Recent zbMATH articles in MSC 74E30 https://zbmath.org/atom/cc/74E30 2021-05-28T16:06:00+00:00 Werkzeug Forced vibration in cutting process considering the nonlinear curvature and inertia of a rotating composite cutter bar. https://zbmath.org/1459.74077 2021-05-28T16:06:00+00:00 "Ren, Yongsheng" https://zbmath.org/authors/?q=ai:ren.yongsheng "Yao, Donghui" https://zbmath.org/authors/?q=ai:yao.donghui Summary: Forced vibration of the cutting system with a three-dimensional composite cutter bar is investigated. The composite cutter bar is simplified as a rotating cantilever shaft which is subjected to a cutting force including regenerative delay effects and harmonic exciting items. The nonlinear curvature and inertia of the cutter bar are taken into account based on inextensible assumption. The effects of the moment of inertia, gyroscopic effect, and internal and external damping are also considered, but shear deformation is neglected. Equation of motion is derived based on Hamilton's extended principle and discretized by the Galerkin method. The analytical solutions of the steady-state response of the cutting system are constructed by using the method of multiple scales. The response of the cutting system is studied for primary and superharmonic resonances. The effects of length-to-diameter ratio, damping ratio, cutting force coefficients, ply angle, rotating speed, and internal and external damping are investigated. The results show that nonlinear curvature and inertia imposed a significant effect on the dynamic behavior of the cutting process. The equivalent nonlinearity of the cutting system shows hard spring characteristics. Multiple solutions and jumping phenomenon of typical Duffing system are found in forced response curves. Stress relaxation in cylindrical glass-to-metal junctions with account for the quality of a junction region. https://zbmath.org/1459.74122 2021-05-28T16:06:00+00:00 "Burenin, A. A." https://zbmath.org/authors/?q=ai:burenin.anatolii-aleksandrovich "Lyubimova, O. N." https://zbmath.org/authors/?q=ai:lyubimova.o-n "Solonenko, E. P." https://zbmath.org/authors/?q=ai:solonenko.e-p Summary: With account for a complex behavior of glass (the phenomenon of glass transition) and the degree of adhesion between glass and metal layers, a numerical-analytical method for calculating the evolution of a stress state of glass-metal composite during temperature treatment is proposed. The effect of relaxation processes in the glass-metal junction region on the technological and residual stresses in the composite is studied. Three-dimensional semianalytical solutions for piezoelectric laminates subjected to underwater shocks. https://zbmath.org/1459.74057 2021-05-28T16:06:00+00:00 "Liang, Xu" https://zbmath.org/authors/?q=ai:liang.xu "Lu, Wenbin" https://zbmath.org/authors/?q=ai:lu.wenbin "Zhu, Ronghua" https://zbmath.org/authors/?q=ai:zhu.ronghua "Ye, Changpeng" https://zbmath.org/authors/?q=ai:ye.changpeng "Liu, Guohua" https://zbmath.org/authors/?q=ai:liu.guohua Summary: In this study, a piezoelectric laminate is analyzed by applying the Laplace transform and its numerical inversion, Fourier transform, differential quadrature method (DQM), and state space method. Based on the modified variation principle for the piezoelectric laminate, the fundamental equations for dynamic problems are derived. The solutions for the displacement, stress, electric potential, and dielectric displacement are obtained using the proposed method. Durbin's inversion method for the Laplace transform is adopted. Four boundary conditions are discussed through the DQM. The proposed method is validated by comparing the results with those of the finite element method (FEM). Moreover, this semianalytical method is further extended to describe the dynamic response of piezoelectric laminated plates subjected to underwater shocks by introducing Taylor's fluid-structure interaction algorithm. Both air-backed and water-backed laminated plates are investigated, and the effect of the fluid is examined. In the time domain, the electric potential and displacements of sample points are calculated under four boundary conditions. The present method is shown to be accurate and can be a useful method to calculate the dynamic response of underwater laminated sensors. Elastic-plastic deformation of flexible plates with spatial reinforcement structures. https://zbmath.org/1459.74113 2021-05-28T16:06:00+00:00 "Yankovskii, A. P." https://zbmath.org/authors/?q=ai:yankovskii.andrei-petrovich|yankovskii.a-p Summary: A mathematical model for the elastic-plastic bending deformation of spatially reinforced plates is constructed based on a leap-frog numerical scheme. The elastic-plastic behavior of the component materials of the composition is described by the theory of flow with isotropic hardening. The low resistance of the composite plates to transverse shear is taken into account using Reddy's theory and the geometric nonlinearity of the problem using the von Kármán approximation. The dynamic elastic-plastic bending deformation of flat and spatially reinforced metal composite and fiberglass rectangular plates exposed to an air blast wave is investigated. It is shown that for relatively thick plates, replacing a flat leap-frog reinforcement structure by a spatial one leads to a decrease (of a few tens of percent for metal composite structures and a few hundred percent for fiberglass structures) in strain intensity in the binder and to a decrease (insignificant for metal composite structures and a factor of almost 1.5 for fiberglass) in the compliance of the plate in the transverse direction. It has been found that for relatively thin plates, replacing the flat reinforcement structure by a spatial one leads to a slight decrease in its compliance. Dynamic analysis of a tapered composite thin-walled rotating shaft using the generalized differential quadrature method. https://zbmath.org/1459.74044 2021-05-28T16:06:00+00:00 "Zhong, Weiyan" https://zbmath.org/authors/?q=ai:zhong.weiyan "Gao, Feng" https://zbmath.org/authors/?q=ai:gao.feng.6|gao.feng.3|gao.feng.1|gao.feng.2|gao.feng.4|gao.feng|gao.feng.5 "Ren, Yongsheng" https://zbmath.org/authors/?q=ai:ren.yongsheng "Wu, Xiaoxiao" https://zbmath.org/authors/?q=ai:wu.xiaoxiao "Ma, Hongcan" https://zbmath.org/authors/?q=ai:ma.hongcan Summary: A dynamic model of a tapered composite thin-walled rotating shaft is presented. In this model, the transverse shear deformation, rotary inertia, and gyroscopic effects have been incorporated. The equations of motion are derived based on a refined variational asymptotic method (VAM) and Hamilton's principle. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the generalized differential quadrature method (GDQM). The validity of the dynamic model is proved by comparing the numerical results with those obtained in the literature and by using ANSYS. The effects of taper ratio, boundary conditions, ply angle, length to mean radius ratios, and mean radius to thickness ratios on the natural frequencies and critical rotating speeds are investigated. Fractal local fields in random composites. https://zbmath.org/1459.74014 2021-05-28T16:06:00+00:00 "Rylko, Natalia" https://zbmath.org/authors/?q=ai:rylko.natalia Summary: The local fields in composites and porous media can have complicated structure because of the fine geometrical inhomogeneity. Numeric examples show that randomly generated local fields can have complicated fractal structure contrary to the local fields in periodic composites. It is demonstrated that the local oscillations of the stresses in random composites are higher than in regular ones. This result implies that the damage risk is higher for irregular elastic composites than for regular ones ceteris paribus. For viscous fluid, this means that irregular locations of obstacles increase local oscillations of the velocity, hence, lead to turbulence. We consider fields governed by the 2D Poisson equation $$\nabla^2u=-1$$ in a perforated domain $$D$$ corresponding to the host material. The holes of $$D$$ correspond to the torsion problem in elasticity and the hard disks to longitudinal flow of viscous fluid. The corresponding Dirichlet problem in randomly generated multiply connected domains is solved. A method of functional equations is applied following Mityushev's scheme for the Riemann-Hilbert type problems in multiply connected domains. It is justified that the rate of convergence for functional equations is of order $$2nr^2$$ where $$n$$ is the connectivity of the domain whose linear size is normalized to unity and $$r$$ the radii of holes. This observation shows that for large $$n$$ and sufficiently small $$r$$ few iterations for the functional equations can give an acceptable numerical result. An anisotropic hyperelastic constitutive model with bending stiffness interaction for cord-rubber composites: comparison of simulation results with experimental data. https://zbmath.org/1459.74022 2021-05-28T16:06:00+00:00 "Sun, Shulei" https://zbmath.org/authors/?q=ai:sun.shulei "Chen, Wenguo" https://zbmath.org/authors/?q=ai:chen.wenguo Summary: Based on the invariant theory of continuum mechanics by Spencer, the strain energy depends on deformation, fiber direction, and the gradients of the fiber direction in the deformed configuration. The resulting extended theory is very complicated and brings a nonsymmetric stress and couple stress. By introducing the gradient of fiber vector in the current configuration, the strain energy function can be decomposed into volumetric, isochoric, anisotropic, and bending deformation energy. Due to the particularity of bending deformation, the reinforced material has tensile deformation and compression deformation. The bending stiffness should be taken into consideration, and it is further verified by the bending simulation. Fuzzy uncertainty propagation in composites using Gram-Schmidt polynomial chaos expansion. https://zbmath.org/1459.74041 2021-05-28T16:06:00+00:00 "Dey, S." https://zbmath.org/authors/?q=ai:dey.sudip "Mukhopadhyay, T." https://zbmath.org/authors/?q=ai:mukhopadhyay.tanmoy "Khodaparast, H. Haddad" https://zbmath.org/authors/?q=ai:khodaparast.h-haddad "Adhikari, S." https://zbmath.org/authors/?q=ai:adhikari.sondipon Summary: The propagation of uncertainty in composite structures possesses significant computational challenges. Moreover, probabilistic descriptions of uncertain model parameters are not always available due to lack of data. This paper investigates on the uncertainty propagation in dynamic characteristics (such as natural frequencies, frequency response function and mode shapes) of laminated composite plates by using fuzzy approach. In the proposed methodology, non-intrusive Gram-Schmidt polynomial chaos expansion (GPCE) method is adopted in uncertainty propagation of structural uncertainty to dynamic analysis of composite structures, when the parameter uncertainties represented by fuzzy membership functions. A domain in the space of input data at zero-level of membership functions is mapped to a zone of output data with the parameters determined by D-optimal design. The obtained meta-model (GPCE) can also be used for higher $$\alpha$$-levels of fuzzy membership function. The most significant input parameters such as ply orientation angle, elastic modulus, mass density and shear modulus are identified and then fuzzified. The proposed fuzzy approach is applied to the problem of fuzzy modal analysis for frequency response function of a simplified composite cantilever plates. The fuzzy mode shapes are also depicted for a typical laminate configuration. Fuzzy analysis of the first three natural frequencies is presented to illustrate the results and its performance. The proposed approach is found more efficient compared to the conventional global optimization approach in terms of computational time and cost. Laminated Timoshenko beams with viscoelastic damping. https://zbmath.org/1459.74107 2021-05-28T16:06:00+00:00 "Mustafa, Muhammad I." https://zbmath.org/authors/?q=ai:mustafa.muhammad-islam Summary: In this paper we consider a viscoelastic laminated beam model. This structure is given by two identical uniform layers on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. We use minimal and general conditions on the relaxation function and establish explicit energy decay formula which gives the best decay rates expected under this level of generality. Our new result generalizes the earlier related results in the literature. Analyzing the bond behavior of fiber-reinforced polymer (FRP) bars embedded in engineered cementitious composites (ECCs) with the nonlocal continuum rod model. https://zbmath.org/1459.74042 2021-05-28T16:06:00+00:00 "Li, Qiuxiang" https://zbmath.org/authors/?q=ai:li.qiuxiang "Fu, Mingfu" https://zbmath.org/authors/?q=ai:fu.mingfu "Xie, Banghua" https://zbmath.org/authors/?q=ai:xie.banghua Summary: In this study, a nonlocal elastic rod model is applied to analytically evaluate the bond behavior between fiber-reinforced polymer (FRP) bars and engineered cementitious composites (ECCs). The second-order differential equation, which is based on nonlocal elasticity theory, governs the bond behavior of the FRP bars along the bond length. The classical elasticity model is a special case of the nonlocal model. The solution of the second-order differential equation can be obtained by substituting three-stage linear bond stress-slip relationship of the FRP bars. The slip values (solution of the second-order differential equation) within the bond length calculated by the nonlocal continuum rod model are affected by the nonlocal parameter $$e_0a$$. The results from a case study show that the maximum pullout force decreases when the nonlocal size effect is considered, thereby providing a closer approximation of the experimental data than the existing local model. Tuning the total displacement of membranes. https://zbmath.org/1459.49002 2021-05-28T16:06:00+00:00 "Kao, Chiu-Yen" https://zbmath.org/authors/?q=ai:kao.chiu-yen "Mohammadi, Seyyed Abbas" https://zbmath.org/authors/?q=ai:mohammadi.seyyed-abbas Summary: In this paper we study a design problem to tune the robustness of a membrane by changing its vulnerability. Consider an energy functional corresponding to solutions of Poisson's equation with Robin boundary conditions. The aim is to find functions in a rearrangement class such that their energies would be a given specific value. We prove that this design problem has a solution and also we propose a way to find it. Furthermore, we derive some topological and geometrical properties of the configuration of the vulnerability. In addition, some explicit solutions are found analytically when the domain is an $$N$$-ball. For general domain we develop a numerical algorithm based on rearrangements to find the solution. The algorithm evolves both minimization and maximization processes over two different rearrangement classes. Our algorithm works efficiently for various domains and the numerical results obtained coincide with our analytical findings. Mathematical modeling of the overall time-dependent behavior of non-ageing viscoelastic reinforced composites. https://zbmath.org/1459.74031 2021-05-28T16:06:00+00:00 "El Kouri, M." https://zbmath.org/authors/?q=ai:el-kouri.m "Bakkali, A." https://zbmath.org/authors/?q=ai:bakkali.a "Azrar, L." https://zbmath.org/authors/?q=ai:azrar.lahcen Summary: New mathematical and numerical formulations are developed for effective time-dependent non ageing viscoelastic behavior of linear viscoelastic composites. The modeling is based on the dynamic Green's functions, integral equations, and Volterra product. The time concentration tensor is derived through numerical solution of the integral equation and the Mori-Tanaka micromechanical model. The developed modeling gives explicit expressions of effective properties through convolution products in the Stieltjes space. A numerical procedure is developed allowing the calculation of the tensoriel convolution product and its inverse. Based on Carson-Laplace transform, the frequency dependent effective properties are also obtained and converted to the time domain. For viscoelastic Prony laws and inclusions with various shapes, numerical results are presented and compared with the approach based on the Laplace transform and the correspondence principle. Second-order two-scale analysis for heating effect of periodical composite structure. https://zbmath.org/1459.74043 2021-05-28T16:06:00+00:00 "Wan, Jianjun" https://zbmath.org/authors/?q=ai:wan.jianjun "Dong, Wen" https://zbmath.org/authors/?q=ai:dong.wen "Zhao, Yongcheng" https://zbmath.org/authors/?q=ai:zhao.yongcheng "Song, Shicang" https://zbmath.org/authors/?q=ai:song.shicang Summary: The multi-scale analysis method is presented for the heat transfer problems of periodical composite structures under irradiation heating. This kind of physical problem can be described as a class of parabolic equations with small periodical oscillating coefficients equipped with the mixed boundary conditions of both Dirichlet and Neumann type. It needs more expensive cost in both computer's memory and CPU time to solve these problems by the usual finite difference method or finite element method, since it is necessary to partition the considering geometrical region finer to capture the heat conduction behavior at small scale. To reduce the computational complexity, an approximate solution is derived by the asymptotic expansion technique. The convergence of asymptotic solution to exact solution is technically proved as the micro-scale parameter tends to zero. Based on the asymptotic expansion formula, a second-order two-scale finite element method is proposed to fully solve this problem in practice. Numerical results show convergent behavior of the proposed method. Determination of damping properties of an elongated plate with an integral damping coating on the base of studying complex eigenfrequencies. https://zbmath.org/1459.74072 2021-05-28T16:06:00+00:00 "Paimushin, V. N." https://zbmath.org/authors/?q=ai:paimushin.vitaliy-n "Firsov, V. A." https://zbmath.org/authors/?q=ai:firsov.v-a "Shishkin, V. M." https://zbmath.org/authors/?q=ai:shishkin.v-m Summary: We describe the structure of a perspective integral damping coating consisting (with respect to the thickness) of two layers of a viscoelastic material with a thin reinforcing layer in-between. We propose a four-layer finite element model with fourteen degrees of freedom for a plate with a mentioned damping coating. This model allows us to take into account the effect of transversal compression of damping layers under high-frequency vibrations of the plate. For determining some lower complex modes and frequencies of free vibrations of the damped plate, we solve a generalized complex eigenvalue problem using the method of iterations in a subspace.