×

A coupled finite element-least squares point interpolation/boundary element method for structure-acoustic system with stochastic perturbation method. (English) Zbl 1464.74351

Summary: Finite element-least squares point interpolation method (FE-LSPIM) developed recently shows some excellent features to improve the calculation accuracy of mechanical problems. In this paper, a coupled finite element-least squares point interpolation method/ boundary element method (FE-LSPIM/BEM) is proposed to analyze plate-like structural-acoustic coupled system. Here, the FE-LSPIM is used to model the structure domain, while the acoustic domain is modeled by BEM. The hybrid method not only inherits advantages of element compatibility of the finite element method (FEM) and the quadratic polynomial completeness of LSPIM, but also improves the calculation accuracy of the structural domain. Moreover, stochastic perturbation method is introduced to process uncertainty parameters of the FE-LSPIM/BEM, so the stochastic perturbation FE-LSPIM/BEM model has been proposed, then several uncertain parameters that have been randomly processed were used to increase the analytical reliability in structural-acoustic coupled system. At last, numerical examples are taken to verify the feasibility of the proposed SP-FE-LSPIM/BEM as compared to Monte Carlo method (MCM) and stochastic perturbation finite element/boundary element method (SP-FEM/BEM). The results show that FE-LSPIM/BEM has higher accuracy in analysis of uncertain structural-acoustic coupling system as compared to the FEM/BEM.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Q05 Hydro- and aero-acoustics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Michler, C.; Hulshoff, S. J.; van Brummelen, E. H.; de Borst, R., A monolithic approach to fluid-structure interaction, Comput Fluids, 33, 5-6, 839-848 (2004) · Zbl 1053.76042
[2] Blom, F. J., A monolithical fluid-structure interaction algorithm applied to the piston problem, Comput Methods Appl Mech Eng, 167, 369-391 (1998) · Zbl 0948.76046
[3] Felippa C A., Park K C., Farhat C. Partitioned analysis of coupled mechanical systems Comput Methods Appl Mech Eng 2001,190:3247-70. · Zbl 0985.76075
[4] Zienkiewicz, O. C.; Bettess, P., Fluid-structure dynamic interaction and wave forces. An introduction to numerical treatment, Int J Numer Methods Eng, 13, 1, 1-16 (1978) · Zbl 0385.73050
[5] Wang, X.; Bathe, K. J., Displacement/pressure based mixed finite element formulations for acoustic fluid-structure interaction problems, Int J Numer Methods Eng, 40, 11, 2001-2017 (1997) · Zbl 0886.73073
[6] Davidsson, P., Structure-acoustic analysisfinite element modeling and reduction methods (2004), Lund University
[7] Everstine, G. C., Finite element formulations of structural acoustics problems, Comput Struct, 2, 65, 307-321 (1997) · Zbl 0918.73240
[8] Abbaszadeh M., Dehghan M.A meshless numerical procedure for solving fractional reaction subdiffusion model via a new combination of alternating direction implicit (ADI) approach and interpolating element free Galerkin (EFG) method, 2015. · Zbl 1443.65189
[9] Farahani, B. V.; Berardo, J. M.; Drgas, R., The axisymmetric analysis of circular plates using the radial point interpolation method, Int J Comput Methods Eng Sci Mech, 16, 6, 336-353 (2015)
[10] Cunefare, K. A.; Koopmann, G.; Brod, K., A boundary element method for acoustic radiation valid for all wavenumbers, J Acoust Soc Am, 85, 1, 39-48 (1989)
[11] Estorff, O. V., Boudary elements in acoustics (2000), Wit Press Southampton
[12] Xiao, Q. Z.; Dhanasekar, M., Coupling of FE and EFG using collocation approach, Adv Eng Software, 33, 7-10, 507-515 (2002) · Zbl 1024.65113
[13] Li, S.; Cui, X. Y., N-sided polygonal smoothed finite element method (nSFEM) with non-matching meshes and their applications for brittle fracture problems, Comput Methods Appl Mech Eng, 359, Article 112672 pp. (2020) · Zbl 1441.74259
[14] Yang, Q.; Wang, B.; Li, S.; Cui, X. Y., A moment-based stochastic edge-based smoothed finite element method for electromagnetic forming process, Sci China Technol Sci (2020)
[15] Zhang, B. R.; Rajendran, S., A “FE-Meshfree” QUAD_4 element for free-vibration analysis, Comput Methods Appl Mech Eng, 197, 3595-3604 (2007) · Zbl 1194.74489
[16] Rajendran, S.; Zhang, B. R., A “FE-Meshfree” QUAD_4 element based on partition of unity, Comput Methods Appl Mech Eng, 197, 128-147 (2007) · Zbl 1169.74628
[17] Yao, L. Y.; Zhou, J. W., Dispersion error reduction for acoustic problems using the finite element-least square point interpolation method, J Vib Acoust-Trans ASME, 137, 2 (2015), 021013-021013-8
[18] Yao, L. Y., A hybrid finite element-least-square point interpolation method for solving multifluid coupling acoustic problems, Noise Control Eng J, 65, 3, 234-243 (2017)
[19] Yao, L. Y.; Wu, F.; Wu, G., Numerical study of exterior acoustic problems using a novel finite element-least square point interpolation method with perfectly matched layer, Eng Anal Bound Elem, 102, 87-96 (2019) · Zbl 1464.76066
[20] Yao, L. Y.; Jiang, G. Q., Band structure computation of two-dimension and three-dimension phonemic crystal using a finite element least square point interpolation method, Appl Math Model, 76, 591-606 (2019) · Zbl 1481.74705
[21] Chen, N.; Yu, D. J.; Xia, B. Z., Analysis of plate structural-acoustic coupling systems based on finite element-least square point interpolation and finite element method, J Vib Eng, 27, 304-310 (2014)
[22] Kopuz, S., Integrated FEM/BEM approach to the dynamic and acoustic analysis of plate structures, Eng Anal Bound Elem, 17, 269-277 (1996)
[23] Tonga, Z.; Zhang, Y.; Zhang, Z.; Hua, H., Dynamic behavior and sound transmission analysis of a fluid-structure coupled system using the direct-BEM/FEM, J Sound Vib, 299, 645-655 (2007)
[24] Choi, P., Application of a directly coupled boundary element and finite element model to the dynamics of coupled acoustic silencers (1997), North Carolina State University
[25] Chen, P. T.; Ju, S. H.; Cha, K. C., A symmetric formulation of coupled BEM/FEM in solving responses of submerged elastic structures for large degree of freedoms, J Sound Vib, 233, 407-422 (2000) · Zbl 1237.74170
[26] He, Z. C.; Li, E.; Liu, G. R., A mass-redistributed finite element method (MR-FEM) for acoustic problems using triangular mesh, J Comput Phys, 323, 149-170 (2016) · Zbl 1415.65257
[27] Yao, L. Y., A cell-based smoothed radial point interpolation-perfectly matched layer method for two-dimensional acoustic radiation problems, J Press Vessel Technol -Trans ASME, 138, 2 (2015), 021301-021301-9
[28] Yao, L. Y., An optimized generalized integration rules for error reduction of acoustic finite element model, Int J Comput Methods, 15, 7 (2018), 1850062-1850062-19 · Zbl 1404.76168
[29] Chen, N.; Xia, S. Y.; Yu, D. J., Hybrid interval and random analysis for structural-acoustic systems including periodical composites and multi-scale bounded hybrid uncertain parameters, Mech Syst Signal Process, 115, 524-544 (2019)
[30] Chen, N.; Yu, D. J.; Xia, B. Z.; Beer, Michael, Uncertainty analysis of a structural-acoustic problem using imprecise probabilities based on p-box representations, Mech Syst Signal Process, 80, 45-57 (2016)
[31] Manolis, Papadrakakis; Papadopoulos, V., Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation, Comput Methods Appl Mech Eng, 134, 3-4, 325-340 (1996) · Zbl 0891.73079
[32] Boulkaibet, I., Finite element model updating using the shadow hybrid Monte Carlo technique, Mech Syst Signal Process, 52-53, 1, 115-132 (2015)
[33] Vlietinck, Jonas, Diagrammatic Monte Carlo study of the acoustic and the Bose-Einstein condensate polaron, N J Phys, 17, 35, 33023 (2015)
[34] Sébastien, Boyaval, A fast Monte-Carlo method with a reduced basis of control variates applied to uncertainty propagation and Bayesian estimation, Comput Methods Appl Mech Eng, 190-205 (2012), 241-244 · Zbl 1354.65010
[35] Shen, Q. Y.; Wu, X. Q.; Chen, J. F.; Han, Z.; Huang, Y. Q., Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method, J Pet Sci Eng, 161, 9-16 (2018)
[36] Ding, C. S.; Deokar, Rohit R.; Ding, Y. J.; Li, G. Y.; Cui, X. Y.; Tamma Kumar, K.; Bordas Stéphane, P. A., Model order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties, Comput Methods Appl Mech Eng, 349, 266-284 (2019) · Zbl 1441.74295
[37] Richardson J N., Coelho R F., Adriaenssens S. Robust topology optimization of 2D and 3D continuum and truss structures using a spectral stochastic finite element method, 2013.
[38] Lehikoinen, A., Spectral stochastic finite element method for electromagnetic problems with random geometry, Electr Eng, 6, 1, 5-12 (2014)
[39] Sepahvand, K.; Marburg, S.; Sepahvand, K.; Marburg, S., Spectral stochastic finite element method in vibroacoustic analysis of fiber-reinforced composites, Procedia Eng, 199, 1134-1139 (2017)
[40] Wu, F.; Chen, K.; Wang, T. Y.; Yao, L. Y.; Hu, M., Stochastic hybrid perturbation technique-based smoothed finite element-statistical energy method for mid-frequency analysis of structure-acoustic systems with parametric and nonparametric uncertainties, Comput Methods Appl Mech Eng, 349, 522-549 (2019) · Zbl 1441.74282
[41] Hu, X. B.; Cui, X. Y.; Feng, H.; Li, G. Y., Stochastic analysis using the generalized perturbation stable node-based smoothed finite element method, Eng Anal Bound Elem, 70, 40-55 (2016) · Zbl 1403.65137
[42] Hu, X. B.; Cui, X. Y.; Liang, Z. M.; Li, G. Y., The performance prediction and optimization of the fiber-reinforced composite structure with uncertain parameters, Compos Struct, 164, 207-218 (2017)
[43] Cui X, Y.; Li, S.; Feng, H.; Li G, Y., A triangular prism solid and shell interactive mapping element for electromagnetic sheet metal forming process, J Comput Phys, 336, 192-211 (2017)
[44] Hu, X.; Cui, X. Y.; Zhang, Q. Y.; Wang, G.; Li, G. Y., The stable node-based smoothed finite element method for analyzing acoustic radiation problems, Eng Anal Bound Elem, 80, 142-152 (2017) · Zbl 1403.76045
[45] Jiang, G. Q.; Yao, L. Y.; Wu, F., A stochastic perturbation finite element-least square point interpolation method for the analysis of uncertain structural-acoustics problems with random variables, Appl Acoust, 137, 18-26 (2018)
[46] Papadimitriou, C.; Katafygiotis, L. S.; Beck, J. L., Approximate analysis of response variability of uncertain linear systems, Probab Eng Mech, 10, 4, 251-264 (1995)
[47] Xia, B. Z.; Yu, D. J.; Liu, J., Transformed perturbation stochastic finite element method for static response analysis of stochastic structures, Finite Elem Anal Des, 79, 2, 9-21 (2014)
[48] He, Z. C.; Hu, J. Y.; Li, E., An uncertainty model of acoustic metamaterials with random parameters, Comput Mech, 62, 1023 (2018) · Zbl 1469.74100
[49] Chen, N.; Yu D, J.; Xia B, Z., Hybrid uncertain analysis for exterior acoustic field prediction with interval random parameters, Int J Comput Methods, 15 (2018), 185006-185006-23
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.