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A coupled smoothed finite element method (S-FEM) for structural-acoustic analysis of shells. (English) Zbl 1403.74325
Summary: In this paper, a coupled smoothed finite element method (S-FEM) is developed to deal with the structural-acoustic problems consisting of a shell configuration interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements that can be generated automatically for any complicated geometries are adopted to discretize the problem domain. A gradient smoothing technique (GST) is introduced to perform the strain smoothing operation. The discretized system equations are obtained using the smoothed Galerkin weakform, and the numerical integration is applied over the further formed edge-based and face-based smoothing domains, respectively. To extend the edge-based smoothing operation from plate structure to shell structure, an edge coordinate system is defined local on the edges of the triangular element. Numerical examples of a cylinder cavity attached to a flexible shell and an automobile passenger compartment have been conducted to illustrate the effectiveness and accuracy of the coupled S-FEM for structural-acoustic problems.

##### MSC:
 74S30 Other numerical methods in solid mechanics (MSC2010) 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74K25 Shells
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##### References:
 [1] Nefske, D. J.; Wolf, J. A.; Howell, L. J., Structural-acoustic finite element analysis of the automobile passenger compartment: a review of current practice, J Sound Vib, 80, 2, 247-266, (1982) [2] Atalla, N.; Bernhard, R. J., Review of numerical solutions for low-frequency structural-acoustic problems, Appl Acoust, 43, 271-294, (1994) [3] Carneal, J. P.; Fuller, C. R., An analytical and experimental investigation of active structural acoustic control of noise transmission through double panel systems, J Sound Vib, 272, 749-771, (2004) [4] Sung, S. H.; Nefske, D. J., A coupled structural-acoustic finite element model for vehicle interior noise analysis, J Vib Acoust, 106, 2, 314-318, (1984) [5] Horacek, J. T.; Zolotarev, I., Acoustic-structural coupling of vibrating cylindrical shells with flowing fluid, J Fluid Struct, 5, 5, 487-501, (1991) [6] Richards, T. L., Finite element analysis of structural-acoustic coupling in tyres, J Sound Vib, 149, 2, 235-243, (1991) [7] Hong, K. L.; Kim, J., Analysis of free vibration of structural-acoustic coupled systems, part I: development and verification of the procedure, J Sound Vib, 188, 4, 561-575, (1995) [8] Hong, K. L.; Kim, J., Analysis of free vibration of structural-acoustic coupled systems, part II: two- and three-dimensional examples, J Sound Vib, 188, 4, 577-600, (1995) [9] Kim, S. M.; Brennan, M. J., A compact matrix formulation using the impedance and mobility approach for the analysis of structural-acoustic systems, J Sound Vib, 223, 1, 97-113, (1999) [10] Bernhard, R. J.; Huff, J. E., Structural-acoustic design at high frequency using the energy finite element method, J Vib Acoust, 121, 295-301, (1999) [11] Lee, Y. Y., Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate, Appl Acoust, 63, 1157-1175, (2002) [12] Deu, J. F.; Larbi, W.; Ohayon, R., Vibration and transient response of structural-acoustic interior coupled systems with dissipative interface, Comput Methods Appl Mech Eng, 197, 4894-4905, (2008) · Zbl 1194.74132 [13] Kang, S. W.; Lee, J. M.; Kim, S. H., Structural-acoustic coupling analysis of the vehicle passenger compartment with the roof, air-gap, and trim boundary, J Vib Acoust, 122, 196, 202, (2000) [14] Marburg, S., A general concept for design modification of shell meshes in structural-acoustic optimization - part I: formulation of the concept, Finite Elem Anal Des, 38, 725-735, (2002) · Zbl 1100.74635 [15] Song, C. K.; Hwang, J. K.; Lee, J. M.; Hedrick, J. K., Active vibration control for structural-acoustic coupling system of a 3-D vehicle cabin model, J Sound Vib, 267, 851-865, (2003) [16] Ahn, C. G.; Choi, H. G.; Lee, J. M., Structural-acoustic coupling analysis of two cavities connected by boundary structures and small holes, J Vib Acoust, 127, 566-574, (2005) [17] Tanaka, M.; Masuda, Y., Boundary element method applied to certain structural-acoustic coupling problems, Comput Methods Appl Mech Eng, 71, 2, 225-234, (1988) · Zbl 0674.73059 [18] Slepyan, L. I.; Sorokin, S. V., Analysis of structural-acoustic coupling problems by a two-level boundary integral method, part 1: a general formulation and test problems, J Sound Vib, 184, 2, 195-211, (1995) · Zbl 1065.74531 [19] Sorokin, S. V., Analysis of structural-acoustic coupling problems by a two-level boundary integral equations method, part 2: vibrations of a cylindrical shell of finite length in an acoustic medium, J Sound Vib, 184, 2, 213-228, (1995) · Zbl 1065.74532 [20] Ju, H. D.; Lee, S. B., Multi-domain structural-acoustic coupling analysis using the finite element and boundary element techniques, KSME Int J, 15, 5, 555-561, (2001) [21] Fritze, D.; Marburg, S.; Hardtke, H. J., FEM-BEM-coupling and structural-acoustic sensitivity analysis for shell geometries, Comput Struct, 83, 143-154, (2005) [22] Gu, Y.; Chen, W.; Zhang, C. Z., Singular boundary method for solving plane strain elastostatic problems, Int J Solids Struct, 48, 2549-2556, (2011) [23] Schneider, S., FE/FMBE coupling to model fluid-structure interaction, Int J Numer Methods Eng, 76, 2137-2156, (2008) · Zbl 1195.74196 [24] Chen, C. S.; Golberg, M. A.; Hon, Y. C., The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations, Int J Numer Methods Eng, 43, 1421-1435, (1998) · Zbl 0929.76098 [25] Fairweather, G.; Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv Comput Mach, 9, 69-95, (1998) · Zbl 0922.65074 [26] Chen, J. T.; Chang, M. H.; Chen, K. H.; Lin, S. R., The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function, J Sound Vib, 257, 4, 667-711, (2002) [27] Chen, W.; Tanaka, M., A meshless, integration-free, and boundary-only RBF technique, Comput Math Appl, 43, 379-391, (2002) · Zbl 0999.65142 [28] Chen, W.; Hon, Y. C., Numerical investigation on convergence of boundary knot method in the analysis of homogeneous Helmholtz, modified Helmholtz, and convection-diffusion problems, Comput Methods Appl Mech Eng, 192, 1859-1875, (2003) · Zbl 1050.76040 [29] Chen, W., Meshfree boundary particle method applied to Helmholtz problems, Eng Anal Bound Elem, 26, 577-581, (2002) · Zbl 1013.65128 [30] Chen, W.; Fu, Z. J., Boundary particle method for inverse Cauchy problems of inhomogeneous Helmholtz equations, J Mar Sci Technol, 17, 3, 157-163, (2009) [31] Fu, Z. J.; Chen, W.; Yang, H. T., Boundary particle method for Laplace transformed time fractional diffusion equations, J Comput Phys, 235, 52-66, (2013) · Zbl 1291.76256 [32] Chen, W.; Fu, Z. J.; Wei, X., Potential problems by singular boundary method satisfying moment condition, Comput Model Eng Sci, 54, 65-85, (2009) · Zbl 1231.65245 [33] Chen, W.; Wang, F. Z., A method of fundamental solutions without fictitious boundary, Eng Anal Bound Elem, 34, 530-532, (2010) · Zbl 1244.65219 [34] Qu, W. Z.; Chen, W., Solution of two-dimensional Stokes flow problems using improved singular boundary method, Adv Appl Math Mech, 7, 1, 13-30, (2015) [35] He, Z. C.; Liu, G. R.; Zhong, Z. H.; Wu, S. C.; Zhang, G. Y.; Cheng, A. G., An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems, Comput Methods Appl Mech Eng, 199, 20-33, (2009) · Zbl 1231.76147 [36] He, Z. C.; Liu, G. R.; Zhong, Z. H.; Zhang, G. Y.; Cheng, A. G., Dispersion free analysis of acoustic problems using the alpha finite element method, Comput Mech, 46, 867-881, (2010) · Zbl 1344.76078 [37] Li, E.; He, Z. C.; Xu, X.; Liu, G. R., Hybrid smoothed finite element method for acoustic problems, Comput Methods Appl Mech Eng, 283, 664-688, (2015) · Zbl 1423.74902 [38] Chen, J. S.; Wu, C. T.; Yoon, S.; You, Y., A stabilized conforming nodal integration for Galerkin meshfree methods, Int J Numer Methods Eng, 50, 435-466, (2001) · Zbl 1011.74081 [39] Yoo, J. W.; Moran, B.; Chen, J. S., Stabilized conforming nodal integration in the natural-element method, Int J Numer Methods Eng, 60, 861-890, (2004) · Zbl 1060.74677 [40] Liu, G. R.; Dai, K. Y.; Nguyen, T. T., A smoothed finite element method for mechanics problems, Comput Mech, 39, 6, 859-877, (2007) · Zbl 1169.74047 [41] Liu, G. R.; Nguyen, T. T.; Dai, K. Y.; Lam, K. Y., Theoretical aspects of the smoothed finite element method (SFEM), Int J Numer Methods Eng, 71, 8, 902-930, (2007) · Zbl 1194.74432 [42] Dai, K. Y.; Liu, G. R., Free and forced vibration analysis using the smoothed finite element method (SFEM), J Sound Vib, 301, 803-820, (2007) [43] Cui, X. Y.; Liu, G. R.; Li, G. Y.; Zhao, X.; Nguyen, T. T.; Sun, G. Y., A smoothed finite element method (SFEM) for linear and geometrically nonlinear analysis of plates and shells, Comput Model Eng Sci, 28, 2, 109-125, (2008) · Zbl 1232.74099 [44] Yao, L. Y.; Yu, D. J.; Cui, X. Y.; Zang, X. G., Numerical treatment of acoustic problems with the smoothed finite element method, Appl Acoust, 71, 743-753, (2010) [45] Liu, G. R., A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible method: part I theory, Int J Numer Methods Eng, 81, 1093-1126, (2010) · Zbl 1183.74358 [46] Liu, G. R., A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: part II applications to solid mechanics problems, Int J Numer Methods Eng, 81, 1127-1156, (2010) · Zbl 1183.74359 [47] Liu, G. R.; Nguyen, T. T.; Nguyen, X. H.; Lam, K. Y., A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems, Comput Struct, 87, 14-26, (2009) [48] Wang, G.; Cui, X. Y.; Li, G. Y., Temporal stabilization nodal integration method for static and dynamic analyses of Reissner-Mindlin plates, Comput Struct, 152, 125-141, (2015) [49] Liu, G. R.; Nguyen, T. T.; Lam, K. Y., An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analysis of solids, J Sound Vib, 320, 1100-1130, (2009) [50] Cui, X. Y.; Liu, G. R.; Li, G. Y.; Zhang, G. Y.; Zheng, G., Analysis of plates and shells using an edge-based smoothed finite element method, Comput Mech, 45, 141-156, (2010) · Zbl 1202.74165 [51] Nguyen, T. T.; Liu, G. R.; Lam, K. Y.; Zhang, G. Y., A face-based smoothed finite element method (FS-FEM) for 3D linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements, Int J Numer Methods Eng, 78, 3, 324-353, (2009) · Zbl 1183.74299 [52] He, Z. C.; Liu, G. R.; Zhong, Z. H.; Cui, X. Y.; Zhang, G. Y.; Cheng, A. G., A coupled edge-/face-based smoothed finite element method for structural-acoustic problems, Appl Acoust, 71, 955-964, (2010) [53] He, Z. C.; Liu, G. R.; Zhong, Z. H.; Zhang, G. Y.; Cheng, A. G., Coupled analysis of 3D structural-acoustic problems using the edge-based smoothed finite element method/finite element method, Finite Elem Anal Des, 46, 1114-1121, (2010) [54] He, Z. C.; Liu, G. R.; Zhong, Z. H.; Zhang, G. Y.; Cheng, A. G., A coupled ES-FEM/BEM method for fluid-structure interaction problems, Eng Anal Bound Elem, 35, 140-147, (2011) · Zbl 1259.74030 [55] Li, W.; Chai, Y. B.; Lei, M.; Liu, G. R., Analysis of coupled structural-acoustic problems based on the smoothed finite element method (S-FEM), Eng Anal Bound Elem, 42, 84-91, (2014) · Zbl 1297.74040 [56] Bletzinger, K. U.; Bischoff, M.; Ramm, E., A unified approach for shear-locking-free triangular and rectangular shell finite elements, Comput Struct, 75, 321-334, (2000) [57] Cook, R. D.; Malkus, D. S.; Plesha, M. E.; Witt, R. J., Concepts and applications of finite element analysis, (2002), John Wiley & Sons Inc. Hoboken
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