical model is developed to predict the temperature, degree of crystallization, residual stress, and strain in the selective laser sintering process for polymeric powder. Especially, a transient heat transfer model is used to calculate the temperature evolution. An elastic-viscoplastic model is developed to describe the temperature- and time-dependent stress-strain behavior of polymeric materials with crystallization-induced strain being included. A crystallization model is used to predict the relative crystallization degree during the cooling process. The sintering process and cooling process of polyamide 12 are simulated using the developed model. The melt pool depth and the deformation of the printed parts are validated by the experimental results. The evolutions of the temperature, relative degree of crystallization, strain, and stress are evaluated. The effects of the cooling rate on the strain and stress evolutions are discussed.A problem with viscoelastic mixtures: numerical analysis and computational experimentshttps://zbmath.org/1487.740222022-07-25T18:03:43.254055Z"Fernández, J. R."https://zbmath.org/authors/?q=ai:fernandez.jose-ramon"Masid, M."https://zbmath.org/authors/?q=ai:masid.maria"Magaña, A."https://zbmath.org/authors/?q=ai:magana.antonio"Quintanilla, R."https://zbmath.org/authors/?q=ai:quintanilla.ramonSummary: In this paper, we study, from the numerical point of view, a dynamic problem involving a mixture of two viscoelastic solids. The mechanical problem is written as a system of two coupled partial differential equations. Its variational formulation is derived and an existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approximations are introduced by using the classical finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are shown, from which we deduce the linear convergence of the algorithm. Finally, some numerical simulations, including examples in one and two dimensions, are presented to show the accuracy of the approximation and the behaviour of the solution.Fiber-reinforced composites: nonlinear elasticity and beyondhttps://zbmath.org/1487.740232022-07-25T18:03:43.254055Z"Wineman, A."https://zbmath.org/authors/?q=ai:wineman.alan-s"Pence, Thomas J."https://zbmath.org/authors/?q=ai:pence.thomas-jSummary: A fiber-reinforced material comprised of a soft polymeric matrix reinforced with polymeric filaments is often modeled as an equivalent anisotropic nonlinearly elastic solid. Although the response of a single constituent polymeric material can be modeled by nonlinear thermo-elasticity over a large range of deformations and temperatures, there can be conditions requiring a theory that extends the range of application to account for other features, such as nonlinear viscoelasticity and an evolving microstructure due to a combination of mechanical and nonmechanical factors. In a multi-constituent fiber-reinforced material these effects can be expected to occur with different initial triggering and ongoing potency in the separate polymer matrix and fiber constituents. This paper summarizes a number of constitutive models for fiber-reinforced materials that include these features, discusses the connection of these models to a nonlinearly elastic scaffold, provides a framework for the incorporation of these features into the constitutive theory for an equivalent general simple solid, and shows how certain terms in the mathematical structure can be associated with the matrix constituent while other terms can associated with the fibrous constituent.Transient thermoelastic problem in a confocal elliptical disc with internal heat sourceshttps://zbmath.org/1487.740242022-07-25T18:03:43.254055Z"Bhad, Pravin P."https://zbmath.org/authors/?q=ai:bhad.pravin-p"Khalsa, Lalsingh H."https://zbmath.org/authors/?q=ai:khalsa.lalsingh-h"Varghese, Vinod"https://zbmath.org/authors/?q=ai:varghese.vinodSummary: An exact solution is found for the thermoelastic responses in an elliptical disc due to interior heat generation within the solid, under thermal boundary conditions that are subjected to arbitrary initial temperature on the upper and lower face at zero temperature, with radiation boundary conditions on both surfaces. The method of integral transformation technique is used to generate an exact solution of heat conduction equation in which sources are generated according to the linear function of the temperature. The determination of displacement and stresses was performed by means of Airy's stress function approach. The numerical results obtained using these computational tools are accurate enough for practical purposes.Basic problems of thermoelasticity with microtemperatures for the circlehttps://zbmath.org/1487.740252022-07-25T18:03:43.254055Z"Bitsadze, L."https://zbmath.org/authors/?q=ai:bitsadze.lamara|bitsadze.l-pSummary: The present paper is devoted to the explicit solution of the Dirichlet type BVP for an elastic circle with microtemperatures. The regular solution of the system of equations for an isotropic materials with microtemperatures is constructed by means of the elementary (harmonic, bi-harmonic and meta-harmonic) functions. The Dirichlet type BVP for a circle is solved explicitly. The obtained solutions are presented as absolutely and uniformly convergent series.Some BVP in the plane theory of thermodynamics with microtemperatureshttps://zbmath.org/1487.740262022-07-25T18:03:43.254055Z"Gulua, B."https://zbmath.org/authors/?q=ai:gulua.bakur"Janjgava, R."https://zbmath.org/authors/?q=ai:janjgava.roman"Kasrashvili, T."https://zbmath.org/authors/?q=ai:kasrashvili.tamar"Narmania, M."https://zbmath.org/authors/?q=ai:narmania.mirandaSummary: In this work we consider the two-dimensional version of statics of the linear theory of elastic materials with inner structure whose particles, in addition to the classical displacement and temperature fields, possess microtemperatures. The Dirichlet BVP is solved for a circle.Irreversible deformation under thermomechanical loading of solidshttps://zbmath.org/1487.740272022-07-25T18:03:43.254055Z"Kikvidze, O. G."https://zbmath.org/authors/?q=ai:kikvidze.o-gSummary: The article considers irreversible deformation of solid under thermomechanical loading, using the phenomenological approach. It is assumed that the strains are small. On the basis of the dilatometric curves and the stress-strain curves, the condition was formulated for the stability of material, and the major inequality and constitutive equations for the irreversible strains under thermo-mechanical loading were obtained. These equations describe the pattern of inelastic deformation of a wide class of metallic materials in the temperature ranges of the phase transformations.Galerkin-type solution for the Moore-Gibson-Thompson thermoelasticity theoryhttps://zbmath.org/1487.740282022-07-25T18:03:43.254055Z"Singh, Bhagwan"https://zbmath.org/authors/?q=ai:singh.bhagwan"Mukhopadhyay, Santwana"https://zbmath.org/authors/?q=ai:mukhopadhyay.santwanaSummary: It is prominent that the Galerkin-type representation plays a dominant role in probing various challenges of mathematical physics, continuum mechanics and occupies an important place in the field of partial differential equations (PDEs). Thus, the contemporary analysis of different boundary value problems (BVPs) in thermoelasticity theory commonly begins by analyzing the Galerkin-type representation of the field equations in terms of elementary functions (harmonic, biharmonic, and metaharmonic, etc). This work is aimed at formulating the representation of a Galerkin-type solution by means of elementary functions for the recently developed Moore-Gibson-Thompson (MGT) thermoelasticity theory. The MGT theory is a generalized form of the Lord-Shulman (LS) model as well as of the Green-Naghdi (GN) thermoelastic model. Here, we establish a theorem and derive the Galerkin-type solution for the basic governing equations under this theory. Later, the Galerkin representation of a system of equations for steady oscillations is derived. Based on this representation, we finally establish the general solution (GS) for the system of homogeneous equations of stable oscillation, neglecting the extrinsic body force and extrinsic heat supply.Modeling of memory dependent derivative under three-phase lag in generalized thermo-viscoelasticityhttps://zbmath.org/1487.740292022-07-25T18:03:43.254055Z"Singh, Biswajit"https://zbmath.org/authors/?q=ai:singh.biswajit"Sarkar, Smita Pal"https://zbmath.org/authors/?q=ai:pal-sarkar.smita"Barman, Krishnendu"https://zbmath.org/authors/?q=ai:barman.krishnenduSummary: In this study, a new generalized model of thermo-viscoelasticity with three phase-lag (TPL) theory concerning memory-dependent derivative (MDD) theory is emphasized. The governing combined equations of the novel model associated with kernel function and time delay are considered in a two-dimensional semi-infinite space. The bounding surface of the medium is assumed to be free of traction and subjected to time-dependent thermal loading. Using Laplace and Fourier Transform techniques, the problem is transformed from the space-time domain and then solved numerically. Suitable numerical technique is used to find the inversion of Fourier and Laplace transforms. In the simulation, the effects of the time-delay parameter and kernel function on the distributions of the displacement components, stresses and temperature field are studied and represented graphically. The results shows that the presence of TPL, the time-delay and kernel function extensively affect all the distributions.Transient-thermoelastic analysis of periodically rotated functionally graded hollow cylinderhttps://zbmath.org/1487.740302022-07-25T18:03:43.254055Z"Yarımpabuç, Durmuş"https://zbmath.org/authors/?q=ai:yarimpabuc.durmusSummary: A closed-form solution for transient thermal stress analysis of functionally graded hollow cylinder exposed to high-temperature difference is obtained under the influence of periodic rotation. All mechanical and thermal properties except the Poisson's ratio are assumed to be graded in the radial direction as a power-law function. The transient heat conduction and equilibrium equations are solved on the Laplace domain by using Bessel functions and the Gauss quadrature integration procedure. The inverse transformation to the real space is achieved by using the modified Durbin method. The novelty of this study is to provide a general solution to the functionally graded cylinder under the effect of periodic rotation in a transient regime. The effects of periodic rotation and high-temperature difference on temperature and thermal stresses are investigated for a specific ceramic-metal mixture by using this solution. The solution presented in this study can be adopted simply by changing the coefficients of inhomogeneity in the power-law variation for any pair of materials.An introduction to quasi-static aeroelasticityhttps://zbmath.org/1487.740312022-07-25T18:03:43.254055Z"Destuynder, Philippe"https://zbmath.org/authors/?q=ai:destuynder.philippe"Fabre, Caroline"https://zbmath.org/authors/?q=ai:fabre.carolineSummary: The aeroelasticity is the science which models, analyses and describes the coupled movements between a flow and a flexible structure. The different phenomena encountered can be classified using three (at least) adimensional numbers: the Strouhal number, the Reynolds number and the reduce frequency number (which despite its name, has no dimension). For sake of clarity, let us just mention in this abstract, that the reduce frequency is the ratio between the time necessary to a flow particle for flying over a flexible structure and the fundamental period of oscillation of this structure.
In the framework of quasi-static aeroelasticity, it is always assumed that the reduce frequency is smaller than the unity. It enables one to define the flow fields (velocity, pressure) from a static position of the structure. The effect of its position with respect to the flow leads to a modification of the stiffness (added aerodynamic stiffness). Furthermore, the relative flow velocity (difference between the flow velocity and the one of the structure) leads to introduce damping due to the flow and therefore modifies the static analysis of stability into the dynamic stability study (aerodynamic damping).
Recently, engineers have upgraded this approach by introducing the added mass concept. This is a mechanical effect due to the fact that the inertia of the structure should take into account the mass of flow which is involved in a movement. This is performed using an incompressible and inviscid model which gives a retroaction effect on the structure proportionally to its velocity. The two first parts of this text are devoted to a formulation of this three effects which are necessary in the dynamic modeling of a flexible (or not) structure immersed in a flow (air or water for instance). Examples in civil engineering and aerodynamics are given in order to illustrate the theoretical formulation. Few control aspects in a dynamic behavior of the coupled fluid-structure modeling are also discussed in a section of this text.
For the entire collection see [Zbl 1471.65004].A closed-form yield criterion for porous materials with Mises-Schleicher-Burzyński matrix containing cylindrical voidshttps://zbmath.org/1487.740322022-07-25T18:03:43.254055Z"dos Santos, Tiago"https://zbmath.org/authors/?q=ai:dos-santos.tiago"Vadillo, Guadalupe"https://zbmath.org/authors/?q=ai:vadillo.guadalupeSummary: This work develops a closed-form yield criterion applicable to porous materials with pressure-dependent matrix presenting tension-compression asymmetry (Mises-Schleicher-Burzyński material) containing parallel cylindrical voids. To develop the strength criterion, the stress-based variational homogenization approach due to [\textit{L. Cheng} et al., ``A stress-based variational model for ductile porous materials'', Int J. Plast. 55, 133--151 (2014; \url{doi:10.1016/j.ijplas.2013.10.003})] is extended to the case of a hollow cylinder under generalized plane strain conditions subjected to axisymmetric loading. Adopting a strictly statically admissible trial stress field, the homogenization procedure results in an approximate yield locus depending on the current material porosity, tension-compression material asymmetry, the mean lateral stress, and an equivalent shear stress. The analytical criterion provides exact solutions for purely hydrostatic loading. Theoretical results are compared with finite element (FE) simulations considering cylindrical unit-cells with distinct porosity levels, different values of the tension-compression asymmetry, and a wide range of stress triaxialities. Based on comparisons, the theoretical results are found to be in good agreement with FE simulations for most of the loading conditions and material features considered in this study. More accurate theoretical predictions are provided when higher material porosities and/or lower tension-compression asymmetries are considered. Overall, the main outcome of this work is a closed-form yield function proving fairly accurate predictions to engineering applications, in which pressure-dependent and tension-compression asymmetric porous materials with cylindrical voids are dealt with. This can be the case of honeycomb structures or additively manufactured materials, in which metal matrix composites are employed.Finite strain modelling for multiphase flow in dual scale porous media during resin infusion processhttps://zbmath.org/1487.740332022-07-25T18:03:43.254055Z"Huang, Ruoyu"https://zbmath.org/authors/?q=ai:huang.ruoyuSummary: Resin infusion is a pressure-gradient-driven composite manufacturing process in which the liquid resin is driven to flow through and fill in the void space of a porous composite preform prior to the heat treatment for resin solidification. It usually is a great challenge to design both the infusion system and the infusion process meeting the manufacturing requirements, especially for large-scale components of aircraft and wind turbine blades. Aiming at addressing the key concerns about flow fronts and air bubble entrapment, the present study proposes a modelling framework of the multiphase flow of resin and air in a dual scale porous medium, i.e. a composite preform. A finite strain formulation is discussed for the fluid-solid interaction during an infusion process. The present study bridges the gap between the microscopic observation and the macroscopic modelling by using the averaging method and first principle method, which sheds new light on the high-fidelity finite element modelling.A simplified model for hydroelasticity of containershipshttps://zbmath.org/1487.740342022-07-25T18:03:43.254055Z"Sengupta, Debasmit"https://zbmath.org/authors/?q=ai:sengupta.debasmit"Datta, Ranadev"https://zbmath.org/authors/?q=ai:datta.ranadev"Sen, Debabrata"https://zbmath.org/authors/?q=ai:sen.debabrataSummary: In this work, a semi-analytic method has been developed to perform the hydroelasticity analysis of containerships. For the solution of the hydrodynamic problem, a time-domain method is developed based on impulse response function (IRF); however, for the solution of the structural responses, modal superposition technique is used assuming the ship is based on Euler-Bernoulli beam theory. The time-domain amplitude of the displacements and velocities corresponding to several modes is then determined using a semi-analytic approach using Duhamel integral technique. In this paper, the effect of structural flexibility in the calculation of structural displacement, shear force, and bending moment is studied. To check the efficiency and correctness of the proposed semi-analytic method, initially, the computed results are compared with published and experimental results for two container ships with different lengths. In the second phase, a comparative study has been made to check the effect of several physical and geometric parameters such as ship length, vessel speed, and wavelength to ship length ratio. It is seen from the comparative study that ship length, Froude number, wave to ship length ratio, etc. have a significant effect in the calculations of global bending moment, shear force. From the computed results, it may be concluded that the proposed semi-analytic approach is capable of generating results within an acceptable range of engineering accuracy with negligible computational effort, and thus, it can be a very useful tool for preliminary design load for larger vessels.Potential method in the coupled theory of elastic double-porosity materialshttps://zbmath.org/1487.740352022-07-25T18:03:43.254055Z"Svanadze, Merab"https://zbmath.org/authors/?q=ai:svanadze.merab-zhSummary: In the present paper the linear coupled model of elastic double-porosity materials is proposed in which the coupled phenomenon of the concepts of Darcy's law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions, and its basic properties are presented. The radiation conditions are established, and Green's identities are obtained. The uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single-layer and double-layer) and volume potentials are constructed, and the basic properties of these potentials are given. The determinants of symbolic matrices of the singular integral operators are calculated explicitly. Then, the BVPs are reduced to the always solvable singular integral equations for which Fredholm's theorems are valid. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.Mathematical model for a magneto-thermoelastic micropolar medium with temperature-dependent material moduli under the effect of mechanical strip loadhttps://zbmath.org/1487.740362022-07-25T18:03:43.254055Z"Alharbi, Amnah M."https://zbmath.org/authors/?q=ai:alharbi.amnah-m"Said, Samia M."https://zbmath.org/authors/?q=ai:said.samia-m"Abd-Elaziz, Elsayed M."https://zbmath.org/authors/?q=ai:abd-elaziz.elsayed-m"Othman, Mohamed I. A."https://zbmath.org/authors/?q=ai:othman.mohamed-ibrahim-ahmedSummary: A new model of equations of generalized thermoelasticity for an isotropic medium with mechanical properties that are dependent on temperature is established. The present problem is a generalization of the three-phase-lag model, Lord and Shulman's coupled theory. The elasticity modulus is a reference temperature function which is linear. Analytical expressions of the considered variables are obtained by using the Laplace-Fourier transforms technique. The results are analysed in a deeper manner by comparing them with unique cases of absence of the magnetic field, temperature-dependent properties of the body, and two types of mechanical loads. The most significant points are highlighted.On the effect of the volumetric deformation in soft dielectric composites with high phase contrasthttps://zbmath.org/1487.740372022-07-25T18:03:43.254055Z"Bardella, Lorenzo"https://zbmath.org/authors/?q=ai:bardella.lorenzo"Volpini, Valentina"https://zbmath.org/authors/?q=ai:volpini.valentina"Gei, Massimiliano"https://zbmath.org/authors/?q=ai:gei.massimilianoSummary: Towards the accurate modelling of soft dielectric composites, this investigation aims at demonstrating that the incompressibility constraint customarily adopted in the literature may lead to largely inaccurate predictions. This claim is grounded on the premise that, even though in these composites each phase may individually be assumed to be incompressible, the volumetric deformation of the softest phase can provide a significant contribution to the effective behaviour if the phase contrast is high enough. To reach our goal, we determine the actuation response of two-phase dielectric laminated composites (DLCs) where the softest phase admits volumetric deformation. Our results, discussed in the light of the limit case in which the softest phase consists of vacuum, on the one hand, challenge the hypotheses usually assumed in the modelling of soft dielectric composites and, on the other hand, are expected to provide useful information for the design of high-performance hierarchical DLCs.Modeling of electro-viscoelastic dielectric elastomer: a continuum mechanics approachhttps://zbmath.org/1487.740382022-07-25T18:03:43.254055Z"Behera, Subrat Kumar"https://zbmath.org/authors/?q=ai:behera.subrat-kumar"Kumar, Deepak"https://zbmath.org/authors/?q=ai:kumar.deepak"Sarangi, Somnath"https://zbmath.org/authors/?q=ai:sarangi.somnathThe authors derive a micro-mechanics-based rheological model for an incompressible isotropic electro-viscoelastic material. Such electroactive polymers may develop large strains under electrical loads.
The proposed model needs only three material parameters: shear modulus, minimal extensibility and viscosity coefficient to fit the available experimental data. This is half the number of material parameters introduced in earlier work.
In deriving the constitutive theory, the authors use a multiplicative deformation gradient decomposition into elastic and viscous parts. The derived constitutive relations are thermodynamically admissible. In developing their theory, the authors assume that the electric field equilibrates faster than the deformation, thus implying that the electric field does not affect the dissipation.
The proposed model is validated using results from uniaxial experimental data, and good agreement is reached.
Some conclusions are discussed concerning the ability of the model to describe the rheological behavior of dielectric elastomers.
Reviewer: Ahmed Ghaleb (Giza)Stress effects on electric currents in antiplane problems of piezoelectric semiconductors over a rectangular domainhttps://zbmath.org/1487.740392022-07-25T18:03:43.254055Z"He, Jialei"https://zbmath.org/authors/?q=ai:he.jialei"Du, Jianke"https://zbmath.org/authors/?q=ai:du.jianke"Yang, Jiashi"https://zbmath.org/authors/?q=ai:yang.jiashiSummary: We study stress-induced electric potential and mobile charge distributions in antiplane deformations of piezoelectric semiconductors. The macroscopic theory of piezoelectric semiconductors is used. A double trigonometric series solution is obtained for the linearized problem over a rectangular domain, showing the formation of electric potential barriers or wells under local mechanical loads. A nonlinear numerical analysis is performed using COMSOL to obtain the current-voltage relation and the current density distribution. Results show that the stress-induced potential barriers/wells affect the electric current distributions and current-voltage relation. Thus, mechanical loads affect the semiconduction in the body, which is the foundation of piezotronic devices made from piezoelectric semiconductors. The effects of various physical and geometric parameters are examined.Seebeck effect on magneto-thermo-viscoelastic homogeneous isotropic hollow cylinder with Green-Naghdi theoryhttps://zbmath.org/1487.740402022-07-25T18:03:43.254055Z"Khamis, A. K."https://zbmath.org/authors/?q=ai:khamis.alaa-k"Nasr, Amir Mohamed Abdel Allah"https://zbmath.org/authors/?q=ai:nasr.amir-mohamed-abdel-allah"El-Bary, A. A."https://zbmath.org/authors/?q=ai:el-bary.alaa-a|el-bary.alla-a"Atef, Haitham M."https://zbmath.org/authors/?q=ai:atef.haitham-mThe authors consider a boundary value problem of magneto-thermo-viscoelasticity for an infinite cylinder of an isotropic, perfect electrical conductor, within the frame of extended thermodynamics under Green and Naghdi hypothesis of zero dissipation. Ohm's law for electric conduction is generalized to include the thermal gradient (Seebeck effect).
The body is subjected to an initially constant magnetic field along the angular coordinate of a cylindrical system of coordinates with z-axis coinciding with the axis of the cylinder. The external boundary is stress-free and subjected to a constant thermal shock.
Symmetry considerations allow for a solution depending only on the radial coordinate and time. The problem is solved by the Laplace transform technique with numerical inversion based on Fourier expansion. Application of the boundary conditions is not shown in the text.
The results for radial displacement, strain and normal stress are plotted as functions of time or distance, for different values of material parameters and initial magnetic field.
Reviewer: Ahmed Ghaleb (Giza)Green's functions for a trigonal piezoelectric half-plane belonging to 3m crystal classhttps://zbmath.org/1487.740412022-07-25T18:03:43.254055Z"Kharrazi, Hossein"https://zbmath.org/authors/?q=ai:kharrazi.hossein"Khojasteh, Ali"https://zbmath.org/authors/?q=ai:khojasteh.ali"Rahimian, Mohammad"https://zbmath.org/authors/?q=ai:rahimian.mohammad-hassan|rahimian.mohammad-amin"Pak, Ronald Y. S."https://zbmath.org/authors/?q=ai:pak.ronald-y-sSummary: Piezoelectric materials have a wide range of industrial applications in different branches of engineering due to their electromechanical coupling. So, investigating their responses to either mechanical or electric loadings helps engineers for efficient design of smart systems. However, most of the studies have assessed the well-known 6 mm piezoelectric materials or piezoceramics and few papers have studied other piezoelectric crystals despite of their application in industry. In this paper, fundamental solutions of a trigonal piezoelectric half-plane belonging to 3m crystal class is obtained. The governing differential equations are derived and solved analytically using potential method. It is shown that the solution for the 3m material can be degenerated to 6 mm solution as a special case. The contour lines were depicted for two practical piezoelectric materials belonging to 3m and 6 mm crystal classes including lithium niobate and PZT-4 and they were compared to each other. The numerical results showed that the response of the trigonal material is asymmetric due to anisotropy and the effect of anisotropy on some responses is considerable causing totally different behavior from 6 mm piezoelectric material.Simulation of antiplane piezoelectricity problems with multiple inclusions using the generalized finite difference methodhttps://zbmath.org/1487.740422022-07-25T18:03:43.254055Z"Yu, Hao"https://zbmath.org/authors/?q=ai:yu.hao.2|yu.hao.4|yu.hao|yu.hao.3|yu.hao.1"Lin, Ji"https://zbmath.org/authors/?q=ai:lin.jiSummary: In this paper, antiplane piezoelectricity problems with multiple inclusions are studied by the generalized finite difference method (GFDM). Developed from the Taylor series and the Moving Least Squares, the GFDM expresses the derivatives of variables as the combination of values of surrounding nodes where the sparse matrix will be obtained considering the boundary conditions and interface conditions. Stress concentration and electric field concentration are analyzed in three numerical examples, which contain circular and elliptical piezoelectric inclusions in various sizes, locations, and material parameters. The applicability and validity of the proposed method are verified through the comparison with reference results.Stability of nanobeams and nanoplates with defectshttps://zbmath.org/1487.740432022-07-25T18:03:43.254055Z"Arif, Hina"https://zbmath.org/authors/?q=ai:arif.hina"Lellep, Jaan"https://zbmath.org/authors/?q=ai:lellep.jaanSummary: The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen's nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement.Extracting stress intensity factors for isotropic cracked domains having stochastic material propertieshttps://zbmath.org/1487.740442022-07-25T18:03:43.254055Z"Omer, Netta"https://zbmath.org/authors/?q=ai:omer.nettaSummary: Material properties are inevitably stochastic due to the manufacturing process and the measurement procedure. In case of a cracked domain, the stochasticity of material properties (as stochastic variables) may manifest in the stress intensity factors (SIFs). Having the stochastic representation of the material properties, Young modulus and Poisson ratio (isotropic material), we approximate the SIFs for 2D cracked domains using the generalized polynomial chaos (gPC). The approximated SIF consists of two families of orthogonal polynomials, selected by the probability distribution function of the material properties. The polynomials are multiplied by a deterministic coefficient, consisting of deterministic SIFs, extracted from a finite element model according to the stochastic properties of both Young modulus and Poisson ratio. Numerical example problems are provided where the stochastic approximation of the SIF is computed. The obtained approximation of the SIF is compared with results obtained using the Monte Carlo method. The results demonstrate the efficiency and accuracy of the proposed method.The advanced convergence method in the problem on torsional oscillations of a circular disc inhomogeneous in thicknesshttps://zbmath.org/1487.740452022-07-25T18:03:43.254055Z"Akulenko, L. D."https://zbmath.org/authors/?q=ai:akulenko.leonid-d"Georgievskii, D. V."https://zbmath.org/authors/?q=ai:georgievskii.dmitrii-vladimirovich"Nesterov, S. V."https://zbmath.org/authors/?q=ai:nesterov.sergei-vSummary: Based on the advanced convergence method developed by the authors, torsional oscillations of a circular disc that is fixed on a shaft are investigated numerically and analytically. The thickness of the disc depends on the radius. The internal boundary of the disc is fixed on a shaft while the external one is load-free. The first few eigenfrequencies of torsional oscillations are obtained for various ratios of the external disc radius and the internal one as well as for various mass distributions.Stability result of laminated beam with internal distributed delayhttps://zbmath.org/1487.740462022-07-25T18:03:43.254055Z"Mpungu, Kassimu"https://zbmath.org/authors/?q=ai:mpungu.kassimu"Apalara, Tijani A."https://zbmath.org/authors/?q=ai:apalara.tijani-abdulazizSummary: In this paper, we consider a laminated Timoshenko beam system with frictional damping and an internal distributed delay feedback on the effective rotational angle. Under appropriate assumptions on the weight of the delay term and wave speeds of the first two equations of the system, we prove that the dissipation through the frictional damping is enough to stabilize the system exponentially.Geometrically nonlinear vibrations of FG-GPLRC cylindrical panels with cutout based on HSDT and mixed formulation: a novel variational approachhttps://zbmath.org/1487.740472022-07-25T18:03:43.254055Z"Ansari, R."https://zbmath.org/authors/?q=ai:ansari.reza"Hassani, R."https://zbmath.org/authors/?q=ai:hassani.ramtin"Hasrati, E."https://zbmath.org/authors/?q=ai:hasrati.e"Rouhi, H."https://zbmath.org/authors/?q=ai:rouhi.hessamSummary: Based on Reddy's third-order shear deformation theory and mixed formulation, a new numerical approach in the variational framework is developed to analyze the geometrically nonlinear free vibration behavior of cylindrical panels having cutouts with various shapes (e.g., square, circular, elliptical) under arbitrary boundary conditions. It is also assumed that the panel is made of functionally graded graphene platelet-reinforced composite with various patterns for the distribution of GPLs along the thickness direction whose effective properties are estimated using the modified Halpin-Tsai model in conjunction with the rule of mixture. The proposed approach can be named VDQFEM as it utilizes the VDQ and FE methods. Efficient matrix formulation, being free from the locking problem, computational efficiency and being able to solve problems with concave and polygon domains are the main features of VDQFEM. Selected numerical results are given to investigate the influences of geometrical parameters and weight fraction/distribution pattern of GPLs on the large-amplitude vibration response of panels with various cutouts and boundary conditions.On the vibrations of pyramidal beams with rectangular cross-Section and application to unswept wingshttps://zbmath.org/1487.740482022-07-25T18:03:43.254055Z"Campos, L. M. B. C."https://zbmath.org/authors/?q=ai:campos.l-m-b-c"Marta, A. C."https://zbmath.org/authors/?q=ai:marta.andre-cSummary: The bending frequencies of an unswept wing are calculated based on the model of a beam clamped at the root and free at the tip. For a tapered wing with straight leading- and trailing-edges, the chord is a linear function of the span; the same linear function of the span applies to thickness, in the case of constant thickness-to-chord ratio. The latter is usually small, so that the beam differs from the more frequent cases of a conical beam with a circular cross-section or a prismatic beam with a square cross-section. Thus, the bending modes of a non-uniform beam are considered, with mass and area moment of inertia which are respectively quadratic and quartic functions of the span. There is no exact solution expressible in finite terms using elementary functions, and thus power series expansions are used. The bending frequencies are calculated for a delta wing and compared with a rectangular wing, with the same span, mean chord and thickness, mass density and Young's modulus. It is shown that the fundamental frequency is higher by a factor 4.96 for the delta wing; it is also shown that the general case of the tapered wing is intermediate between the delta and the rectangular wing. Lastly, the analytical results obtained for the bending modes are compared with numerical modal analyses of general tapered wing beams using high-fidelity finite-element model software.Applying adjustment factors in the Rayleigh method to calculate the principal frequency of the vibrations of a shell with a rectangular cross sectionhttps://zbmath.org/1487.740492022-07-25T18:03:43.254055Z"Dzebisashvili, G. T."https://zbmath.org/authors/?q=ai:dzebisashvili.g-tSummary: The application of adjustment factors in the Rayleigh method to calculate the principal frequency of the vibrations of a shell with a rectangular cross section is considered in this paper. The behavior patterns of the adjustment factors are generalized. The relationship between the adjustment factors and properties of the approximate formulas is analyzed.Theoretical analyses and numerical simulation of flexural vibration based on Reddy and modified higher-order plate theories for a transversely isotropic circular platehttps://zbmath.org/1487.740502022-07-25T18:03:43.254055Z"Ji, Ming"https://zbmath.org/authors/?q=ai:ji.ming"Wu, Yi-Chuang"https://zbmath.org/authors/?q=ai:wu.yi-chuang"Ma, Chien-Ching"https://zbmath.org/authors/?q=ai:ma.chien-chingThe main purpose of this paper is to present analytically the exact solutions of out-of-plane dominated vibration of thick transversely isotropic circular plates based on Reddy plate theory and Modified Higher-Order Shear Deformation Theory (MHSDT) instead of three-dimensional theory. Hamilton's principle is used to derive the equations of motion and boundary conditions for the circular plate. Natural frequencies are determined from the solution of the governing equations and boundary conditions along the circular edge. Comparisons of natural frequencies and mode shapes arising from the Mindlin plate theory, the Reddy plate theory, MHSDT, and finite element method are made for fully free and clamped circular plates. The comparison of results show that MHSDT has better accuracy than the other analytical plate theories in terms of the natural frequencies and corresponding mode shapes. Generally, the two analytical methods predict more accurate natural frequencies than the Mindlin plate theory. For the clamped boundary conditions, Reddy plate theory predicts more accurate natural frequencies than MHSDT when ratio of radius to thickness R/H = 10 and 5; however, MHSDT predicts more accurate natural frequencies than the Reddy plate theory when R/H = 2. A large amount of data (natural frequencies and mode shapes) is presented for direct use of design engineers. It would have been useful if the authors had indicated the border line value of R/H so as to enable the reader to know in advance which theory to use to get accurate results.
Reviewer: Girish Kumar Ramaiah (Bangalore)Adaptation of energy dissipation in a laminated module with tunable twin wellshttps://zbmath.org/1487.740512022-07-25T18:03:43.254055Z"Li, Dejian"https://zbmath.org/authors/?q=ai:li.dejian"Fang, Hui"https://zbmath.org/authors/?q=ai:fang.huiSummary: Vibration energy dissipation in structural components has specific requirements, and the low damping of structural metal favors a lasting dynamic response. This chapter proposes a hysteresis damper realized with a specifically designed laminated metal module consisting of a preloaded beam bimorph and linear springs. Through continuous vibration modeling and simplification, the dynamic governing equations of the laminated module are obtained. In the solution process of the multiple scales method, we focus on the interwell motion characteristics that bring about an order of magnitude increase in energy dissipation compared to a linear module. Our studies employ analytical and numerical findings to probe how the parameters of the system affect energy dissipation. When carefully designed, a twin-well metal module can provide significant damping even for a small excitation amplitude.
For the entire collection see [Zbl 1464.70003].Vibration isolation and energy harvesting integrated in a Stewart platform with high static and low dynamic stiffnesshttps://zbmath.org/1487.740522022-07-25T18:03:43.254055Z"Lu, Ze-Qi"https://zbmath.org/authors/?q=ai:lu.zeqi"Wu, Dao"https://zbmath.org/authors/?q=ai:wu.dao"Ding, Hu"https://zbmath.org/authors/?q=ai:ding.hu"Chen, Li-Qun"https://zbmath.org/authors/?q=ai:chen.liqunSummary: An electromagnetic Stewart platform with high static and low dynamic stiffness is explored to reduce the vibration in six degrees of freedom (6-dofs) and simultaneously harvest energy. Each strut in the Stewart platform contains a moving electromagnet suspended between two fixed permanent magnets that are configured so that the magnet spring has both negative stiffness and soft nonlinearity. The use of stiffness nonlinearity improves vibration isolation efficiency. To obtain the frequency-response function for transmissibility and the power output in the first primary resonance, we apply the harmonic balance method, which is based on rigid-body dynamics and nonlinear elastic theory. The frequency response curves of the 6-dofs have peaks that redshift and bend leftward (toward lower frequencies), and a bubble-shaped resonance curve appears around the first resonance frequency. The numerical simulations support the analytical results. For various mechanical and electrical parameters, the analytical and numerical results both demonstrate that the frequency band of vibration isolation extends to lower frequencies and produces considerable power output. Moreover, the increase in energy harvesting leads to reduced vibration transmissibility under varying some parameters.Dynamics of a system of two coupled MEMS oscillatorshttps://zbmath.org/1487.740532022-07-25T18:03:43.254055Z"Rand, Richard H."https://zbmath.org/authors/?q=ai:rand.richard-h"Zehnder, Alan T."https://zbmath.org/authors/?q=ai:zehnder.alan-t"Shayak, B."https://zbmath.org/authors/?q=ai:shayak.b"Bhaskar, Aditya"https://zbmath.org/authors/?q=ai:bhaskar.adityaSummary: We investigate the dynamics of two limit cycle MEMS oscillators connected via spring coupling. Each individual oscillator is based on a MEMS structure which moves within a laser-driven interference pattern. As the structure vibrates, it changes the interference gap, causing the quantity of absorbed light to change, producing a feedback loop between the motion and the absorbed light and resulting in a limit cycle oscillation. A simplified model of this MEMS oscillator, omitting parametric feedback and structural damping, has been previously presented [the first three authors, ``Analysis of a simplified MEMS oscillator'', in: Proceedings of 9th European nonlinear dynamics conference, ENOC'17. Budapest: CongressLine Ltd. Article ID 77, 2 p. (2017)]. For the coupled system, a perturbation method is used to obtain a slow flow which is investigated using AUTO and numerical integration. Various bifurcations which occur as a result of changing the coupling strength are identified.
For the entire collection see [Zbl 1472.74004].Vibration characteristics of piezoelectric functionally graded carbon nanotube-reinforced composite doubly-curved shellshttps://zbmath.org/1487.740542022-07-25T18:03:43.254055Z"Tham, V. V."https://zbmath.org/authors/?q=ai:tham.v-v"Tran, H. Q."https://zbmath.org/authors/?q=ai:tran.h-q"Tu, T. M."https://zbmath.org/authors/?q=ai:tu.te-ming|tu.tran-minhSummary: This paper presents an analytical solution for the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shells with integrated piezoelectric layers. Here, the linear distribution of electric potential across the thickness of the piezoelectric layer and five different types of carbon nanotube (CNT) distributions through the thickness direction are considered. Based on the four-variable shear deformation refined shell theory, governing equations are obtained by applying Hamilton's principle. Navier's solution for the shell panels with the simply supported boundary condition at all four edges is derived. Several numerical examples validate the accuracy of the presented solution. New parametric studies regarding the effects of different material properties, shell geometric parameters, and electrical boundary conditions on the free vibration responses of the hybrid panels are investigated and discussed in detail.Non-linear free vibrations of a hanging cable with small saghttps://zbmath.org/1487.740552022-07-25T18:03:43.254055Z"Vernizzi, Guilherme Jorge"https://zbmath.org/authors/?q=ai:vernizzi.guilherme-jorge"Franzini, Guilherme Rosa"https://zbmath.org/authors/?q=ai:franzini.guilherme-rosa"Pesce, Celso Pupo"https://zbmath.org/authors/?q=ai:pesce.celso-pupoSummary: This paper presents a method for evaluating non-linear modes and the corresponding natural frequencies of hanging cables with small sag. The use of a Galerkin temporal scheme on the governing equations of motion associated with a fictitious normal force accounting for the effects of the resulting non-linear terms leads to a closed-form solution for the non-linear free vibration problem. The influence of amplitude on the modal shapes and frequencies are presented.
For the entire collection see [Zbl 1472.74004].Nonlinear dynamics of suspended cables under periodic excitation in thermal environments: two-to-one internal resonancehttps://zbmath.org/1487.740562022-07-25T18:03:43.254055Z"Zhao, Yaobing"https://zbmath.org/authors/?q=ai:zhao.yaobing"Lin, Henghui"https://zbmath.org/authors/?q=ai:lin.henghuiAdvanced computational technique based on kriging and Polynomial Chaos Expansion for structural stability of mechanical systems with uncertaintieshttps://zbmath.org/1487.740572022-07-25T18:03:43.254055Z"Denimal, E."https://zbmath.org/authors/?q=ai:denimal.e"Sinou, J.-J."https://zbmath.org/authors/?q=ai:sinou.jean-jacquesSummary: In this paper, a numerical strategy based on the combination of the kriging approach and the Polynomial Chaos Expansion (PCE) is proposed for the prediction of buckling loads due to random geometric imperfections and fluctuations in material properties of a mechanical system. The original computational approach is applied on a beam simply supported at both ends by rigid supports and by one punctual spring whose location and stiffness vary. The beam is subjected to a deterministic axial compression load. The PCE-kriging meta-modelling approach is employed to efficiently perform a parametric analysis with random geometrical and material properties. The approach proved to be computationally efficient in terms of number of model evaluations and in terms of computational time to predict accurately the buckling loads of a beam system. It is demonstrated that the buckling loads are substantially impacted not only by both the location and the stiffness of the spring, but also by the random parameters.Two-mode long-wave low-frequency approximations for anti-plane shear deformation of a high-contrast asymmetric laminatehttps://zbmath.org/1487.740582022-07-25T18:03:43.254055Z"Alkinidri, Mohammed"https://zbmath.org/authors/?q=ai:alkinidri.mohammed"Kaplunov, Julius"https://zbmath.org/authors/?q=ai:kaplunov.julius-d"Prikazchikova, Ludmila"https://zbmath.org/authors/?q=ai:prikazchikova.ludmilaSummary: The anti-plane shear of a three-layered laminate of an asymmetric structure is considered. The chosen geometry of the laminate assumes coupling its symmetric and anti-symmetric modes, which is not a feature of a symmetric structure. A high contrast in mechanical properties of the inner and outer layers is assumed. A specific contrast setup supporting an asymptotically small lowest shear cut-off frequency is studied. For a laminate with traction-free faces two-mode long-wave low-frequency approximation of the full dispersion relations incorporating both the fundamental mode and the first harmonic is derived. The accuracy of the derived approximations is tested by numerical comparison with the exact solution. The 1D partial differential equation corresponding to the aforementioned two-mode shortened dispersion relation is also presented.
For the entire collection see [Zbl 1477.93110].The spectra of non-axisymmetric normal elastic waves in functionally graded transversely isotropic hollow cylindershttps://zbmath.org/1487.740592022-07-25T18:03:43.254055Z"Moiseenko, I. A."https://zbmath.org/authors/?q=ai:moiseenko.i-aSummary: The wave motion is described on the basis of a complete system of linear dynamical equations of elasticity theory. The elastic modules and density of the cylinder material are taken as a exponentially-power function of the radial coordinate. The general solution of a system of differential equations of the model is constructed for an arbitrary wavenumber circular in the form of expansions of radial components of the solution in a uniformly and absolutely convergent matrix series on generalized ring coordinate. Dispersion relations describing the harmonic spectra of non-axisymmetric normal waves for both cases of free or rigidly fixed boundary surfaces are obtained. The effect of radial non-homogeneity ratios on the topology of the dispersion spectrums, distribution of the phase and group velocities of normal propagating waves studied.A wave based method for two-dimensional time-harmonic elastic wave propagation in anisotropic mediahttps://zbmath.org/1487.740602022-07-25T18:03:43.254055Z"Sun, Linlin"https://zbmath.org/authors/?q=ai:sun.linlin"Chen, Zhikang"https://zbmath.org/authors/?q=ai:chen.zhikang"Zhang, Suyu"https://zbmath.org/authors/?q=ai:zhang.suyu"Chu, Liu"https://zbmath.org/authors/?q=ai:chu.liuSummary: In this paper, the wave based method (WBM) is extended to solve two-dimensional anisotropic elastic wave problems. The wave functions satisfying the governing equations are employed as basis functions in the WBM. To remedy the absence of the basis functions for the general anisotropic elastic wave problems, a new method is proposed. In the method, the two governing equations are transformed into one high-order scalar equation and the basis functions are obtained by using the wave functions of the scalar equation. Two examples are carried out to validate the accuracy and efficiency of the present method.The spectra of normal elastic waves in transversely isotropic waveguides with sector-shaped cross section and functionally graded radial non-homogeneityhttps://zbmath.org/1487.740612022-07-25T18:03:43.254055Z"Moiseyenko, I. A."https://zbmath.org/authors/?q=ai:moiseyenko.i-aSummary: In this paper, of constructing solutions for the propagation of normal waves in radially non-homogeneous transversely isotropic cylinder with sector-shaped cross section problems is investigated. The elastic modules and density are taken as an exponential-power function of the radial coordinate. Expansions in uniformly and absolutely convergent series on radial coordinate for the components of the vector displacements and the components of the tensor stresses obtained. Dispersion relations describing the spectra of harmonics for symmetric and antisymmetric normal waves in the radially non-homogeneous cylindrical waveguide with perfectly flexible inextensible membrane covering boundary surfaces of the channel and free or rigidly fixed of the cylindrical portion of the lateral surface made of transversely isotropic material obtained. The effect of radial non-homogeneity ratios and angular channel measure on the topology of the dispersion spectrums and distribution of the phase velocities of normal propagating waves studied.Generation and propagation of SH waves due to shearing stress discontinuity in linear orthotropic viscoelastic layered structurehttps://zbmath.org/1487.740622022-07-25T18:03:43.254055Z"Singh, Abhishek Kumar"https://zbmath.org/authors/?q=ai:singh.abhishek-kumar"Koley, Siddhartha"https://zbmath.org/authors/?q=ai:koley.siddhartha"Chaki, Mriganka Shekhar"https://zbmath.org/authors/?q=ai:chaki.mriganka-shekharSummary: This present paper deals with the generation and propagation of SH wave due to shearing-stress discontinuity at the common interface of a linear orthotropic viscoelastic layer of finite thickness overlying linear orthotropic viscoelastic half-space. Laplace and Fourier transformations in combination with the modified Cagniard-De Hoop method have been adopted as the solution technique for the present problem. The free surface displacement field has been obtained in integral form for four distinct cases of shear-stress discontinuity (Case 1, 2, 3 and 4) at the common interface of stratum and substrate of the layered structure. Numerical computation and graphical demonstration have been carried out to observe the profound effects of various affecting parameters viz. time of disturbance, distance from the source of disturbance, attenuation parameter and angular frequency on free surface displacement field which serve as major highlights of the present study.Diffraction of shear waves on internal tunnel cylindrical inhomogeneities in the form of a cavity and inclusion in the elastic layer with free facehttps://zbmath.org/1487.740632022-07-25T18:03:43.254055Z"Volchkov, Vit. V."https://zbmath.org/authors/?q=ai:volchkov.vitalii-vladimirovich"Vukolov, D. S."https://zbmath.org/authors/?q=ai:vukolov.d-s"Storozhev, V. I."https://zbmath.org/authors/?q=ai:storozhev.v-iSummary: Numerical-analytical solutions of two-dimensional boundary problems of diffraction scattering of symmetric normal shear waves on cylindrical cavity or on isotropic elastic inclusion in plane-parallel deformable layer with free faces are obtained using the method of images. Solution of the problem is reduced to an infinite system of linear algebraic equations for the coefficients of representations of wave fields in the areas of cross-section of layer and inclusion in rows by the basic set of particular solutions of wave equations in cylindrical functions. The results of numerical investigation are presented, which characterize a number of leading effects in the distribution of the wave motion in the near- and far-field diffraction under varying the relative radius of cavities and inclusions, the relative length of the incident wave from the lowest mode of dispersion spectrum, and the ratio of the shear modulus for the material layer and inclusion.Love wave transference in piezomagnetic layered structure guided by an imperfect interfacehttps://zbmath.org/1487.740642022-07-25T18:03:43.254055Z"Goyal, Suman"https://zbmath.org/authors/?q=ai:goyal.suman"Sahu, Sanjeev A."https://zbmath.org/authors/?q=ai:sahu.sanjeev-anandSummary: The problem presents an analytical study of the wave transference in piezo-composite layer lying over an elastic substrate. The interface of the geometry is assumed to be imperfect. The imperfection is characterized by Linear Spring Model. Dynamics of the media taken are framed in form of direct Sturm-Liouville problem. Dispersion relations are found for both magnetically open and magnetically short case. Velocity profile of Love wave has been delineated through graphs for different affecting parameters (i.e., imperfection at the interface, layer thickness and heterogeneity in the substrate). It has been shown that the increase in these parameters increases the phase velocity of the Love wave. Further, layer thickness is noted to have a less effect on the velocity profile of the wave as compared to heterogeneity in the substrate. Moreover, a comparative study has been shown between the aforementioned cases with the variation in imperfect parameter. The velocity in open case is found to be higher than that of short case. The obtained results may provide guidance towards optimization of Surface Acoustic Wave devices and measurement of imperfections.Fuzzy evaluation for the velocities of surface waves of Rayleigh type in an elastic half-spacehttps://zbmath.org/1487.740652022-07-25T18:03:43.254055Z"Volchkov, Vit. V."https://zbmath.org/authors/?q=ai:volchkov.vitalii-vladimirovich"Storozhev, S. V."https://zbmath.org/authors/?q=ai:storozhev.s-vSummary: On the basis of the heuristic principle of generalization, fuzzy multiple estimates are built for the phase velocities of ultrasonic surface elastic waves of Rayleigh type in isotropic and transversely isotropic half-spaces with a free boundary surface in the case of variation in the experimentally determined values of physical and mechanical constants of materials. An example of the implementation of the synthesized technique is presented.Dispersion relations for localized waves of deformations in a water-saturated anisotropic layer between elastic half-spaceshttps://zbmath.org/1487.740662022-07-25T18:03:43.254055Z"Vyskub, V. G."https://zbmath.org/authors/?q=ai:vyskub.v-g"Glukhov, I. A."https://zbmath.org/authors/?q=ai:glukhov.i-a"Storozhev, V. I."https://zbmath.org/authors/?q=ai:storozhev.v-iSummary: A numerical-analytic solution of the problem of propagation of localized three-partial deformation waves in arbitrarily oriented direction in the plane of a saturated elastic-porous orthotropic layer contacting along the faces with the enclosing orthotropic half-spaces made of various elastic-porous materials is constructed. The general dispersion relation is obtained. A qualitative characteristic of the features of the asymptotic behavior of the velocities of the investigated wave motions in the high-frequency short-wave range for various orientation of the propagation
direction is given.Diffraction and vibration attenuation by obstacles in elastic mediahttps://zbmath.org/1487.740672022-07-25T18:03:43.254055Z"Israilov, M. Sh."https://zbmath.org/authors/?q=ai:israilov.m-shSummary: It is shown on the example of elastic \(SH\) wave diffraction by an obstacle like a half-plane that barriers can be used to attenuate vibrations and waves in elastic media. It is found that not only a solid barrier, but also a cut or a natural fracture in soil can protect foundations and buildings against shear bulk waves.Dispersion of longitudinal waves by four coplanar mode-I cracks in an infinite elastic mediumhttps://zbmath.org/1487.740682022-07-25T18:03:43.254055Z"Mandal, Palas"https://zbmath.org/authors/?q=ai:mandal.palas"Somala, Surendra Nadh"https://zbmath.org/authors/?q=ai:somala.surendra-nadh"Narayanakumar, S."https://zbmath.org/authors/?q=ai:narayanakumar.sSummary: A study is made of incident P-waves between four coplanar Griffith cracks, which are located symmetrically in the midplane of an infinite elastic medium. A two-dimensional elastic wave equation is considered for an isotropic medium. The Fourier integral transform has been applied to convert the fundamental problem to an integral equation problem. We have utilized the finite Hilbert transform technique and Cook's result to solve five integral equation. This work's main objective is to investigate the dynamic stress intensity factors and crack opening displacement at the cracks' tips. The study of these physical quantities (SIF, COD) predicts possible arrest of the damages within a specific range of wave frequency by monitoring the applied load. For low frequency, we have shown the graphs of SIF and COD for various types of isotropic materials and concluded that crack propagation could arrest quickly within a specific range of frequency. We presented a parametric study to explore the influence of crack growth and propagation.Asymptotics of near-cloakinghttps://zbmath.org/1487.740692022-07-25T18:03:43.254055Z"Ockendon, J. R."https://zbmath.org/authors/?q=ai:ockendon.john-r"Ockendon, H."https://zbmath.org/authors/?q=ai:ockendon.hilary"Sleeman, B. D."https://zbmath.org/authors/?q=ai:sleeman.brian-d"Tew, R. H."https://zbmath.org/authors/?q=ai:tew.richard-hSummary: This paper describes how asymptotic analysis can be used to gain new insights into the theory of cloaking of spherical and cylindrical targets within the context of acoustic waves in a class of linear elastic materials. In certain cases, these configurations allow solutions to be written down in terms of eigenfunction expansions from which high-frequency asymptotics can be extracted systematically. These asymptotics are compared with the predictions of ray theory and are used to describe the scattering that occurs when perfect cloaking models are regularised.Scattering of a plane sound waves by an elastic cylinder with an non-uniform coating situated near to a flat surfacehttps://zbmath.org/1487.740702022-07-25T18:03:43.254055Z"Tolokonnikov, Lev Alekseevich"https://zbmath.org/authors/?q=ai:tolokonnikov.lev-alekseevich"Efimov, Dmitriĭ Yur'evich"https://zbmath.org/authors/?q=ai:efimov.dmitrii-yurevichSummary: In article the problem of the scattering of an obliquely incident plane monochromatic sound wave by an elastic cylinder with a radially non-uniform elastic coating in presence of a flat surface (absolutely rigid and acoustically soft) is considered. The analytical solution of the problem by the method of imaginary sources using addition theorems for cylindrical wave functions is received. Wave fields in a containing medium and homogeneous elastic cylinder are found in the form of expansions in wave cylindrical functions. The boundary-value problem for the system of ordinary second order differential equations is constructed for determination of the displacement fields in inhomogeneous coatings.
Numerical calculations of frequency and angular characteristics of the scattered field for elastic homogeneous cylinders with and without coating located near the underlying plane are performed. Influence of continuously inhomogeneous elastic coatings on sound-reflecting properties of elastic cylindrical bodies are revealed.Waves in a viscoelastic cylindrical waveguide with a defecthttps://zbmath.org/1487.740712022-07-25T18:03:43.254055Z"Vatul'yan, Aleksandr Ovanesovich"https://zbmath.org/authors/?q=ai:vatulyan.aleksandr-ovanesovich"Yurov, Viktor Olegovich"https://zbmath.org/authors/?q=ai:yurov.viktor-olegovichSummary: In this paper, we consider a direct problem on waves in a viscoelastic inhomogeneous cylindrical waveguide with annular delamination and investigate an inverse problem on the identification of the delamination parameters on the basis of the additional data on the displacement field at the outer boundary of the waveguide. In order to account rheological properties within the framework of the complex modules concept, we use a model of a standard viscoelastic body. After applying the integral Fourier transform along the axial coordinate in the transform space, the problem is reduced to solving a canonical system of first-order differential equations with two spectral parameters. The corresponding boundary-value problems are solved numerically by using the shooting method. To satisfy the boundary conditions on the delamination, a system of two hypersingular integral equations for the opening functions (radial and axial displacements jumps) are compiled and solved on the basis of the boundary element method. To construct the displacement field on the outer boundary of the waveguide, the techniques of direct numerical integration by quadrature formulas and the residue theorem are used. When using the theorem on residues, the calculations are performed considering the three smallest complex poles in the absolute value, which corresponds to the retention of three non-uniform vibration modes. We carry out a series of computational experiments allowing to construct the wave field at the waveguide's outer boundary. We perform the analysis of the effect of the delamination width and geometric characteristics of loading on the wave fields. On the basis of the asymptotic formula for the field at the outer boundary of the waveguide and additional data on the radial and axial displacements at one given point, a system of transcendental equations is compiled to find the delamination width and distance to the loading region. A series of computational experiments on the reconstruction of the axial position of the defect and its width are also carried out. We also perform the analysis of the damping effect on the inverse problem equations and estimate the error. Finally, we reveal the area of applicability of the proposed reconstruction method.Energy decay for damped shear beam model and new facts related to the classical Timoshenko systemhttps://zbmath.org/1487.740722022-07-25T18:03:43.254055Z"Almeida Júnior, D. S."https://zbmath.org/authors/?q=ai:almeida.dilberto-s-jun|almeida-junior.dilberto-da-silva"Ramos, A. J. A."https://zbmath.org/authors/?q=ai:ramos.anderson-j-a"Freitas, M. M."https://zbmath.org/authors/?q=ai:freitas.mirelson-mSummary: In this paper, we consider a beam model known as Shear beam model (no rotary inertia). We assure, based on behavior of the wave speeds, that the Shear beam model corresponds to a part of the classical Timoshenko beam model which is governed only by one wave speed. Unlike the classical dissipative Timoshenko type system with viscous damping acting on transverse displacement, we prove that the corresponding dissipative Shear beam model has an energy exponential decay regardless any relationship between coefficients of the system. This happens because such model has only one finite wave speed for all wave numbers.Nonlinear analysis of laminated FG-GPLRC beams resting on an elastic foundation based on the two-phase stress-driven nonlocal modelhttps://zbmath.org/1487.740732022-07-25T18:03:43.254055Z"Ansari, R."https://zbmath.org/authors/?q=ai:ansari.reza"Faraji Oskouie, M."https://zbmath.org/authors/?q=ai:faraji-oskouie.mohammad|oskouie.m-faraji"Roghani, M."https://zbmath.org/authors/?q=ai:roghani.mohammad"Rouhi, H."https://zbmath.org/authors/?q=ai:rouhi.hessamSummary: In this paper, a nonlinear formulation for beam-type structures is presented within the framework of two-phase stress-driven (SD) nonlocal theory. Various boundary conditions are considered for the beams, and it is assumed that they are on the Winkler- and Pasternak-type elastic foundations. It is considered that the beams are made of laminated functionally graded-graphene platelet-reinforced composite (FG-GPLRC) whose properties are estimated by means of the Halpin-Tsai model. The Euler-Bernoulli beam theory is also used for the modeling. The governing equations are derived based on the integral form of SD nonlocal theory using a variational approach considering geometrical nonlinearity. The equations of the SD model in differential form in conjunction with associated constitutive boundary conditions are also obtained. Moreover, a numerical approach based upon the generalized differential quadrature (GDQ) method is developed for the solution of the nonlinear bending problem. The influences of volume fraction/distribution pattern of GPLs, nonlocality, elastic foundation, and geometrical parameters on the bending response of beams under different end conditions are investigated. Furthermore, comparisons are given between the linear and nonlinear results.Numerical and experimental investigations on the band-gap characteristics of metamaterial multi-span beamshttps://zbmath.org/1487.740742022-07-25T18:03:43.254055Z"Hao, Shuaimin"https://zbmath.org/authors/?q=ai:hao.shuaimin"Wu, Zhijing"https://zbmath.org/authors/?q=ai:wu.zhijing"Li, Fengming"https://zbmath.org/authors/?q=ai:li.fengming"Zhang, Chuanzeng"https://zbmath.org/authors/?q=ai:zhang.chuanzeng.1Summary: A novel metamaterial multi-span beam with periodic simple supports and local resonators is designed and investigated. The frequency responses of the proposed metamaterial multi-span beam are computed by the spectral element method (SEM). The accuracy and feasibility of the SEM are verified by the finite element method (FEM) and the vibration experiments. The results show that the metamaterial multi-span beam could generate both the local resonance band-gaps in the low-frequency ranges and the Bragg band-gaps in the medium and high frequency regions. By adjusting the natural frequencies of the local resonators, the thickness of the base beam and the length of the unit-cell, the local resonance and the Bragg band-gaps can be controlled, respectively. The coupling effects of these two kinds of band-gaps are investigated by the parametrical design, which broadens the band-gaps and consequently improves the vibration reduction performance.Exact solutions for stochastic Bernoulli-Euler beams under deterministic loadinghttps://zbmath.org/1487.740752022-07-25T18:03:43.254055Z"Malkiel, Nachman"https://zbmath.org/authors/?q=ai:malkiel.nachman"Rabinovitch, Oded"https://zbmath.org/authors/?q=ai:rabinovitch.oded"Elishakoff, Isaac"https://zbmath.org/authors/?q=ai:elishakoff.isaacSummary: This study deals with two general solutions for a simply supported linear elastic Bernoulli-Euler beam with a stochastic bending flexibility, subjected to a deterministic loading. Two model problems are considered. The first problem is associated with a trapezoidally distributed load, whereas the second problem treats a sinusoidally distributed load. The importance of the solution for the trapezoidal load lies in its practicality. The derivation of stochastic characteristics for random beams under a sinusoidal load is useful due to the expandability to generally distributed loads by a Fourier sine series expansion. Numerical results are reported for various cases illustrating the effect of stochasticity of the beam's properties on its flexural response.Transient response of a thermo-diffusive elastic thick circular plate with variable conductivity and diffusivityhttps://zbmath.org/1487.740762022-07-25T18:03:43.254055Z"Bajpai, Ankit"https://zbmath.org/authors/?q=ai:bajpai.ankit"Sharma, P. K."https://zbmath.org/authors/?q=ai:sharma.poonam-kumar"Kumar, Rajneesh"https://zbmath.org/authors/?q=ai:kumar.rajneeshSummary: This article describes the impacts of variable thermal conductivity and diffusivity on an infinite thermoelastic diffusion circular plate of finite width with a heat source due to axisymmetric thermal and chemical potential loadings in the light of two-temperature generalized thermoelastic diffusion theory. The thermal conductivity and diffusivity are assumed to be linear functions of thermodynamic temperature and concentration, respectively. The governing equations are transformed into the linear form by applying Kirchhoff's transform. These equations are solved by using the Laplace-Hankel transform technique. In the transformed region, the closed form expressions for conductive and thermodynamic temperatures, displacement and stress components, concentration, and chemical potential are obtained. To transform the solutions to the original domain, a numerical inversion technique is applied. Numerical results for thermodynamic and conductive temperatures, normal stress component, and chemical potential are depicted graphically to illustrate the impacts of two temperatures, ramping time parameter, variable thermal conductivity and diffusivity. A validation of the obtained results is also presented.On one problem for the platehttps://zbmath.org/1487.740772022-07-25T18:03:43.254055Z"Gulua, B."https://zbmath.org/authors/?q=ai:gulua.bakur"Kasrashvili, T."https://zbmath.org/authors/?q=ai:kasrashvili.tamarSummary: In this work we consider equations of equilibrium of the isotropic elastic plate. By means of Vekua's method, the system of differential equations for plates is obtained (approximation \(N=1)\), when on upper and lower face surfaces displacements are assumed to be known. The general solution for approximations \(N=1\) is constructed. The concrete problem is solved.Analysis and active control of bending and vibration responses of the MRE multifunctional grid composite sandwich plateshttps://zbmath.org/1487.740782022-07-25T18:03:43.254055Z"Li, Hui"https://zbmath.org/authors/?q=ai:li.hui.1|li.hui.3|li.hui|li.hui.2|li.hui.5|li.hui.4"Hu, Xiaoyue"https://zbmath.org/authors/?q=ai:hu.xiaoyue"Ha, Sung Kyu"https://zbmath.org/authors/?q=ai:ha.sung-kyu"Sun, Jiming"https://zbmath.org/authors/?q=ai:sun.jiming"Han, Qingkai"https://zbmath.org/authors/?q=ai:han.qingkai"Wang, Xiangping"https://zbmath.org/authors/?q=ai:wang.xiangpingSummary: This paper investigates the active control effect on the bending and vibration responses of the magnetorheological elastomer (MRE) multifunctional grid composite sandwich plates (MREMGCSPs), which consist of top and bottom carbon fibre/epoxy panels and one MRE-based grid functional core with many grid functional components (GFCs) and several grid frame beams (GFBs). First, based on the first-order shear deformation theory, the energy principle, the Ritz method, the Duhamel integral approach, etc., the solution to bending and the pulse vibration responses of such a structure under cantilever boundary condition are successfully obtained. Thereafter, to verify the current model as well as evaluate the bending and vibration resistance, a MREMGCSP structure is fabricated and measured with different measuring points and magnetic field magnitudes. Finally, the influence of critical geometric and control parameters on static and dynamic properties is discussed to summarize some practical conclusions for engineering applications. This study provides a useful model for estimating both static and dynamic behaviors of the MREMGCSPs, which can assist researchers in designing, manufacturing, and optimisation of similar multifunctional structures with MRE.Fuzzy identification of mechanical characteristics of thin isotropic plates based on resonance wave methodologyhttps://zbmath.org/1487.740792022-07-25T18:03:43.254055Z"Mitrushkin, E. I."https://zbmath.org/authors/?q=ai:mitrushkin.e-i"Priymenko, S. A."https://zbmath.org/authors/?q=ai:priymenko.s-a"Storozhev, S. V."https://zbmath.org/authors/?q=ai:storozhev.s-vSummary: A description is given of the theoretical algorithm for obtaining estimates of the values of elastic constants of isotropic materials, determined on the basis of non-contrast experimental data on the measurement of the velocities of elastic waves and the resonance frequencies of the
flexural vibrations of thin plates of rectangular or circular shapes. The algorithm is based on the representation for experimental data in fuzzy-interval form and on the alpha-level modification of the heuristic generalization principle upon transition to fuzzy representations of arguments in mathematical formulas for the Young's modulus and for the Poisson's ratio. Representations for velocity of shear elastic waves in the materials of plate, and for resonance frequency of transverse vibrations of plates in the framework of the applied theory of their dynamic bending
is used. Examples of numerical implementation of the described algorithm are presented.Analysis of nonlinear deformation task of layered cylindrical shell by local surface force and temperature fieldhttps://zbmath.org/1487.740802022-07-25T18:03:43.254055Z"Abramidze, Ed."https://zbmath.org/authors/?q=ai:abramidze.edison"Abramidze, El."https://zbmath.org/authors/?q=ai:abramidze.eleneSummary: Based on one of the variants of improved theory, in the case of axisymmetric loading of layered cylindrical shell by local surface force and temperature field, for numerical solution of the nonlinear deformation task is obtained for this class the system of decision differential equations. \par A particular example of deformation of cylindrical shell is considered. It is given an appropriate analysis based on the results obtained from numerical realization of the example.Conditions for the existence of neutral surface of an elastic shell and the boundary value problems for generalized analytic functionshttps://zbmath.org/1487.740812022-07-25T18:03:43.254055Z"Akhalaia, G."https://zbmath.org/authors/?q=ai:akhalaia.giorgi"Meunargia, T."https://zbmath.org/authors/?q=ai:meunargia.tamar|meunargia.tengiz|meunargia.t-v|meunargia.t-tSummary: In this paper the conditions for the existence of a neutral surface of elastic shells is consider, when the neutral surfaces are not the middle surface of the shell, it is the equidistant surface of the middle surface. Boundary value problems of the theory of generalized analytic functions are used for convex shells.Mathematical and asymptotic analysis of thermoelastic shells in normal damped response contacthttps://zbmath.org/1487.740822022-07-25T18:03:43.254055Z"Cao-Rial, M. T."https://zbmath.org/authors/?q=ai:cao-rial.m-t"Castiñeira, G."https://zbmath.org/authors/?q=ai:castineira.gonzalo"Rodríguez-Arós, Á."https://zbmath.org/authors/?q=ai:rodriguez-aros.angel-d"Roscani, S."https://zbmath.org/authors/?q=ai:roscani.sabrina-dSummary: The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for this problem. Then, we study the particular case when the deformable body is, in fact, a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.On the nonlinear theory of non-shallow shellshttps://zbmath.org/1487.740832022-07-25T18:03:43.254055Z"Meunargia, T."https://zbmath.org/authors/?q=ai:meunargia.tamar|meunargia.tengiz|meunargia.t-v|meunargia.t-tSummary: I. Vekua constructed several versions of the refined linear theory of thin and shallow shells, containing the regular processes by means of the method of reduction of 3-D problems of elasticity to 2-D ones. By means of I. Vekua's method the system of differential equations for the nonlinear theory of non-shallow shells is obtained. The general solutions of the approximation of Order \(N=0,1,2,3,4\) are obtained.Thermomechanical waves in the elastic lithosphere-viscous asthenosphere systemhttps://zbmath.org/1487.740842022-07-25T18:03:43.254055Z"Lobkovsky, L. I."https://zbmath.org/authors/?q=ai:lobkovsky.l-i"Ramazanov, M. M."https://zbmath.org/authors/?q=ai:ramazanov.m-mSummary: The problem of the development of thermomechanical waves in the system consisting of two horizontal layers with rheology of a linearly elastic medium for the upper layer (lithosphere) and a viscous fluid for the lower layer (asthenosphere) is considered with regard to phase transition on their common boundary. The exact solution to the problem is found and its properties as functions of the parameters are studied. It is shown that for the characteristic physical parameters of the lithosphere and asthenosphere there exist solutions in the form of moderately damped strain tectonic waves and a geophysical interpretation of the results obtained is given.Librations of a body composed of a deformable mantle and a fluid corehttps://zbmath.org/1487.740852022-07-25T18:03:43.254055Z"Ragazzo, Clodoaldo"https://zbmath.org/authors/?q=ai:ragazzo.clodoaldo"Boué, Gwenaël"https://zbmath.org/authors/?q=ai:boue.gwenael"Gevorgyan, Yeva"https://zbmath.org/authors/?q=ai:gevorgyan.yeva"Ruiz, Lucas S."https://zbmath.org/authors/?q=ai:ruiz.lucas-sSummary: We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP19a (Integration Planétaire de l'Observatoire de Paris) Fienga et al. (INPOP19a planetary ephemerides. Notes Scientifiques et Techniques de l'Institut de Mécanique Céleste, vol 109, 2019), and by JPL (Jet Propulsion Laboratory) [Park et al., The JPL Planetary and Lunar Ephemerides DE440 and DE441. Astron J. 161, No. 3, 105 (2021; \url{doi:10.3847/1538-3881/abd414})], to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those related to the ``permanent deformation'', have a physical interpretation. The paper also contains: (1) A physical model to explain the usual lack of hydrostaticity of the mantle (permanent deformation). (2) Formulas for free librations of bodies in and out-of spin-orbit resonance that are valid for any linear viscoelastic rheology of the mantle. (3) Formulas for the offset between the mantle and the idealised rigid-body motion (Peale's Cassini states). (4) Applications to the librations of Moon, Earth, and Mercury that are used for model validation.Modelling of fibre dispersion and its effects on cardiac mechanics from diastole to systolehttps://zbmath.org/1487.740862022-07-25T18:03:43.254055Z"Guan, Debao"https://zbmath.org/authors/?q=ai:guan.debao"Zhuan, Xin"https://zbmath.org/authors/?q=ai:zhuan.xin"Holmes, William"https://zbmath.org/authors/?q=ai:holmes.william-s-iii|holmes.william-r"Luo, Xiaoyu"https://zbmath.org/authors/?q=ai:luo.xiaoyu"Gao, Hao"https://zbmath.org/authors/?q=ai:gao.haoSummary: Detailed fibre architecture plays a crucial role in myocardial mechanics both passively and actively. Strong interest has been attracted over decades in mathematical modelling of fibrous tissue (arterial wall, myocardium, etc.) by taking into account realistic fibre structures, i.e. from perfectly aligned one family of fibres, to two families of fibres, and to dispersed fibres described by probability distribution functions. It is widely accepted that the fibres, i.e. collage, cannot bear the load when compressed, thus it is necessary to exclude compressed fibres when computing the stress in fibrous tissue. In this study, we have focused on mathematical modelling of fibre dispersion in myocardial mechanics, and studied how different fibre dispersions affect cardiac pump function. The fibre dispersion in myocardium is characterized by a non-rotationally symmetric distribution using a \(\pi \)-periodic Von Mises distribution based on recent experimental studies. In order to exclude compressed fibres for passive response, we adopted the discrete fibre dispersion model for approximating a continuous fibre distribution with finite fibre bundles, and then the general structural tensor was employed for describing dispersed active tension. We first studied the numerical accuracy of the integration of fibre contributions using the discrete fibre dispersion approach, then compared different mechanical responses in a uniaxially stretched myocardial sample with varied fibre dispersions. We finally studied the cardiac pump functions from diastole to systole in two heart models, a rabbit bi-ventricle model and a human left ventricle model. Our results show that the discrete fibre model is preferred for excluding compressed fibres because of its high computational efficiency. Both the diastolic filling and the systolic contraction will be affected by dispersed fibres depending on the in-plane and out-of-plane dispersion degrees, especially in systolic contraction. The in-plane dispersion seems affecting myocardial mechanics more than the out-of-plane dispersion. Despite different effects in the rabbit and human models caused by the fibre dispersion, large differences in pump function exist when fibres are highly dispersed at in-plane and out-of-plane. Our results highlight the necessity of using dispersed fibre models when modelling myocardial mechanics, especially when fibres are largely dispersed under pathological conditions, such as fibrosis.Parallel-elastic actuation of a back-support exoskeletonhttps://zbmath.org/1487.740872022-07-25T18:03:43.254055Z"Toxiri, Stefano"https://zbmath.org/authors/?q=ai:toxiri.stefano"Calanca, Andrea"https://zbmath.org/authors/?q=ai:calanca.andreaSummary: In this chapter, we discuss the implementation of compliant actuators on a back-support exoskeleton developed at Istituto Italiano di Tecnologia (Italy). The exoskeleton provides physical assistance to the lower back during lifting tasks, reducing the associated loading and, consequently, the risk of injuries. A detailed analysis of the actuation requirements, along with experiments with different physical prototypes, indicate the advantages of parallel elasticity for this specific application.
For the entire collection see [Zbl 1470.93004].On the control of viscoelastic damped swelling porous elastic soils with internal delay feedbackshttps://zbmath.org/1487.740882022-07-25T18:03:43.254055Z"Apalara, Tijani A."https://zbmath.org/authors/?q=ai:apalara.tijani-abdulaziz"Yusuf, Moruf O."https://zbmath.org/authors/?q=ai:yusuf.moruf-o"Salami, Babatunde A."https://zbmath.org/authors/?q=ai:salami.babatunde-aSummary: We consider a swelling porous-elastic system with viscoelastic damping and delay feedbacks acting on the fluid equation. Using the multiplier method and under the well-known assumption on the weight of delay term, we unexpectedly establish a general decay result without imposing the usual condition of equal wave speeds of the system, unlike the case of Timoshenko and porous systems where damping on only one of the equations requires equal wave speeds propagation. Our coupling and the result give new contributions to the theory associated with asymptotic behaviors of swelling porous elastic soils.Robust tracking error feedback control for output regulation of Euler-Bernoulli beam equationhttps://zbmath.org/1487.740892022-07-25T18:03:43.254055Z"Guo, Bao-Zhu"https://zbmath.org/authors/?q=ai:guo.baozhu"Meng, Tingting"https://zbmath.org/authors/?q=ai:meng.tingtingSummary: In this paper, we consider robust output tracking for an Euler-Bernoulli beam equation under the guidance of the internal model principle, where the disturbances in all possible channels are considered. Three typical cases are investigated in terms of different regulated outputs. The first case is based on boundary displacement output, for which only asymptotic convergence can be achieved due to the compactness of the observation operator. The second case considers two outputs of both boundary displacement and velocity. Since the control is one-dimensional, we can only arbitrarily regulate the boundary displacement and at the same time, the velocity is regulated to track the derivative of the reference. This is not the standard form investigated in the literature for robust error feedback control of abstract infinite-dimensional systems. The last case represents an extreme case that the system is non-well posed. In all the above cases, this paper demonstrates the same technique of an observer-based approach to robust control design. In the latter two cases, we can achieve exponential convergence and the closed loop is also shown to be robust to system uncertainties. Numerical simulations are carried out in all cases to illustrate the effectiveness of the proposed controls.On a problem of controlling a moving cart with elastic rodhttps://zbmath.org/1487.740902022-07-25T18:03:43.254055Z"Ukhobotov, V. I."https://zbmath.org/authors/?q=ai:ukhobotov.viktor-ivanovich"Livanov, N. D."https://zbmath.org/authors/?q=ai:livanov.nikita-dmitrievichSummary: This article discusses the problem of controlling the process of longitudinal oscillations of an elastic homogeneous rod of uniform cross section. A rod is understood as a body, the length of which significantly exceeds its cross dimensions. The rod is on a moving cart, the right end of which is rigidly fixed, and the left end is not fixed. There is no friction between the rod and the cart surface in the problem under consideration. When the cart moves, the rod performs constrained longitudinal oscillations in a non-inertial frame of reference associated with the cart. The control is the acceleration of the cart, the magnitude of which is limited. The boundaries of its accepted values are set. The value of the combined external forces acting on the rod is not known exactly, but only its limits of variation are given. The purpose of the control process is to ensure that at a given moment in time, the average value of the stretch of the rod is within a given interval. This average is calculated using the specified function.
In order to solve the problem, the method of optimizing a guaranteed result is applied. A transition to a new one-dimensional variable is made, with the help of which the considered problem of control of the longitudinal oscillations of a rod is reduced to a similar control problem in the presence of noise. The necessary and sufficient conditions are found, under which it is possible to accomplish the set goal for any admissible external forces, the total value of which satisfies the given constraints. A corresponding algorithm for constructing the law of variation of the cart acceleration is proposed. An example that clearly shows how to build the cart control, which will guarantee the achievement of the set goal, has been analyzed.Mathematical regularities of the sliding friction process of a porous material based on iron impregnated with lubricating oil with dispersed particles of fluorinated graphenehttps://zbmath.org/1487.740912022-07-25T18:03:43.254055Z"Breki, Aleksandr Dzhalyul'evich"https://zbmath.org/authors/?q=ai:breki.aleksandr-dzhalyulevich"Chulkin, Sergeĭ Georgievich"https://zbmath.org/authors/?q=ai:chulkin.sergei-georgievich"Dobrovol'skiĭ, Nikolaĭ Mikhaĭlovich"https://zbmath.org/authors/?q=ai:dobrovolskii.n-m"Kuzovleva, Ol'ga Vladimirovna"https://zbmath.org/authors/?q=ai:kuzovleva.olga-vladimirovna"Gvozdev, Aleksandr Evgen'evich"https://zbmath.org/authors/?q=ai:gvozdev.aleksandr-evgenevich"Mazin, Evgeniĭ Vladimirovich"https://zbmath.org/authors/?q=ai:mazin.evgenii-vladimirovichSummary: The paper presents the results of a study of the sliding friction process of a porous material based on iron impregnated with lubricating oil with dispersed particles of fluorinated graphene. It is established that the regularities of the kinetics of external sliding friction have a sigmoidal and sigmoidal-linear character. Experimental results have been obtained showing that with an increase in the concentration of aggregates from flakes of fluorinated graphene in the lubricating oil, the average force and coefficient of friction decrease, while a good anti-friction effect is observed.On the evolution of mathematical models of friction sliding of solidshttps://zbmath.org/1487.740922022-07-25T18:03:43.254055Z"Breki, Aleksandr Dzhalyul'evich"https://zbmath.org/authors/?q=ai:breki.aleksandr-dzhalyulevich"Chulkin, Sergeĭ Georgievich"https://zbmath.org/authors/?q=ai:chulkin.sergei-georgievich"Gvozdev, Aleksandr Evgen'evich"https://zbmath.org/authors/?q=ai:gvozdev.aleksandr-evgenevich"Kuzovleva, Ol'ga Vladimirovna"https://zbmath.org/authors/?q=ai:kuzovleva.olga-vladimirovnaSummary: The paper provides information about the evolution of mathematical models of sliding friction of solids. It is Shown that taking into account deviations from the Leonardo da Vinci-Amonton-Coulomb law, it is necessary to Refine it using the correction function of the normal force. A mathematical model of the generalized sliding friction law has been created that takes into account the abrupt changes in the linear dependence of the friction force on the normal force.Mathematical regularities of changes in the characteristics of the friction process of a porous composite material based on copper containing oil with graphene particleshttps://zbmath.org/1487.740932022-07-25T18:03:43.254055Z"Breki, Aleksandr Dzhalyul'evich"https://zbmath.org/authors/?q=ai:breki.aleksandr-dzhalyulevich"Chulkin, Sergeĭ Georgievich"https://zbmath.org/authors/?q=ai:chulkin.sergei-georgievich"Kolmakov, Alekseĭ Georg'evich"https://zbmath.org/authors/?q=ai:kolmakov.aleksei-georgevich"Kuzovleva, Ol'ga Vladimirovna"https://zbmath.org/authors/?q=ai:kuzovleva.olga-vladimirovna"Gvozdev, Aleksandr Evgen'evich"https://zbmath.org/authors/?q=ai:gvozdev.aleksandr-evgenevich"Mazin, Evgeniĭ Vladimirovich"https://zbmath.org/authors/?q=ai:mazin.evgenii-vladimirovich"Kuz'min, Alekseĭ Mikhaĭlovich"https://zbmath.org/authors/?q=ai:kuzmin.aleksei-mikhailovichSummary: The paper presents the results of a study of the sliding friction processes of a porous copper-based material impregnated with lubricating oil with dispersed particles of fluorinated graphene. Mathematical regularities of changes in the characteristics of the friction interaction are established. It is shown that the regularities of changes in the average friction force have a sigmoid-step character. Experimental results have been obtained showing that with an increase in the concentration of aggregates from flakes of fluorinated graphene in the lubricating oil, the average friction force and coefficient of friction decrease, while a good anti-friction effect is observed. It is shown that the average work of the friction force, and consequently the energy losses due to friction, when adding 0.01\% of aggregates from fluorinated graphene flakes to the lubricating oil decreases by 3721 j, and when adding 0.1\% by 4098 j. It was found that the average coefficient of friction when adding 0.01\% of fluorinated graphene flake aggregates to the lubricating oil decreases by 27\%, and when adding 0.1\% by 30\%.Numerical moving mesh solution for the JKR adhesive contact between an incompressible layer and an axisymmetric rigid indenterhttps://zbmath.org/1487.740942022-07-25T18:03:43.254055Z"Ahn, Young Ju"https://zbmath.org/authors/?q=ai:ahn.young-juSummary: Recent research extended the non-adhesive contact problems between an incompressible layer and a rigid indenter to adhesive cases in the limit of the Johnson-Kendall-Roberts (JKR) model, where it simply changes the boundary condition. The governing equation of this problem is in the form of Poisson's equation, and there are two boundary conditions, one of which serves to determine the extent of the contact area. This makes it possible to develop a numerical solution of an adhesive thin incompressible layer indentation problem. For a numerical implementation, we have devised a finite element formulation with a moving mesh technique satisfying the slope boundary condition, which determines the actual extent of the contact area. We shall apply the proposed numerical method to an adhesive contact problem by a spherical rigid indenter to demonstrate the validity of the method. Furthermore, we will compare the characteristics of the JKR indentation solutions between a half-space and a thin incompressible layer.On the positive definiteness of the Poincaré-Steklov operator for elastic half-planehttps://zbmath.org/1487.740952022-07-25T18:03:43.254055Z"Bobylev, A. A."https://zbmath.org/authors/?q=ai:bobylev.a-aSummary: The Poincaré-Steklov operator that maps normal stresses to normal displacements on a part of a half-plane boundary is studied. A boundary value problem is formulated to introduce the associated Poincaré-Steklov operator. An integral representation based on the solution to the Flamant problem for an elastic half-plane subjected to a concentrated normal force is given for the operator under consideration. It is found that the properties of the Poincaré-Steklov operator depend on the choice of kinematic conditions specifying the rigid-body displacements of the half-plane. Positive definiteness conditions of the Poincaré-Steklov operator are obtained. It is shown that a suitable scaling of the computational domain can be used to provide the positive definiteness of this operator.Wheel-rail contact simulation with lookup tables and KEC profiles: a comparative studyhttps://zbmath.org/1487.740962022-07-25T18:03:43.254055Z"Escalona, José L."https://zbmath.org/authors/?q=ai:escalona.jose-luis"Yu, Xinxin"https://zbmath.org/authors/?q=ai:yu.xinxin"Aceituno, Javier F."https://zbmath.org/authors/?q=ai:aceituno.javier-fSummary: This paper describes and compares the use and limitations of two constraint-based formulations for the wheel-rail contact simulation in multibody dynamics: (1) the use of contact lookup tables and (2) the Knife-edge Equivalent Contact constraint method (KEC-method). Both formulations are presented and an accurate procedure to interpolate within the data in the lookup table is also described. Since the wheel-rail constraint contact approach finds difficulties at simultaneous tread and flange contact scenarios, the lookup table method is implemented with a penetration-based elastic contact model for the flange, turning the method into a hybrid (constant in the tread and elastic in the flange) approach. To deal with the two-point contact scenario in the KEC-method, a regularisation of the tread-flange transition allows the use of the constraint approach in the tread and also in the flange. To show the applicability and limitations of both methods, they are studied and compared with special emphasis in the calculation of normal and tangential contact forces. Numerical results are based on the simulation of a two-wheeled bogie vehicle in different case studies that consider irregular tracks and two wheel-rail profiles combinations: profiles that do not show two-point wheel-rail contacts and profiles that do show two-point wheel-rail contacts. Although results show a good agreement between both approaches, the use of the KEC-method is more extensive since it allows to reproduce the wheel-climbing scenario that cannot be simulated with the lookup table method with the hybrid contact approach. It is concluded that simulations with this later method may not be on the safe side.A bi-potential contact formulation of orthotropic adhesion between soft bodieshttps://zbmath.org/1487.740972022-07-25T18:03:43.254055Z"Hu, L. B."https://zbmath.org/authors/?q=ai:hu.liangbing|hu.leibo|hu.liang-bo|hu.liangbin|hu.lianbo"Cong, Y."https://zbmath.org/authors/?q=ai:cong.yuan|cong.yirui|cong.yan|cong.yang|cong.yuhao|cong.yuancai|cong.yongzheng|cong.yulai|cong.yunyue|cong.yu|cong.yue"Renaud, C."https://zbmath.org/authors/?q=ai:renaud.christophe|renaud.christine"Feng, Z.-Q."https://zbmath.org/authors/?q=ai:feng.zhiqin|feng.ziqin|feng.zhouquan|feng.zhiqiang|feng.zi-qiang|feng.zhiquanSummary: An orthotropic adhesion model is proposed based on the bi-potential method to solve adhesive contact problems with orthotropic interface properties between hyperelastic bodies. The model proposes a straightforward description of interface adhesion with orthotropic adhesion stiffness, whose components are conveniently expressed according to the local coordinate system. Based on this description, a set of extended unilateral and tangential contact laws has been formulated. Furthermore, we use an element-wise scalar parameter \(\beta\) to characterize the strength of interface adhesive bonds, and the effects of damage. Therefore, complete cycles of bonding and de-bonding of adhesive links with the account for orthotropic interface effects can be modelled. The proposed model has been tested on cases involving both tangential and unilateral contact kinematics. The test cases allowed emergence of orthotropic interface effects between elastomer bodies involving hyperelasticity. Meanwhile, the model can be implemented with minimum effort, and provides inspiration for the modelling of adhesive interface effects in areas of applications such as biomechanics.The punch problems of the plane theory of viscoelasticity for the half planehttps://zbmath.org/1487.740982022-07-25T18:03:43.254055Z"Kapanadze, Gogi"https://zbmath.org/authors/?q=ai:kapanadze.gogi"Gulua, Bakur"https://zbmath.org/authors/?q=ai:gulua.bakurSummary: The paper considers the concrete problems of the punch for a viscoelastic half-plane by the Kelvin-Voigt model. It is known that many buildings and composite materials exhibit viscoelastic properties which are reflected in Hooke's law in which the stresses are proportional both to the deformations and to their derivatives in time.A nonlinear viscoelastic contact interphase modeled as a Cosserat rod-like stringhttps://zbmath.org/1487.740992022-07-25T18:03:43.254055Z"Rubin, M. B."https://zbmath.org/authors/?q=ai:rubin.miles-bSummary: A nonlinear viscoelastic contact interphase is modeled using a Cosserat rod-like string. This Cosserat model is a rod with a deformable cross-section, but with no constitutive resistance to bending. The model allows for axial extension, tangential shear deformation and normal extension of the cross-section which are determined by finite deformations of the interphase. Moreover, the constitutive response of this string model can be determined directly by three-dimensional constitutive equations for a hyperelastic component and a Maxwell elastic-viscoplastic component that together produce viscoelastic response of the interphase. The example of vibrations of a rigid outer ring connected to a fixed inner disk by a nonlinear viscoelastic interphase is used to show that the Cosserat string model of the interface predicts torque and force applied to the outer ring which include nonlinear coupling that is not present in simple uncoupled models of Maxwell components for torque and force applied to the outer ring by the interphase.Dynamic theory of sandwich meta-panel under blast loadhttps://zbmath.org/1487.741002022-07-25T18:03:43.254055Z"He, Huguang"https://zbmath.org/authors/?q=ai:he.huguang"Fan, Hualin"https://zbmath.org/authors/?q=ai:fan.hualinSummary: Metamaterials and metastructures have attenuation effect on blast load. Instead of the blast wave attenuation, this research analyzed the displacement attenuation effect of a composite meta-panel with resonators embedded in the core under blast load. The calculation model of the meta-panel is obtained by equivalence and simplification, and then the analytical solution of the displacement of the meta-panel under blast load is solved. The finite element analysis is carried out and is in good agreement with the theory. It is found that the energy of the resonators in the meta-panel account for nearly half of the total energy. Compared with ordinary sandwich panel of equal mass, the displacement of meta-panel can be reduced to 60\% or less by modifying resonator parameters. Adding the viscous damping term to the vibration equation, the peak displacement of the meta-panel will be further attenuated when the damping of the sandwich panel and the resonator are both considered. This research provides a theoretical basis for the explosion resistance application of locally resonant metamaterial sandwich panels.Assessment of four-variable refined shear deformation theory for low-velocity impact analysis of curved sandwich beamshttps://zbmath.org/1487.741012022-07-25T18:03:43.254055Z"Lezgy-Nazargah, M."https://zbmath.org/authors/?q=ai:lezgy-nazargah.m"Etemadi, E."https://zbmath.org/authors/?q=ai:etemadi.e"Hosseinian, S. R."https://zbmath.org/authors/?q=ai:hosseinian.s-rSummary: In this paper, the accuracy of the four-variable refined global-local (FRGL) shear deformation theory in the prediction of dynamic responses of curved sandwich beams under low-velocity impact has been investigated. The governing equations of motion of the curved sandwich beams are derived by employing a finite element (FE) model based on FRGL shear deformation theory. By using the method of truncated superimposition of modes, the size of the total dynamic system is firstly reduced. Then, the resulting dynamic system is solved via the state-space (SS) approach. For validation, curved sandwich beams with various deepness ratios and different boundary conditions are analyzed using the proposed model. Different materials and lay-up configurations were assumed for the face-sheets. The obtained results are validated through comparison with the results of ABAQUS simulations and other analytical and numerical results reported in the open literature. The comparisons show that the FRGL shear deformation theory in conjunction with the truncated reduced modal SS approach is a precise and computationally low-cost model for solving the dynamic problems of curved sandwich beams under impact loads.On the role of mathematical calculations in the expert study of the processes of structure formation and phase transformations in metal materialshttps://zbmath.org/1487.741022022-07-25T18:03:43.254055Z"Kuzovleva, Ol'ga Vladimirovna"https://zbmath.org/authors/?q=ai:kuzovleva.olga-vladimirovna"Gvozdev, Aleksandr Evgen'evich"https://zbmath.org/authors/?q=ai:gvozdev.aleksandr-evgenevich"Malyarov, Andreĭ Viktorovich"https://zbmath.org/authors/?q=ai:malyarov.andrei-viktorovichSummary: The article illustrates the role of mathematics in research in the field of technical sciences, devoted to the study of the properties of metallic materials on the example of titanium.Mixed-integer second-order cone optimization for composite discrete ply-angle and thickness topology optimization problemshttps://zbmath.org/1487.741032022-07-25T18:03:43.254055Z"He, Sicheng"https://zbmath.org/authors/?q=ai:he.sicheng"Shahabsafa, Mohammad"https://zbmath.org/authors/?q=ai:shahabsafa.mohammad"Lei, Weiming"https://zbmath.org/authors/?q=ai:lei.weiming"Mohammad-Nezhad, Ali"https://zbmath.org/authors/?q=ai:nezhad.ali-mohammad"Terlaky, Tamás"https://zbmath.org/authors/?q=ai:terlaky.tamas"Zuluaga, Luis"https://zbmath.org/authors/?q=ai:zuluaga.luis-fernando"Martins, Joaquim R. R. A."https://zbmath.org/authors/?q=ai:martins.joaquim-r-r-aSummary: Discrete variable topology optimization problems are usually solved by using solid isotropic material with penalization (SIMP), genetic algorithms (GA), or mixed-integer nonlinear optimization (MINLO). In this paper, we propose formulating discrete ply-angle and thickness topology optimization problems as a mixed-integer second-order cone optimization (MISOCO) problem. Unlike SIMP and GA methods, MISOCO efficiently finds the problem's globally optimal solution. Furthermore, in contrast with existing MISOCO formulations of discrete ply-angle optimization problems, our reformulations allow the structure to change topology, consider the more realistic Tsai-Wu stress yield criteria constraint, and eliminate checkerboard patterns using simple linear constraints. We address two types of discrete ply-angle and thickness problems: a structural mass minimization problem and a compliance optimization problem where the objective is to maximize the structural stiffness. For each element, one first chooses if the element is present or not in the structure. One can then choose the element's ply-angle and thickness from a finite set of possibilities for the former case. The discrete design space for ply-angle and thickness is a result of manufacturing limitations. To improve the problem's MISOCO solution approach, we develop valid inequality constraints to tighten the continuous relaxation of the MISOCO reformulation. We compare the performance of various MISOCO solvers: Gurobi, CPLEX, and MOSEK to solve the MISOCO reformulation. We also use BARON to solve the original MINLO formulations of the problems. Our results show that solving the MISOCO problem's formulation using MOSEK is the most efficient solution approach.Risk-averse approach for topology optimization of fail-safe structures using the level-set methodhttps://zbmath.org/1487.741042022-07-25T18:03:43.254055Z"Martínez-Frutos, J."https://zbmath.org/authors/?q=ai:martinez-frutos.jesus"Ortigosa, R."https://zbmath.org/authors/?q=ai:ortigosa.rogelioThis paper is concerned with the derivation and numerical evaluation of a level-set method in the context of topology optimization for structures under uncertain failures. The authors inspect the linearized elasticity equation
\[
-\nabla\cdot \sigma(u(x,\omega)) = b(x) \quad \text{in } D \times \Omega\tag{1}
\]
with uncertain Dirichlet and Neumann boundary conditions in a spatial domain \(D\subset \mathbb{R}^2\) and sample space \(\Omega\) of a probability space. The random variable \(\omega\) is assumed to follow a discrete probability function.
The topology optimization is then performed by minimization of the cost functional
\[
\min_{\chi_\mathcal{O}\subset \mathcal{U}_{ad}} \mathcal{J}(\chi_\mathcal{O},\omega) = \int_D \chi_\mathcal{O} b u~dx + \int_{\Gamma_N} \bar{t}u~ds,
\]
where \(\bar{t}\) represents the body and surface forces applied in normal direction of the boundary and \(\mathcal{U}_{ad}\) is the set of admissible shapes.
The uncertainty of the optimization problem is investigated by comparing multiple variants of the cost functional, namely the worst case formulation (where the worst failure is optimized), its smoothed approximation with a penalized exponential-logarithmic transformation, the excess probability (the probability of the performance exceeding a given threshold \(\eta\)) and the expected excess (expected value of the highest overshoot of the cost function over the threshold \(\eta\)).
To tackle the problem numerically, following [\textit{S. Osher} and \textit{J. A. Sethian}, J. Comput. Phys. 79, No. 1, 12--49 (1988; Zbl 0659.65132)], it is approximated with the level-set method, which is a novel approach in this area. The system is therefore transformed into a suitable reaction-diffusion equation which is then solved using a semi-implicit time integration and finite elements.
In total, three numerical experiments are conducted, investigating the performance of excess probability and expected excess compared to the worst case formulation. ``The numerical results included show that the proposed risk-averse formulations yield redundant structures which are less sensitive to inherent losses of stiffness resulting from possible failures. Subtle differences have been reported from the results obtained by means of the two risk-averse functions. On the one hand, the excess probability formulation permits to minimize the number of scenarios with compliance above a given threshold, but does not take into account the possible excess or shortfall with respect to the threshold, yielding (few cases) with considerably larger values than the threshold. On the other hand, the expected excess formulation does take into account the amount of degradation of the structural performance, or equivalently, the excess with respect to the specified threshold value. Furthermore, the numerical examples reveal that the worst-case approach yields a topology very similar to that of the expected excess formulation for high values of the threshold. However, in contrast to the worst-case formulation, which penalizes all the damage cases regardless of their probability of occurrence, the expected excess formulation allows designers to assume an a priori level of risk by means of the use of a threshold in the structural performance.'' (as written in the original manuscripts conclusions)
Reviewer: Dimitris P. Vartziotis (Ioannina)A generalized Bayesian regularization network approach on characterization of geometric defects in lattice structures for topology optimization in preliminary design of 3D printinghttps://zbmath.org/1487.741052022-07-25T18:03:43.254055Z"Xie, Yuxi"https://zbmath.org/authors/?q=ai:xie.yuxi"Li, Shaofan"https://zbmath.org/authors/?q=ai:li.shaofan"Wu, C. T."https://zbmath.org/authors/?q=ai:wu.cheng-tao|wu.chien-ting|wu.cheng-tien|wu.chi-ting|wu.chu-tao|wu.chuntao|wu.chi-tsung|wu.ching-tang|wu.chentao|wu.cheng-tang|wu.ching-tien|wu.ching-ting|wu.chun-te|wu.cheng-tai|wu.chung-te|wu.chin-tien|wu.c-thomas|wu.chin-tung|wu.changtai"Lyu, Dandan"https://zbmath.org/authors/?q=ai:lyu.dandan"Wang, Chao"https://zbmath.org/authors/?q=ai:wang.chao|wang.chao.1|wang.chao.2|wang.chao.3"Zeng, Danielle"https://zbmath.org/authors/?q=ai:zeng.danielleSummary: In this work, we developed a Generalized Bayesian Regularization Network (GBRN) approach that can quantitatively identify the defect shapes and locations by mapping the distorted lattice structure to its original designed configuration, making registration between manufactured parts with defects and the perfect design models in the preliminary design stage of 3D printing. On the one hand, it shows the proposed GBRN method has quantitatively comparable accuracy to the Coherent Point Drift (CPD) method in 2D boundary points registration problems. On the other hand, we have shown that the proposed GBRN method can find the possible geometric defects in the 3D printed lattice structure model and identify inherent defect-prone lattice structure parameters with obvious advantages over those two-dimensional point registration methods, i.e., coherent point drift (CPD) method, in registration of interior points of 3D lattice structures.Elastic characteristics of digital cores from longmaxi shale using lattice spring modelshttps://zbmath.org/1487.741062022-07-25T18:03:43.254055Z"Liu, Ning"https://zbmath.org/authors/?q=ai:liu.ning"Fu, Li-Yun"https://zbmath.org/authors/?q=ai:fu.li-yunSummary: Effective medium methods for the attribution of micro-structures to macro elastic properties of shales are important for the prediction of sweet spots in the shale-gas production. With X-ray micro-computed tomography (XMCT), the micro-structures of shale core samples from Longmaxi Formation are visualized and characterized by 3D digital images. As an efficient alternative to conventional effective medium methods for estimating elastic properties, we propose a consistent workflow of lattice spring modeling (LSM) to emulate the digital cores using three types of lattices. Particular attention is paid to investigate the effective Young's moduli, Poisson's ratios, and preferred orientations, by uniaxial compression tests along two directions. Within elastic deformation, the impact of lattice arrangements on the anisotropy is even more than those of stress disturbances and micro-structural features. Compared with analytical approximations and theoretical predictions, the LSM numerical scheme shows general applicability for heterogeneous porous rocks.From unit inclusion cell to large representative volume element: comparison of effective elastic propertieshttps://zbmath.org/1487.741072022-07-25T18:03:43.254055Z"Zhan, Y. L."https://zbmath.org/authors/?q=ai:zhan.yunlei|zhan.yu-lin|zhan.yongliang"Kaddouri, W."https://zbmath.org/authors/?q=ai:kaddouri.w"Kanit, T."https://zbmath.org/authors/?q=ai:kanit.toufik"Jiang, Q."https://zbmath.org/authors/?q=ai:jiang.qifeng"Liu, L."https://zbmath.org/authors/?q=ai:liu.landong.1|liu.lanchu|liu.liwu|liu.lijie|liu.liqian|liu.laura|liu.lei.1|liu.lun|liu.liwei|liu.lujia|liu.lofei|liu.li.1|liu.lianfang|liu.lipei|liu.liheng|liu.ligong|liu.lipin|liu.leibo|liu.li.4|liu.lei.2|liu.lianghuan|liu.lingfeng|liu.luoqin|liu.li.2|liu.lufang|liu.lingling.1|liu.lihuei|liu.lingling|liu.lingshun|liu.lintao|liu.li.3|liu.linfang|liu.lihong|liu.lujuan|liu.linqui|liu.lijing|liu.lizhi|liu.lai|liu.lianwu|liu.luyin|liu.lianjun|liu.lianmeng|liu.lixian|liu.lifu|liu.lijun|liu.lingyun|liu.linghui|liu.lungang|liu.laiyang|liu.lianshou|liu.lianlian|liu.lanjuan|liu.linna|liu.liangdong|liu.liangming|liu.lanjun|liu.li.6|liu.laishan|liu.lang|liu.lidan|liu.lianggui|liu.lianyi|liu.lidong|liu.ling|liu.lingxia|liu.lianshan|liu.liuming|liu.lihui|liu.li|liu.luoman|liu.liyu|liu.longfu|liu.lanming|liu.linlin|liu.luyuan|liu.liwei.1|liu.linxian|liu.lishi|liu.lei.3|liu.longfei|liu.luxin|liu.lilin|liu.longlong|liu.limei|liu.liangxin|liu.leiming|liu.lianguang|liu.longshen|liu.linwen|liu.lele|liu.landon|liu.luju|liu.li.7|liu.lina|liu.lingli|liu.lingxi|liu.longzhang|liu.luqin|liu.lishan|liu.laiqi|liu.lijiao|liu.lulu|liu.luhua|liu.liya.1|liu.lubo|liu.lingyang|liu.liao|liu.liqiao|liu.liqiong|liu.lianjie|liu.lishing|liu.liquan|liu.lianfu|liu.luping|liu.lianming|liu.lizhao|liu.liguang|liu.lichan|liu.lihan|liu.ligang|liu.licheng|liu.lizhen|lyu.liangxinbu|liu.lechun|liu.lihua|liu.linniang|liu.liping|liu.liangliang|liu.liqin|liu.luchuan|liu.lingtao|liu.like|liu.lingjun|liu.lirong|liu.lindong|liu.linshan|liu.lanlan|liu.liren|liu.liangang|liu.laiyou|liu.lianhua|liu.liying|liu.lizhuo|liu.lianghua|liu.liangfeng|liu.lingjia|liu.leian|liu.lichen|liu.lishan.1|liu.lin|liu.liang|liu.lianchen|liu.lei|liu.liwen|liu.liqiang|liu.litong|liu.lingchen|liu.longsheng|liu.lianzhu|liu.liman|liu.libo|liu.longxi|liu.lufeng|liu.lingzhi|liu.liqing|liu.limin|liu.lizuo|liu.linyun|liu.lvqiao|liu.lu|liu.lan|liu.longjiang|liu.lingqiao|liu.lijiu|liu.linjie|liu.luofei|liu.leyuan|liu.linqi|liu.lixin|liu.le|liu.liyan|liu.longhua|liu.li.5|liu.leping|liu.liaoxue|liu.lanhui|liu.lixia|liu.liansheng|liu.lianzhen|liu.liyuan|liu.leipo|liu.lutao|liu.linchao|liu.lixing|liu.lengning|liu.lianggang|liu.linan|liu.liucheng|liu.lisheng|liu.longcheng|liu.leiyan|liu.lizhuang|liu.liming|liu.lizhu|liu.laifu|liu.liling|liu.longgeng|liu.luoluo|liu.liqi|liu.lixi|liu.liangyuan|liu.longzhao|liu.luyan|liu.lanze|liu.lifeng|liu.longhe|liu.linzhi|liu.linzhong|liu.lihuan|liu.luohua|liu.li-cai|liu.lingyan|liu.liwuj|liu.lingtong|liu.lanqi|liu.linfeng|liu.lijia|liu.lian|liu.liandong|liu.leilei|liu.liangmei|liu.lianfeng|liu.luzheng|liu.lingyu|liu.linfei|liu.lanrong|liu.liyu.1|liu.lifang|liu.linxu|liu.lie|liu.lianbing|liu.liangshen|liu.long|liu.lijue|liu.luning|liu.longgui|liu.longjun|liu.longkang|liu.liqun|liu.lili|liu.lixiang|liu.lixiong|liu.lijuan|liu.liu|liu.lining|liu.lemao|liu.linyuan|liu.landong.2|liu.lanbo|liu.lanzhe|liu.linghua|liu.laiguo|liu.liuyan|liu.liyue|liu.lingfei|liu.lanying|liu.li-bin"Imad, A."https://zbmath.org/authors/?q=ai:imad.abdellatifThe authors apply the finite element method to few two-dimensional microstructures composed of linear elastic circular or elliptical inclusions embedded in a linear elastic continuous matrix. A rigid matrix and a rigid inclusion with high Young's modulus are considered; the Poisson's ratio is equal to \(0.3\). Few selected positions of inclusions are called random. The computations are performed for the fraction of inclusions equal to \(0.15\), \(0.3\) and \(0.45\). The obtained results are compared.
Reviewer: Vladimir Mityushev (Kraków)A singular nonlinear history-dependent cohesive zone model: is it possible?https://zbmath.org/1487.741082022-07-25T18:03:43.254055Z"Argatov, I. I."https://zbmath.org/authors/?q=ai:argatov.ivan-iSummary: A history-dependent cohesive zone model is considered in the linear elasticity framework with the cohesive stresses governed by the fracture condition formulated in terms of a nonlinear Abel-type integral operator. A possibility for the cohesive stresses to possess a weak singularity has been examined by utilizing asymptotic modeling approach. It has been shown that the balance of the leading-term asymptotic representations in the model equations is possible for nonsingular cohesive stresses only.Models of plane fractures expansionhttps://zbmath.org/1487.741092022-07-25T18:03:43.254055Z"Khabirov, S. V."https://zbmath.org/authors/?q=ai:khabirov.salavat-valeevich"Khabirov, S. S."https://zbmath.org/authors/?q=ai:khabirov.s-sSummary: Approximate models of crack opening in the reservoir under the action of the filtered fluid are derived. The cross-sections of the fracture are assumed to be plane-parallel and have a small thickness. The models are based on exact solutions of the equations for viscous fluid motion including invariant solutions. Filtration of a fluid through a moving boundary, the absence of a tangential motion at the boundary, and elastic forces compressing the crack are taken into account.Calculation of critical depth of edge crack in the main oil pipeline in the neighborhood of a transverse welded jointhttps://zbmath.org/1487.741102022-07-25T18:03:43.254055Z"Pokrovskiy, A. M."https://zbmath.org/authors/?q=ai:pokrovskiy.a-m"Dubovitskiy, E. I."https://zbmath.org/authors/?q=ai:dubovitskiy.e-i"Chermoshentseva, A. S."https://zbmath.org/authors/?q=ai:chermoshentseva.a-sSummary: A numerical method for calculating the critical depth of an edge semi-elliptical crack in the main oil pipeline in the zone of a transverse weld was developed. To calculate the structural composition of steel after welding and the residual welding stresses is used the author-developed finite element software package in Fortran Visual environment. The nonlinear nonstationary heat conductivity problem was solved by the finite difference method using the boundary conditions of third kind. Modeling of the kinetics of conversion of austenite to ferrite and bainite under nonisothermal conditions during welding was carried out based on the theory of isokinetic reactions. The calculation of the residual welding stress is performed by solving the problem of thermoelastic plasticity using the finite element method for material with nonstationary structure. The calculation of the crack resistance is based on Irwin's force failure criterion, and the dependence of the failure viscosity on the structural composition is considered. The ANSYS finite element software was used for calculating the maximum stress intensity factor along the edge of an edge semi-elliptical longitudinal crack in the pipeline. The distribution of fracture toughness as a function of the distance to the weld center is presented, as well as the results of crack resistance analysis in the form of dependences of the critical crack depth on the distance to the middle of the weld and the ratio of the crack half-length to its depth.Decoupled scaled boundary finite element method for analysing dam-reservoir dynamic interactionhttps://zbmath.org/1487.741112022-07-25T18:03:43.254055Z"Babaee, Reza"https://zbmath.org/authors/?q=ai:babaee.reza"Khaji, Naser"https://zbmath.org/authors/?q=ai:khaji.naserSummary: In this study, an efficient method is developed for solving systems of partial differential equations governing seismic analysis of 2D dam reservoir interaction, in the frequency domain. Using Chebyshev higher-order polynomials as mapping function, special shape function, integration method of Clenshaw-Curtis and the integral form used to weighted residual method, coefficient matrices of the system of governing equations become diagonal. This means that the governing partial differential equation for each degree of freedom becomes independent from others. This feature and discretizing only boundaries of domain significantly reduce computational costs in comparison with other methods. In this regard, various problems such as dynamic analysis of empty gravity dam, calculating the hydrodynamic pressure on rigid dam, and dam-reservoir interaction analysis due to the horizontal motion of foundation are examined. Comparing the results of this method with other analytical/numerical methods shows high capability and accuracy of the proposed method.Computational homogenization with million-way parallelism using domain decomposition methodshttps://zbmath.org/1487.741122022-07-25T18:03:43.254055Z"Klawonn, Axel"https://zbmath.org/authors/?q=ai:klawonn.axel"Köhler, Stephan"https://zbmath.org/authors/?q=ai:kohler.stephan"Lanser, Martin"https://zbmath.org/authors/?q=ai:lanser.martin"Rheinbach, Oliver"https://zbmath.org/authors/?q=ai:rheinbach.oliverSummary: Parallel computational homogenization using the well-knwon \(\mathrm{FE}^2\) approach is described and combined with domain decomposition and algebraic multigrid solvers. It is the purpose of this paper to show that and how the \(\mathrm{FE}^2\) method can take advantage of the largest supercomputers available and those of the upcoming exascale era for virtual material testing of micro-heterogeneous materials such as advanced steel. The \(\mathrm{FE}^2\) method is a computational micro-macro homogenization approach where at each Gauss integration point of the macroscopic finite element problem a microscopic finite element problem, defined on a representative volume element (RVE), is attached. Note that the \(\mathrm{FE}^2\) method is not embarrassingly parallel since the RVE problems are coupled through the macroscopic problem. Numerical results considering different grids on both, the macroscopic and microscopic level as well as weak scaling results for up to a million parallel processes are presented.Non-intrusive global-local analysis of heterogeneous structures based on a second-order interface couplinghttps://zbmath.org/1487.741132022-07-25T18:03:43.254055Z"Wangermez, Maxence"https://zbmath.org/authors/?q=ai:wangermez.maxence"Allix, Olivier"https://zbmath.org/authors/?q=ai:allix.olivier"Guidault, Pierre-Alain"https://zbmath.org/authors/?q=ai:guidault.pierre-alain"Ciobanu, Oana"https://zbmath.org/authors/?q=ai:ciobanu.oana"Rey, Christian"https://zbmath.org/authors/?q=ai:rey.christian-aSummary: In [\textit{M. Wangermez} et al., Comput. Methods Appl. Mech. Eng. 365, Article ID 113032, 24 p. (2020; Zbl 1442.74030)] a second-order coupling strategy of a macroscopic description of a structure and an heterogeneous lower scale description of some local details was proposed. As such, the proposed coupling technique is quite elaborate and not suited for an implementation in a legacy code. The purpose of this paper is to facilitate its implementation by means of a dedicated non-intrusive technique. This leads to several implementation propositions, including the use of MPC conditions, which are available in most of the finite element solver. Its interest is that it does not require any modification of the numerical models and can be implemented with any finite element simulation software. The proposed method has been implemented in the finite element Software Z-set{\texttrademark} used by Safran and is illustrated on an example of a 3D woven composite plate in which a severe weaving defect is introduced.Modeling a synthesized element of complex geometry based upon three-dimensional and two-dimensional finite elementshttps://zbmath.org/1487.741142022-07-25T18:03:43.254055Z"Yakupov, S. N."https://zbmath.org/authors/?q=ai:yakupov.s-n"Kiyamov, H. G."https://zbmath.org/authors/?q=ai:kiyamov.h-g"Yakupov, N. M."https://zbmath.org/authors/?q=ai:yakupov.n-mSummary: This paper offers a description of an approach to modeling a synthesized element featuring a complex geometry. Owing to the region under examination being pre-parametrized with parameters of a parallelepiped and a synthesis of three-dimensional elements with a cubic approximation of unknown variables in all three directions of the region under examination and two-dimensional elements with cubic approximation of unknown variables in a thin layer on its edges, one is enabled to obtain high-precision curved aligned finite elements. The synthesized element obtained substantially expands the range of tasks which now may be solved. Specifically, it enables one to calculate the stress-strain state of coated structures, including those with local fibration while also allowing for specific surface properties which differ from the properties of the primary array to be taken into consideration, including the presence of distributed surface features resultant, for instance, from ion implantation, surface treatment and defects. Different cases have been studied to provide illustration for the method, in particular, a calculation of the stress-strain state of a three-layer plate.Analysis of closed branched and intersecting cracks by the boundary element methodhttps://zbmath.org/1487.741152022-07-25T18:03:43.254055Z"Fedelinski, Piotr"https://zbmath.org/authors/?q=ai:fedelinski.piotrSummary: The boundary element method (BEM) and a computer code for the analysis of plates with closed branched and intersecting cracks are developed. The BEM enables simple and accurate modelling of cracked plates by using boundary elements. Contact tractions between crack surfaces are computed using an iterative procedure. Stress intensity factors (SIFs) are determined using the path-independent integral. Three numerical examples are studied: a star-shaped crack in a square plate, multiple interacting cracks in an infinite plate and randomly distributed and intersecting cracks in a square plate. The examples demonstrate the simplicity of numerical modelling, the accuracy of the method and the possible applications. The influences of load directions, distances between cracks and the contact of the crack surfaces on SIF are investigated. For the plate with randomly distributed cracks, the effective elastic properties are additionally computed by considering or neglecting contact of crack surfaces. The results show that the importance of the contact procedure depends on how the cracked material is loaded.A displacement discontinuity method of high-order accuracy in fracture mechanicshttps://zbmath.org/1487.741162022-07-25T18:03:43.254055Z"Zvyagin, A. V."https://zbmath.org/authors/?q=ai:zvyagin.andrey-v|zvyagin.alexander-v"Udalov, A. S."https://zbmath.org/authors/?q=ai:udalov.a-s.1Summary: In this paper the displacement discontinuity method of high-order accuracy and its application to the problems of fracture mechanics are considered. In common practice of applications of boundary element methods, the methods with the piecewise-constant function of boundary displacement are often used. Their advantage against other algorithms is the simplicity of calculation scheme with a rather good accuracy of the solution at the points of region distant from the boundary. In the fracture mechanics (with lines of surfaces of discontinuity of the displacement field), it is required to describe the stress behavior in the proximity of the crack edges with the highest accuracy possible, which leads to necessity of increasing the degree of accuracy of the used numerical methods. It is shown that the methods with high-order continuity of displacements at the boundary proposed in this work substantially improve the accuracy of computation of displacement and stress fields in the neighborhood of crack edges within the region.Stable and accurate numerical methods for generalized Kirchhoff-Love plateshttps://zbmath.org/1487.741172022-07-25T18:03:43.254055Z"Nguyen, Duong T. A."https://zbmath.org/authors/?q=ai:nguyen.duong-t-a"Li, Longfei"https://zbmath.org/authors/?q=ai:li.longfei"Ji, Hangjie"https://zbmath.org/authors/?q=ai:ji.hangjieSummary: Kirchhoff-Love plate theory is widely used in structural engineering. In this paper, efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff-Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. The generalization stems from the inclusion of additional physics to the classical Kirchhoff-Love model that accounts for bending only. We solve the model equation by discretizing the spatial derivatives using second-order finite-difference schemes, and then advancing the semi-discrete problem in time with either an explicit predictor-corrector or an implicit Newmark-Beta time-stepping algorithm. Stability analysis is conducted for the schemes, and the results are used to determine stable time steps in practice. A series of carefully chosen test problems are solved to demonstrate the properties and applications of our numerical approaches. The numerical results confirm the stability and 2nd-order accuracy of the algorithms and are also comparable with experiments for similar thin plates. As an application, we illustrate a strategy to identify the natural frequencies of a plate using our numerical methods in conjunction with a fast Fourier transformation power spectrum analysis of the computed data. Then we take advantage of one of the computed natural frequencies to simulate the interesting physical phenomena known as resonance and beat for a generalized Kirchhoff-Love plate.Time-domain spectral finite element based on third-order theory for efficient modelling of guided wave propagation in beams and panelshttps://zbmath.org/1487.741182022-07-25T18:03:43.254055Z"Jain, Mayank"https://zbmath.org/authors/?q=ai:jain.mayank"Kapuria, Santosh"https://zbmath.org/authors/?q=ai:kapuria.santoshSummary: We develop a computationally efficient time-domain spectral finite element (SFE) based on Levinson-Bickford-Reddy's third-order theory to accurately predict guided wave propagation in beam- and panel-type structures. The deflection is interpolated using the \(\mathrm{C}^1\)-continuous Lobatto spectral interpolation function recently developed by the authors, while the axial displacement and shear rotation are interpolated using the \(\mathrm{C}^0\)-continuous Lobatto basis functions. A comprehensive numerical study assesses the accuracy and efficiency of the developed element for free vibration and wave propagation response of beams and infinite strips under narrowband tone burst and broadband impact excitations. In terms of accuracy, convergence, and computational effort, we show that the new spectral element performs far better than its conventional counterpart and other available one-dimensional spectral elements with a similar number of degrees of freedom. Although SFEs in the literature often use under-integration for mass matrices to make them diagonal or near-diagonal to gain efficiency, we evaluate the relative performance of full integration and under-integration of mass matrices in terms of convergence rate and computational efficiency. The element will be of immense use for model-based structural health monitoring applications requiring fast and accurate analysis.Time domain spectral element-based wave finite element method for periodic structureshttps://zbmath.org/1487.741192022-07-25T18:03:43.254055Z"Mukherjee, Shuvajit"https://zbmath.org/authors/?q=ai:mukherjee.shuvajit"Gopalakrishnan, S."https://zbmath.org/authors/?q=ai:gopalakrishnan.sathish|gopalakrishnan.sankara-hari|gopalakrishnan.shivasubramanian|gopalakrishnan.srinivasan|gopalakrishnan.srimathy|gopalakrishnan.sugilal|gopalakrishnan.shyam-sunder|gopalakrishnan.sarang"Ganguli, Ranjan"https://zbmath.org/authors/?q=ai:ganguly.ranjanSummary: In this work, a time domain spectral element-based wave finite element method is proposed to analyze periodic structures. Time domain spectral element-based formulation reduces the total degrees of freedom and also renders a diagonal mass matrix resulting in substantial reduction in computation time for the wave finite element method. The formulation is then considered to obtain the stop band characteristics for a periodic bar and a Timoshenko beam considering geometric as well as material periodicity. The impact of geometric parameters on the stop bands of 1-D structures is then investigated in detail. It is shown that the stop bands can be obtained in the frequency range of interest, and its width can be varied by tuning those geometric parameters. Also, the effect of material uncertainty is studied in detail on the stop band characteristics of periodic 1-D structures, and the same formulation is utilized for Monte Carlo simulations. Results show that randomness in density influences more the bandwidth of the stop bands than that of elastic parameters.An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problemshttps://zbmath.org/1487.741202022-07-25T18:03:43.254055Z"Garhuom, Wadhah"https://zbmath.org/authors/?q=ai:garhuom.wadhah"Usman, Khuldoon"https://zbmath.org/authors/?q=ai:usman.khuldoon"Düster, Alexander"https://zbmath.org/authors/?q=ai:duster.alexanderSummary: Broken cells in the finite cell method -- especially those with a small volume fraction -- lead to a high condition number of the global system of equations. To overcome this problem, in this paper, we apply and adapt an eigenvalue stabilization technique to improve the ill-conditioned matrices of the finite cells and to enhance the robustness for large deformation analysis. In this approach, the modes causing high condition numbers are identified for each cell, based on the eigenvalues of the cell stiffness matrix. Then, those modes are supported directly by adding extra stiffness to the cell stiffness matrix in order to improve the condition number. Furthermore, the same extra stiffness is considered on the right-hand side of the system -- which leads to a stabilization scheme that does not modify the solution. The performance of the eigenvalue stabilization technique is demonstrated using different numerical examples.An efficient meshless method for bimaterial interface cracks in 2D thin-layered coating structureshttps://zbmath.org/1487.741212022-07-25T18:03:43.254055Z"Jiang, Songwei"https://zbmath.org/authors/?q=ai:jiang.songwei"Gu, Yan"https://zbmath.org/authors/?q=ai:gu.yan"Golub, Mikhail V."https://zbmath.org/authors/?q=ai:golub.mikhail-vSummary: The interface crack problems in thin-layered coating/substrate structures are analyzed by using the generalized finite difference method, a recently developed meshless collocation method. Since the method is meshless, no element connectivity is needed and the burdensome remeshing of the domain similar to the finite element method is avoided. The multi-domain technique is employed to handle the non-homogeneity of the composite materials. The complex stress intensity factors of the bimaterial interface cracks are computed by using the displacement extrapolation method. Accurate and reliable numerical results with only a small number of degrees of freedom can be obtained for relatively small layer-to-substrate thicknesses. Numerical results calculated by using the boundary element method are also given for the purpose of comparison.Parallel computing with the thick level set methodhttps://zbmath.org/1487.741222022-07-25T18:03:43.254055Z"Mororó, L. A. T."https://zbmath.org/authors/?q=ai:mororo.l-a-t"van der Meer, F. P."https://zbmath.org/authors/?q=ai:van-der-meer.frans-pMetaball based discrete element method for general shaped particles with round featureshttps://zbmath.org/1487.741232022-07-25T18:03:43.254055Z"Zhang, Pei"https://zbmath.org/authors/?q=ai:zhang.pei"Dong, Yueshi"https://zbmath.org/authors/?q=ai:dong.yueshi"Galindo-Torres, S. A."https://zbmath.org/authors/?q=ai:galindo-torres.sergio-andres"Scheuermann, A."https://zbmath.org/authors/?q=ai:scheuermann.a"Li, Ling"https://zbmath.org/authors/?q=ai:li.lingSummary: Discrete element method (DEM) has achieved considerable success on simulating complex granular material behaviours. One of the key challenges of DEM simulations is how to describe particles with realistic geometries. Many shape description methods have been developed including sphere-clustering, polyhedrons, sphero-polyhedrons, superquadric particles to name a few. However, to model general shaped particles with round features, these techniques are either introducing artificial surface roughness or are limited to a few regular shapes. Here we proposed a metaball based DEM where the metaball equation is used to describe particle shapes. Because of its flexibility on choosing control points in the metaball equation, many complex shaped particles can be modelled within this framework. The particle collision is handled by solving an optimization problem. A Newton-Raphson method based algorithm of finding the closest points for metaball DEM is developed accordingly. Using 3D printed particles, the proposed scheme is validated by comparing the simulated ran-out distance with granular column collapses experimental results. The model is further applied to study shape effects on vibration induced segregations. It is shown that the proposed metaball DEM can capture shape influence which may crucial in many engineering and science applications.Fluid mechanics of viscoplasticityhttps://zbmath.org/1487.760012022-07-25T18:03:43.254055Z"Huilgol, Raja R."https://zbmath.org/authors/?q=ai:huilgol.raja-r"Georgiou, Georgios C."https://zbmath.org/authors/?q=ai:georgiou.georgios-cPublisher's description: This book considers the kinematics and dynamics of the flows of fluids exhibiting a yield stress. Continuum mechanics governing the fluid mechanics is described. Two chapters are dedicated to analytical solutions to several steady and unsteady flows of viscoplastic fluids, including flows with pressure-dependent rheological parameters.
Perturbation methods, variational inequalities to solve fluid flow problems, and the use of energy methods are discussed. Numerical modeling using augmented Lagrangian, operator splitting, finite difference, and lattice Boltzmann methods are employed.
The second edition provides new sections on flows of yield stress fluids with pressure-dependent rheological parameters, on flows with wall slip, and on deriving the fundamental equations for Boltzmann lattice materials. Furthermore new material on the lubrication approximation and applications of finite differences has been added.
See the review of the first edition in [Zbl 1328.76001].Differential equations in engineering. Research and applicationshttps://zbmath.org/1487.760032022-07-25T18:03:43.254055ZPublisher's description: Differential Equations in Engineering: Research and Applications describes advanced research in the field of the applications of differential equations in engineering and the sciences, and offers a sound theoretical background, along with case studies.
It describes the advances in differential equations in real life for engineers. Along with covering many advanced differential equations and explaining the utility of these equations, the book provides a broad understanding of the use of differential equations to solve and analyze many real-world problems, such as calculating the movement or flow of electricity, the motion of an object to and from, like a pendulum, or explaining thermodynamics concepts by making use of various mathematical tools, techniques, strategies, and methods in applied engineering.
This book is written for researchers and academicians, as well as for undergraduate and postgraduate students of engineering.
The articles of this volume will be reviewed individually.
Indexed articles:
\textit{Pant, Mohit}, Element-free Galerkin method for computational fracture mechanics, 1-35 [Zbl 1476.74150]
\textit{Awasthi, Mukesh Kumar; Asthana, Rishi; Uddin, Ziya}, Evaporative capillary instability of swirling fluid layer with mass transfer, 37-53 [Zbl 1480.76053]
\textit{Mbock, Koumbe; Magloire, Etoua Remy; Domingo, Ayissi Raoul}, Control instruments of regularized problems based on mathematical modeling of structural perturbations with applications at the nodes of 25-bar truss systems, 55-76 [Zbl 1476.74125]
\textit{Arora, Geeta; Vaid, Mandeep Kaur}, Numerical simulation of singularly perturbed differential equation with large delay using exponential B-spline collocation method, 77-93 [Zbl 07420575]
\textit{Sharma, Jyoti}, Application of differential equations to instability of nanofluids, 95-106 [Zbl 1480.76050]
\textit{Pandit, Purnima; Singh, Payal; Patel, Tanvi}, Analysis of prey-predator model, 107-124 [Zbl 1475.92137]
\textit{Mitra, R. K.}, Incremental harmonic balance method for multi-degree-of-freedom system with time-delays, 125-143 [Zbl 07420577]
\textit{Pandey, S. K.}, Solution to the Dirac equation, 145-154 [Zbl 1479.81022]
\textit{Zhao, Jun}, Periodic solution of a nonlinear economic cycle model with a generic investment function, 155-170 [Zbl 1479.91214]
\textit{Zhu, Haitao; Geng, Guoqian; Yu, Yang; Xu, Lixin}, Response evolution of a marine riser in random sea waves, 171-185 [Zbl 1480.76019]
\textit{Alam, P.; Kapoor, S.}, Solution of system of PDE governed in natural convective flow in a rectangular porous cavity, 187-205 [Zbl 1480.76111]On the role of added mass and vorticity release for self-propelled aquatic locomotionhttps://zbmath.org/1487.760142022-07-25T18:03:43.254055Z"Paniccia, D."https://zbmath.org/authors/?q=ai:paniccia.d"Graziani, G."https://zbmath.org/authors/?q=ai:graziani.giorgio"Lugni, C."https://zbmath.org/authors/?q=ai:lugni.claudio"Piva, R."https://zbmath.org/authors/?q=ai:piva.renzoSummary: Aquatic locomotion of a deformable body from rest up to its asymptotic speed is given by the unsteady motion which is produced by a series of periodic reactions dictated by the body configuration and by the style of swimming. The added mass plays a crucial role, not only for the initial burst, but also along each manoeuvre, to accelerate the surrounding fluid for generating the kinetic energy and to enable vortex shedding in the wake. The estimate of these physical aspects has been largely considered in most theoretical models, but not sufficiently deepened in many experimental and numerical investigations. As a motivation, while the vortical structures are easily detectable from the flow field, the added mass, on the contrary, is usually embedded in the overall forcing terms. By the present impulse formulation, we are able to separate and to emphasize the role of the added mass and vorticity release to evaluate in a neat way their specific contributions. The precise identification of the added mass is also instrumental for a well-posed numerical problem and for easily readable results. As a further point, the asymptotic speed is found to be guided either by the phase velocity of the prescribed undulation and by the unavoidable recoil motion induced by the self-propelled swimming. The numerical results reported in the present paper concern simplified cases of non-diffusing vorticity and two-dimensional flow.Use of Galerkin technique to the rolling of a plate in deep waterhttps://zbmath.org/1487.760192022-07-25T18:03:43.254055Z"Ray, Swagata"https://zbmath.org/authors/?q=ai:ray.swagata"De, Soumen"https://zbmath.org/authors/?q=ai:de.soumen"Mandal, B. N."https://zbmath.org/authors/?q=ai:mandal.birendra-nathSummary: The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.An efficient and generalized solid boundary condition for SPH: applications to multi-phase flow and fluid-structure interactionhttps://zbmath.org/1487.760602022-07-25T18:03:43.254055Z"Zhang, Chi"https://zbmath.org/authors/?q=ai:zhang.chi"Zhu, Yujie"https://zbmath.org/authors/?q=ai:zhu.yujie"Lyu, Xiuxiu"https://zbmath.org/authors/?q=ai:lyu.xiuxiu"Hu, Xiangyu"https://zbmath.org/authors/?q=ai:hu.xiangyuSummary: In this paper, we generalize the solid boundary condition where a one-sided Riemann solver is introduced to determine the fluid-solid interaction for weakly compressible smoothed particle hydrodynamics (SPH) presented in [\textit{C. Zhang} et al., J. Comput. Phys. 337, 216--232 (2017; Zbl 1415.76514)] to model multi-phase flows with large density ratio and multi-phase fluid-structure interaction (FSI) in multi-resolution scenario. Compared with the boundary condition proposed by \textit{S. Adami} et al. [``A generalized wall boundary condition for smoothed particle hydrodynamics'', J. comput. Phys. 231--21, 7057--7075 (2012; \url{doi:10.1016/j.jcp.2012.05.005})] where solid is discretized by dummy particles whose physical quantities are extrapolated from surrounding fluid particles, the present method is very simple and efficient as extra extrapolation is avoided by constructing a one-sided Riemann problem for each interacting fluid-solid particle pair. This feature makes its extension to multi-phase flow and FSI straightforward. Furthermore, we adopt a penalty method in multi-resolution discretization to prevent particle penetration in violent multi-phase simulation. A set of examples involving multi-phase flows with high density ratio and complex interface, and multi-phase FSI are studied to demonstrate the accuracy, robustness and versatility of the present method. The validations presented herein and those reported by Zhang et al. [loc. cit.] where free-surface flows exhibiting violent events such as impact and breaking are studied indicate that the present method provides a unified approach for addressing the solid, i.e., rigid and flexible, boundary condition in multi-physics SPH applications.Fuzzy model of interaction of hydroacoustic waves with flat viscoelastic transversal-isotropic screenhttps://zbmath.org/1487.760742022-07-25T18:03:43.254055Z"Bolnokin, V. E."https://zbmath.org/authors/?q=ai:bolnokin.v-e"Mitrushkin, E. I."https://zbmath.org/authors/?q=ai:mitrushkin.e-i"Hai, Duong Minh"https://zbmath.org/authors/?q=ai:hai.duong-minh"Storozhev, S. V."https://zbmath.org/authors/?q=ai:storozhev.s-vSummary: A theoretical algorithm for the analysis of uncertainty factors in the model of a hydroacoustic screen in the form of a viscoelastic transversally isotropic deformable layer that contacts along the faces with arrays of an ideal weakly compressible liquid is developed and tested. The fuzzy-set technique for allowance of uncertainties for the values of non-contrast experimental parameters of the geometric and physico-mechanical properties of the screen and the liquids separated by the screen is presented. The synthesized algorithm is based on the use of analytical results of a clear deterministic version of the model and the application of the alpha-level modification of the heuristic generalization principle to the transition to fuzzy representations of exogenous parameters.Dynamic simulations of an encapsulated microbubble translating in a tube at low capillary and Reynolds numbershttps://zbmath.org/1487.760942022-07-25T18:03:43.254055Z"Vlachomitrou, M."https://zbmath.org/authors/?q=ai:vlachomitrou.m"Lytra, A."https://zbmath.org/authors/?q=ai:lytra.a"Pelekasis, N."https://zbmath.org/authors/?q=ai:pelekasis.nikos-a|pelekasis.nikolaos-aSummary: The dynamic translation of a micron-sized encapsulated bubble is investigated numerically inside a horizontal tube where liquid flows under constant pressure drop, when the effect of gravity is neglected. The coating of the bubble is treated as an infinitesimally thin viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed to solve the axisymmetric flow configuration combined with the spine or elliptic mesh generation techniques for updating the mesh. The microbubble is initially elongated and the Reynolds number of the flow is relatively small, i.e. \(\operatorname{Re}< 5\). Benchmark simulations for long free bubbles robustly recover the scaling of the film thickness with the 2/3 power of the capillary number based on surface tension. In the case of encapsulated bubbles, for a sufficiently small capillary number and after a short transient period, the bubble acquires a Bretherton type shape that slowly expands in order to accommodate changes in the liquid pressure. The speed of translation is nearly constant, close to the mean velocity of the flow, and does not depend on surface tension, shell elasticity or bending resistance. Fluid motion in the thin film ``contact'' region that forms in the gap between the tube and the shell is seen to be a stable flow arrangement that entails a mixture of pressure driven and shear driven flow, with the latter greatly affected by the area dilatation modulus via the tangential stress balance. By introducing a modified capillary number based on the area dilatational modulus, rather than surface tension, it is seen that the dimensionless film thickness that occupies the region between the bubble and the tube wall increases with the 1/3 power of the modified capillary number with increasing area dilatation. Simulations when surface tension is absent indicate that tangential shear generated due to variation of the membrane stress in the transition region that joins the bulk of the flow configuration with the contact region, leads to film thinning via the 5/7 power of the modified capillary number. Variations in the transverse shear of the viscoelastic shell generate large lubrication overpressures in the thin film region between the tube and the shell that are exerted radially on the shell and are conjectured to be responsible for the onset of 3d buckled shapes. The latter are often observed experimentally in similar flow configurations of capsules and are characterized by wrinkles that develop in the azimuthal direction around the shell equator.An energy approach to the calculation of forces acting on solid bodies in ferrofluidshttps://zbmath.org/1487.780032022-07-25T18:03:43.254055Z"Ivanov, A. S."https://zbmath.org/authors/?q=ai:ivanov.aleksandr-sSummary: The main advantages of the energy approach to solving the problem of determining magnetic forces acting on solid bodies immersed into magnetized ferrofluids (FFs) are shown. Characteristic disadvantages of the standard approach to the calculation of magnetic forces using the Bernoulli equation for FFs and an equation for the magnetic pressure jump at the interface are considered. A review of works devoted to the study of forces acting on solid bodies immersed in magnetized FFs is presented. This literature review convincingly demonstrates the need for and potential advantage of using the energy approach to these problems, since the analytical expressions significantly depend on the body shape and obtaining the final numerical results is complicated by the error of magnetic field calculation at the ``solid body-FF'' interface where the normal component of induction and the tangential component of the magnetic field exhibit a discontinuity. In contrast, the energy approach allows using the standard functions of program packages for determining thermodynamic potentials. The choice of a thermodynamic potential correctly describing experimental data is discussed. The method of magnetic energy determination is justified by the problem setting and verified by comparison of the results of several numerical solutions obtained using the open software package FEMM for FFs obeying a nonlinear magnetization law. This analysis was previously performed neither experimentally nor theoretically in view of the commonly accepted use of simplifying assumptions (approximations of weak and strong magnetic fields or a noninductive approximation). Here, the energy approach to determining forces acting on solid bodies in FFs has been justified by pairwise comparison of the results obtained in the framework of this approach to the data of laboratory experiment and the results of standard calculations.Effect of magnetic field and non-uniform surface on squeeze film lubricationhttps://zbmath.org/1487.780052022-07-25T18:03:43.254055Z"Muthu, P."https://zbmath.org/authors/?q=ai:muthu.p"Pujitha, V."https://zbmath.org/authors/?q=ai:pujitha.vSummary: In the present paper, the combined effect of magnetic field and nonuniform shape of the surface on squeeze film characteristics is investigated. The non-uniform squeeze film thickness is calculated using Lagrange interpolation technique. Numerical integration procedure is used to obtain the solution for pressure, load carrying capacity. The effects of field parameters on squeeze film characteristics are discussed and are presented graphically. It is observed that externally applied magnetic field and non-uniform shape of the bearing surface enhance the squeeze film lubrication.Joint phase reconstruction and magnitude segmentation from velocity-encoded MRI datahttps://zbmath.org/1487.780132022-07-25T18:03:43.254055Z"Corona, Veronica"https://zbmath.org/authors/?q=ai:corona.veronica"Benning, Martin"https://zbmath.org/authors/?q=ai:benning.martin"Gladden, Lynn F."https://zbmath.org/authors/?q=ai:gladden.lynn-f"Reci, Andi"https://zbmath.org/authors/?q=ai:reci.andi"Sederman, Andrew J."https://zbmath.org/authors/?q=ai:sederman.andrew-j"Schönlieb, Carola-Bibiane"https://zbmath.org/authors/?q=ai:schonlieb.carola-bibianeSummary: Velocity-encoded MRI is an imaging technique used in different areas to assess flow motion. Some applications include medical imaging such as cardiovascular blood flow studies, and industrial settings in the areas of rheology, pipe flows, and reactor hydrodynamics, where the goal is to characterise dynamic components of some quantity of interest. The problem of estimating velocities from such measurements is a nonlinear dynamic inverse problem. To retrieve time-dependent velocity information, careful mathematical modelling and appropriate regularisation is required. In this work, we use an optimisation algorithm based on non-convex Bregman iteration to jointly estimate velocity-, magnitude- and segmentation-information for the application of bubbly flow imaging. Furthermore, we demonstrate through numerical experiments on synthetic and real data that the joint model improves velocity, magnitude and segmentation over a classical sequential approach.
For the entire collection see [Zbl 1471.65006].Nonstationary thermokinetic model of surface laser scanninghttps://zbmath.org/1487.800082022-07-25T18:03:43.254055Z"Knyazeva, A. G."https://zbmath.org/authors/?q=ai:knyazeva.anna-georgievnaSummary: This paper presents a thermophysical model of laser beam scanning of the surface of a two-layer plate whose top layer melts and undergoes shrinkage due to changes in porosity and whose bottom layer (substrate) does not melt. The dependences of the heat capacity, thermal conductivity, and reflection coefficient on porosity are taken into account. Heat loss can occur by both radiation and convection. Results illustrating the non-stationarity of the process throughout the scan are presented. It is shown that the complex thermal cycles and inhomogeneous temperature field are directly related to inhomogeneous shrinkage, leading to the surface topography typical of selective laser melting processes.An analytical model for effective thermal conductivity of the media embedded with fracture networks of power law length distributionshttps://zbmath.org/1487.800102022-07-25T18:03:43.254055Z"Miao, Tongjun"https://zbmath.org/authors/?q=ai:miao.tongjun"Chen, Aimin"https://zbmath.org/authors/?q=ai:chen.aimin"Jiang, Lijuan"https://zbmath.org/authors/?q=ai:jiang.lijuan"Zhang, Huajie"https://zbmath.org/authors/?q=ai:zhang.huajie"Liu, Junfeng"https://zbmath.org/authors/?q=ai:liu.junfeng"Yu, Boming"https://zbmath.org/authors/?q=ai:yu.bomingDirac structures in thermodynamics of non-simple systemshttps://zbmath.org/1487.800132022-07-25T18:03:43.254055Z"Yoshimura, Hiroaki"https://zbmath.org/authors/?q=ai:yoshimura.hiroaki"Gay-Balmaz, François"https://zbmath.org/authors/?q=ai:gay-balmaz.francoisSummary: We present the Dirac structures and the associated Dirac system formulations for \textit{non-simple} thermodynamic systems by focusing upon the cases that include irreversible processes due to friction and heat conduction. These systems are called non-simple since they involve several entropy variables. We review the variational formulation of the evolution equations of such non-simple systems. Then, based on this, we clarify that there exists a Dirac structure on the Pontryagin bundle over a thermodynamic configuration space and we develop the Dirac dynamical formulation of such non-simple systems. The approach is illustrated with the example of an adiabatic piston.
For the entire collection see [Zbl 1482.94007].Thermomechanical effects of radiation origin in microelectronics productshttps://zbmath.org/1487.800162022-07-25T18:03:43.254055Z"Volkov, Yu. A."https://zbmath.org/authors/?q=ai:volkov.yurii-aleksandrovich"Vyrostkov, M. Yu."https://zbmath.org/authors/?q=ai:vyrostkov.m-yu"Markov, M. B."https://zbmath.org/authors/?q=ai:markov.mikhail-b"Tarakanov, I. A."https://zbmath.org/authors/?q=ai:tarakanov.ilya-alekseevichSummary: A mathematical model of the thermomechanical effect of penetrating radiation on a microelectronic product is presented. The model is based on the thermoelasticity equations, which are a consequence of the quantum kinetic equations for phonons. Heat transport is described by the law of conservation of energy and the Cattaneo equation, which takes into account the finite rate of heat propagation. Lattice vibrations are considered in the approximation of the linear theory of elasticity. In general, the model determines the distribution of temperature, energy flow, deformation and stress. Difference schemes have been developed for solving the model equations. The effectiveness of the developed model was tested by solving the problem of thermal shock.Robust and fast excitation fluctuations transfer between two membranes in an optomechanical systemhttps://zbmath.org/1487.810232022-07-25T18:03:43.254055Z"Zhang, Chun-Ling"https://zbmath.org/authors/?q=ai:zhang.chunling"Chen, Xiang"https://zbmath.org/authors/?q=ai:chen.xiang"Liao, Chang-Geng"https://zbmath.org/authors/?q=ai:liao.chang-geng"Lin, Xiu-Min"https://zbmath.org/authors/?q=ai:lin.xiu-minSummary: The quantum state control or entanglement preparation for macroscopic matter is an attractive research. Optomechanical system provides an ideal platform to observe the quantum behaviors of macroscopic matter. In this paper, we present a scheme to implement the average excitation fluctuations transfer between two membranes in an optomechanical system via shortcut to adiabatic passage which is based on transitionless quantum driving. In order to quickly attain the transfer, we choose a suitable evolution path and optimize the experimental parameters. Numerical simulation demonstrates that the proposed scheme is robust against membrane damping and cavity decay. Furthermore, this idea can be used to generate entanglement of two membrane modes in a short time. Finally, we also discuss the experimental implementation of this scheme. This work may provide a new method for generating the macroscopic superposition state in the optomechanical system.Towards an analytical solution for the triple quantum dot shuttlehttps://zbmath.org/1487.811002022-07-25T18:03:43.254055Z"Peralta, Prat Vázquez"https://zbmath.org/authors/?q=ai:peralta.prat-vazquez"Cota, E."https://zbmath.org/authors/?q=ai:cota.erikaSummary: In this paper we look for analytical solutions of the triple-quantum-dot shuttle (TQDS) in the linear tunneling regime. This system consists of three quantum dots arranged in a straight line, where the end dots remain fixed while the center dot oscillates between them and its motion is modeled by a quantum harmonic oscillator. In the linear tunneling approximation for the Hamiltonian \(\hat{H}_{TQDS}\), we consider an analytical method developed by Kuś and Lewenstein in 1986 that enables us to find exact isolated solutions for a Hamiltonian of the \(\hat{H}_{TQDS}\)-type using the Bargmann representation. This allows us to obtain some energy values and their respective eigenvectors with the condition that the parameters that describe the system comply with certain constraints called compatibility conditions. The latter give rise to the possibility of developing a criterion that leads us to establish under what conditions the Kuś method is applicable in the solution of systems represented by Hamiltonians of the \(\hat{H}_{TQDS}\)-type.Quantum integrability of massive anisotropic SU(N) fermionic modelshttps://zbmath.org/1487.811042022-07-25T18:03:43.254055Z"Melikyan, A."https://zbmath.org/authors/?q=ai:melikyan.arik-artavazdovich|melikyan.arsen|melikyan.a-o"Weber, G."https://zbmath.org/authors/?q=ai:weber.gerhard-wilhelm|weber.gunther-h|weber.gerald|weber.gerhald-wilhelm|weber.guglielmo|weber.g-g|weber.griffin|weber.gustavo|weber.glenn-mSummary: We consider a general anisotropic massive SU(N) fermionic model, and investigate its quantum integrability. In particular, by regularizing singular operator products, we derive a system of equations resulting in the S-matrix and find some non-trivial solutions. We illustrate our findings on the example of a SU(3) model, and show that the Yang-Baxter equation is satisfied in the massless limit for all coupling constants, while in the massive case the solutions are parameterized in terms of the exceptional solutions to the eight-vertex model.Negative string tension of a higher-charge Schwinger model via digital quantum simulationhttps://zbmath.org/1487.811482022-07-25T18:03:43.254055Z"Honda, Masazumi"https://zbmath.org/authors/?q=ai:honda.masazumi"Itou, Etsuko"https://zbmath.org/authors/?q=ai:itou.etsuko"Kikuchi, Yuta"https://zbmath.org/authors/?q=ai:kikuchi.yuta"Tanizaki, Yuya"https://zbmath.org/authors/?q=ai:tanizaki.yuya(no abstract)Energetics and coarsening analysis of a simplified non-linear surface growth modelhttps://zbmath.org/1487.820162022-07-25T18:03:43.254055Z"Khalfi, Hamza"https://zbmath.org/authors/?q=ai:khalfi.hamza"Aarab, Amal"https://zbmath.org/authors/?q=ai:aarab.amal"Alaa, Nour Eddine"https://zbmath.org/authors/?q=ai:alaa.noureddineSummary: We study a simplified multidimensional version of the phenomenological surface growth continuum model derived in [\textit{Z. Csahók} et al., Physica D 128, No. 1, 87--100 (1999; Zbl 0947.76028)]. The considered model is a partial differential equation for the surface height profile \(u\) which possesses the following free energy functional:
\[
E(u)=\int_{\Omega}\left[\frac{1}{2}\ln\left(1+|\nabla u|^2\right)-|\nabla u|\arctan(|\nabla u|)+\frac{1}{2}|\Delta u|^2 \right]\mathrm{d}x,
\]
where \(\Omega\) is the domain of a fixed support on which the growth is carried out. The term \(|\Delta u|^2\) designates the standard surface diffusion in contrast to the second order term which phenomenologically describes the growth instability. The energy above is mainly carried out in regions of higher surface slope \((|\nabla u|)\). Hence minimizing such energy corresponds to reducing surface defects during the growth process from a given initial surface configuration. Our analysis is concerned with the energetic and coarsening behaviours of the equilibrium solution. The existence of global energy minimizers and a scaling argument are used to construct a sequence of equilibrium solutions with different wavelength. We apply our minimum energy estimates to derive bounds in terms of the linear system size \(|\Omega|\) for the characteristic interface width and average slope. We also derive a stable numerical scheme based on the convex-concave decomposition of the energy functional and study its properties while accommodating these results with \(1\)d and \(2\)d numerical simulations.Einstein's energy and space isotropyhttps://zbmath.org/1487.830012022-07-25T18:03:43.254055Z"Hill, James M."https://zbmath.org/authors/?q=ai:hill.james-murraySummary: In this note, we derive an extension of the conventional Einstein variation of mass formula with a specific expression arising from a Lorentz invariant equation for the energy rate \(\mathrm{d}e/\mathrm{d}p\) where \(e = mc^2\) is the particle energy, \(p = mu\) the particle momentum and \(u\) the velocity. This is the simplest one-parameter Lorentz-invariant extension of the Einstein mass-energy relation. Implicit in the new expression is space-time anisotropy such that the particle has different rest masses in the positive and negative \(x\) directions. While numerous experiments have been undertaken aimed at testing such hypothesis, and all indicate the veracity of the assumption that space is isotropic, nevertheless since it is generally believed that black-holes exist at the centres of galaxies, space must be intrinsically anisotropic in some sense. Finally, we note a very curious connection with both the conventional Einstein energy-mass expression \(e = e_0/ (1 - (u/c)^2)^{1/2}\) and the new expression derived here with certain singular integral equations usually associated with aero-foil problems, fluid mechanics and punch problems in elasticity, and that this connection is not some vague intangible relationship, but involves an exact correspondence.Gravitationally decoupled non-static anisotropic spherical solutionshttps://zbmath.org/1487.830042022-07-25T18:03:43.254055Z"Sharif, M."https://zbmath.org/authors/?q=ai:sharif.masoud|sharif.mhd-saeed|sharif.muhammad-a-r"Ahmed, Shehrbano"https://zbmath.org/authors/?q=ai:ahmed.shehrbanoInhomogeneous generalization of Einstein's static universe with Sasakian spacehttps://zbmath.org/1487.830052022-07-25T18:03:43.254055Z"Ishihara, Hideki"https://zbmath.org/authors/?q=ai:ishihara.hideki"Matsuno, Satsuki"https://zbmath.org/authors/?q=ai:matsuno.satsuki(no abstract)Robustness of particle creation in the formation of a compact objecthttps://zbmath.org/1487.830152022-07-25T18:03:43.254055Z"Okabayashi, Kazumasa"https://zbmath.org/authors/?q=ai:okabayashi.kazumasa"Harada, Tomohiro"https://zbmath.org/authors/?q=ai:harada.tomohiro"Nakao, Ken-ichi"https://zbmath.org/authors/?q=ai:nakao.ken-ichi(no abstract)Gravity of two photon decay and its quantum coherencehttps://zbmath.org/1487.830332022-07-25T18:03:43.254055Z"Mackewicz, Kris"https://zbmath.org/authors/?q=ai:mackewicz.kris"Hogan, Craig"https://zbmath.org/authors/?q=ai:hogan.craig-jAxion-photon conversion in strongly magnetised plasmashttps://zbmath.org/1487.830692022-07-25T18:03:43.254055Z"Millar, Alexander J."https://zbmath.org/authors/?q=ai:millar.alexander-j"Baum, Sebastian"https://zbmath.org/authors/?q=ai:baum.sebastian"Lawson, Matthew"https://zbmath.org/authors/?q=ai:lawson.matthew"Marsh, M. C. David"https://zbmath.org/authors/?q=ai:marsh.m-c-david(no abstract)Chaotic dynamics of a suspended string in a gravitational background with magnetic fieldhttps://zbmath.org/1487.830802022-07-25T18:03:43.254055Z"Colangelo, P."https://zbmath.org/authors/?q=ai:colangelo.pietro"Giannuzzi, F."https://zbmath.org/authors/?q=ai:giannuzzi.f"Losacco, N."https://zbmath.org/authors/?q=ai:losacco.nSummary: We study the effects of a magnetic field on the chaotic dynamics of a string with endpoints on the boundary of an asymptotically \(\mathrm{AdS}_5\) space with black hole. We study Poincaré sections and compute the Lyapunov exponents for the string perturbed from the static configuration, for two different orientations, with position of the endpoints on the boundary orthogonal and parallel to the magnetic field. We find that the magnetic field stabilizes the string dynamics, with the largest Lyapunov exponent remaining below the Maldacena-Shenker-Stanford bound.Gravitational decoupling algorithm modifies the value of the conserved charges and thermodynamics properties in Lovelock unique vacuum theoryhttps://zbmath.org/1487.830882022-07-25T18:03:43.254055Z"Estrada, Milko"https://zbmath.org/authors/?q=ai:estrada.milkoSummary: We provide an extension of the Gravitational Decoupling (algorithm) for the Lovelock theory with Unique Vacuum (LUV), which represents a simple way to solve the equations of motion. Due to the application of this algorithm, the energy of the system splits in the \textit{energy of the seed solution} and the \textit{energy of each quasi-LUV sector}. Under certain assumptions imposed, the total energy varies due to the contribution of energy of each quasi-LUV sector. It is provided a new solution, whose energy differs from the energy of the seed solution in a quantity that depends on the number of extra sources. The new solution has two inner horizons, which is a proper characteristic of itself. Furthermore, its thermodynamics differs from the seed solution, since our solution is always stable and does not have phase transitions. Since the first law of thermodynamics is modified by the presence of the matter fields, we provide a new version of the first law for LUV, where a local definition of the variation of energy is defined, and, where the entropy and temperature are consistent for LUV theory.Evaporation of black holes in flat space entangled with an auxiliary universehttps://zbmath.org/1487.831012022-07-25T18:03:43.254055Z"Miyata, Akihiro"https://zbmath.org/authors/?q=ai:miyata.akihiro"Ugajin, Tomonori"https://zbmath.org/authors/?q=ai:ugajin.tomonori(no abstract)Supermassive black holes surrounded by dark matter modeled as anisotropic fluid: epicyclic oscillations and their fitting to observed QPOshttps://zbmath.org/1487.831042022-07-25T18:03:43.254055Z"Stuchlík, Z."https://zbmath.org/authors/?q=ai:stuchlik.zdenek"Vrba, J."https://zbmath.org/authors/?q=ai:vrba.jan|vrba.josef(no abstract)Testing the early universe with anisotropies of the gravitational wave backgroundhttps://zbmath.org/1487.831212022-07-25T18:03:43.254055Z"Dimastrogiovanni, Ema"https://zbmath.org/authors/?q=ai:dimastrogiovanni.ema"Fasiello, Matteo"https://zbmath.org/authors/?q=ai:fasiello.matteo"Malhotra, Ameek"https://zbmath.org/authors/?q=ai:malhotra.ameek"Meerburg, P. Daniel"https://zbmath.org/authors/?q=ai:meerburg.p-daniel"Orlando, Giorgio"https://zbmath.org/authors/?q=ai:orlando.giorgio(no abstract)Primordial tensor bispectra in \(\mu\)-CMB cross-correlationshttps://zbmath.org/1487.831322022-07-25T18:03:43.254055Z"Orlando, Giorgio"https://zbmath.org/authors/?q=ai:orlando.giorgio"Meerburg, P. Daniel"https://zbmath.org/authors/?q=ai:meerburg.p-daniel"Patil, Subodh P."https://zbmath.org/authors/?q=ai:patil.subodh-p(no abstract)Dynamical forces and the influence of an equation of state on gravitational collapsehttps://zbmath.org/1487.850032022-07-25T18:03:43.254055Z"Govender, Wesley"https://zbmath.org/authors/?q=ai:govender.wesley"Bogadi, Robert S."https://zbmath.org/authors/?q=ai:bogadi.robert-s"Govender, Megandhren"https://zbmath.org/authors/?q=ai:govender.megandhren"Duffy, Kevin J."https://zbmath.org/authors/?q=ai:duffy.kevin-janSummary: We investigate the equation of state (EoS) parameter on the collapse of a star undergoing dissipative collapse. The collapse starts from an initial static configuration described by the anisotropic generalisation of the Vaidya-Tikekar superdense model. The initial matter profile obeys a linear EoS and starts to radiate energy in the form of a radial heat flux as it leaves hydrostatic equilibrium. We study the evolution of the hydrostatic, gravitational, anisotropic and dissipative forces at play within the collapsing body via the dynamic Tolman-Oppenheimer-Volkoff equation. We show that the EoS parameter has a significant impact on the various forces which influences the outcome of gravitational collapse. The effect of the EoS parameter on the temperature profiles is also studied by employing a causal heat transport equation of Maxwell-Cattaneo form. Our investigation shows that the stiffness of the fluid which is related to its compressibility, is compromised in the presence of pressure anisotropy and heat flow.Study of anisotropic and non-uniform gravastars by gravitational decoupling in \(f(R,T)\) gravityhttps://zbmath.org/1487.850062022-07-25T18:03:43.254055Z"Azmat, Hina"https://zbmath.org/authors/?q=ai:azmat.hina"Zubair, M."https://zbmath.org/authors/?q=ai:zubair.mohammad|zubair.muhammad|zubair.mohammed"Ahmad, Zahid"https://zbmath.org/authors/?q=ai:ahmad.zahidSummary: Adopting gravitational decoupling through minimal geometric deformation (MGD) procedure, we develop an analytical version of gravastar model with non-uniform and anisotropic features, in the framework of \(f(R,T)\) gravity. This new non-uniform model describes an ultracompact stellar structure of radius \(\mathcal{R}_S=2\mathcal{M}\), whose interior solution smoothly joins a conformally deformed Schwarzschild exterior solution, and also it is matched to the standard Schwarzschild exterior solution under some restrictions on \(f(R,T)\) coupling constant \(\lambda\). The constructed solution presents a family of stellar models satisfying some of the fundamental properties of a stable configuration, including a positive energy density everywhere with monotonically decreasing behavior from the center to surface. Besides, a non-uniform pressure is observed with monotonic behavior. All the energy conditions except the strong one are satisfied inside the ultracompact stellar configuration for all the values of \(f(R,T)\) coupling constant \(\lambda\), which are compatible with regularity condition.An anisotropic charged fluids with Chaplygin equation of statehttps://zbmath.org/1487.850142022-07-25T18:03:43.254055Z"Estevez-Delgado, Joaquin"https://zbmath.org/authors/?q=ai:estevez-delgado.joaquin"Rodríguez Maya, Noel Enrique"https://zbmath.org/authors/?q=ai:rodriguez-maya.noel-enrique"Martínez Peña, José"https://zbmath.org/authors/?q=ai:martinez-pena.jose"Cleary-Balderas, Arthur"https://zbmath.org/authors/?q=ai:cleary-balderas.arthur"Paulin-Fuentes, Jorge Mauricio"https://zbmath.org/authors/?q=ai:paulin-fuentes.jorge-mauricioA new way to test the cosmological principle: measuring our peculiar velocity and the large-scale anisotropy independentlyhttps://zbmath.org/1487.850182022-07-25T18:03:43.254055Z"Nadolny, Tobias"https://zbmath.org/authors/?q=ai:nadolny.tobias"Durrer, Ruth"https://zbmath.org/authors/?q=ai:durrer.ruth"Kunz, Martin"https://zbmath.org/authors/?q=ai:kunz.martin"Padmanabhan, Hamsa"https://zbmath.org/authors/?q=ai:padmanabhan.hamsa(no abstract)Computation of new degree-based topological indices of graphenehttps://zbmath.org/1487.920652022-07-25T18:03:43.254055Z"Shigehalli, V. S."https://zbmath.org/authors/?q=ai:shigehalli.v-s"Kanabur, Rachanna"https://zbmath.org/authors/?q=ai:kanabur.rachannaSummary: Graphene is one of the most promising nanomaterials because of its unique combination of superb properties, which opens a way for its exploitation in a wide spectrum of applications ranging from electronics to optics, sensors, and biodevices. Inspired by recent work on Graphene of computing topological indices, here we propose new topological indices, namely, Arithmetic-Geometric index (AG\(_1\) index), SK index, SK\(_1\) index, and SK\(_2\) index of a molecular graph \(G\) and obtain the explicit formulae of these indices for Graphene.Control of opto-mechanical scanners with elastic linkshttps://zbmath.org/1487.930232022-07-25T18:03:43.254055Z"Bolnokin, V. E."https://zbmath.org/authors/?q=ai:bolnokin.v-e"Vyskub, V. G."https://zbmath.org/authors/?q=ai:vyskub.v-g"Dianov, V. N."https://zbmath.org/authors/?q=ai:dianov.v-n"Storozhev, V. I."https://zbmath.org/authors/?q=ai:storozhev.v-iSummary: The paper describes the features of the control for mirror scanners with elastic links. The analysis of various structural solutions is carried out. Considered the problem of stabilization, positioning, programmed movement. The advisability of multi-mode control is shown.