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A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise deformation theory for dynamic response of composite plates resting on viscoelastic foundation. (English) Zbl 1296.74125
Summary: A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) based on the first-order shear deformation theory (FSDT) was recently proposed for static and dynamics analyses of Mindlin plates. In this paper, the CS-FEM-DSG3 is extended to the layerwise deformation theory for dynamic response of sandwich and laminated composite plates resting on viscoelastic foundation subjected to a moving mass. The plate-foundation system is modeled as a discretization of triangular plate elements supported by discrete springs and dashpots at the nodal points representing the viscoelastic foundation. The position of the moving mass with specified velocity on triangular elements at any time is defined, and then the moving mass is transformed into loads at nodes of elements. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of others available numerical results.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74A50 Structured surfaces and interfaces, coexistent phases
74K20 Plates
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[1] R.S. Ayre, L.S. Jacobson, C.S. Hsu, Transverse vibration of one and two-span beam under the action of a moving mass load, in: Proceedings of the First US National Congress of Applied Mechanics, 1951, pp. 81-90.
[2] Yoshida, D. M.; Weaver, W., Finite element analysis of beams and plates with moving loads, Int. Assoc. Bridge Struct. Engrg., 31, 179-195, (1971)
[3] Taheri, M. R.; Ting, E. C., Dynamic response of plates to moving loads: structural impedance method, Comput. Struct., 33, 1379-1393, (1989) · Zbl 0703.73088
[4] Taheri, M. R.; Ting, E. C., Dynamic response of plate to moving loads: finite element method, Comput. Struct., 34, 509-521, (1990) · Zbl 0721.73041
[5] Thompson, W. E., Analysis of dynamic behavior of roads subject to longitudinally moving loads, HRB, 39, 1-24, (1963)
[6] Gbadeyan, J. A.; Oni, S. T., Dynamic response to moving concentrated masses of elastic plates on a non-Winkler elastic foundation, J. Sound Vib., 154, 343-358, (1992) · Zbl 0920.73206
[7] Kim, S. M.; Roesset, J. M., Moving loads on a plate on elastic foundation, J. Engrg. Mech., 124, 1010-1017, (1998)
[8] Pan, G.; Okada, H.; Atluri, S. N., Elasto-plastic dynamic response of the pavement soil under aircraft takeoff and landing by a field-boundary element method, Bound. Elem. Methods Engrg., 14, 99-112, (1994)
[9] Zaman, M.; Taheri, M. R.; Alvappillai, A., Dynamic response of a thick plate on viscoelastic foundation to moving loads, Int. J. Numer. Anal. Meth. Geomech., 15, 627-647, (1991)
[10] Sun, L., Dynamic response of Kirchhoff plate on a viscoelastic foundation to harmonic circular loads, J. Appl. Mech., 70, 595-600, (2003) · Zbl 1110.74695
[11] Malekzadeh, K.; Khalili, S. M.R.; Abbaspour, P., Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses, Compos. Struct., 92, 1478-1484, (2010)
[12] Zenkour, A. M.; Allam, M. N.M.; Radwan, A. F., Bending of cross-ply laminated plates resting on elastic foundations under thermo-mechanical loading, Int. J. Mech. Mater. Des., (2013)
[13] Shen, H. S., Nonlinear analysis of composite laminated thin plates subjected to lateral pressure and thermal loading and resting on elastic foundations, Compos. Struct., 49, 115-128, (2000)
[14] Lal, A.; Singh, B. N.; Kumar, R., Nonlinear free vibration of laminated composite plates on elastic foundation with random system properties, Int. J. Mech. Sci., 50, 1203-1212, (2008) · Zbl 1264.74091
[15] Chien, R. D.; Chen, C. S., Nonlinear vibration of laminated plates on an elastic foundation, Thin-Walled Struct., 44, 852-860, (2006)
[16] Shen, H. S.; Wang, Z. X., Nonlinear vibration of hybrid laminated plates resting on elastic foundations in thermal environments, Appl. Math. Model., 36, 6275-6290, (2012) · Zbl 1349.74186
[17] Pirbodaghi, T.; Fesanghary, M.; Ahmadian, M. T., Non-linear vibration analysis of laminated composite plates resting on non-linear elastic foundations, J. Franklin Inst., 348, 353-368, (2011) · Zbl 1429.74054
[18] Chen, W. R.; Chen, C. S.; Yu, S. Y., Nonlinear vibration of hybrid composite plates on elastic foundations, Struct. Eng. Mech., 37, 367-383, (2011)
[19] Huang, X. L.; Zheng, J. J., Nonlinear vibration and dynamic response of simply supported shear deformable laminated plates on elastic foundations, Engrg. Struct., 25, 1107-1119, (2003)
[20] Lee, S. Y.; Yhim, S. S., Dynamic analysis of composite plates subjected to multi-moving loads based on a third order theory, Int. J. Solids Struct., 41, 4457-4472, (2004) · Zbl 1079.74548
[21] Vosoughi, A. R.; Malekadeh, P.; Razi, H., Response of moderately thick laminated composite plates on elastic foundation subjected to moving load, Compos. Struct., 97, 286-295, (2013)
[22] Ferreira, A. J.M., Analysis of composite plates using a layerwise theory and multiquadrics discretization, Mech. Adv. Mater. Struct., 12, 99-112, (2005)
[23] Ferreira, A. J.M.; Fasshauer, G. E.; Batra, R. C.; Rodrigues, J. D., Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter, Compos. Struct., 86, 328-343, (2008)
[24] G.R. Liu, Nguyen ThoiTrung, Smoothed Finite Element Methods, Taylor and Francis Group, New York, 2010.
[25] Liu, G. R.; Dai, K. Y.; Nguyen-Thoi, T., A smoothed finite element for mechanics problems, Comput. Mech., 39, 859-877, (2007) · Zbl 1169.74047
[26] Nguyen-Thoi, T.; Liu, G. R.; Dai, K. Y.; Lam, K. Y., Selective smoothed finite element method, Tsinghua Sci. Technol., 12, 5, 497-508, (2007)
[27] Liu, G. R.; Nguyen-Thoi, T.; Nguyen-Xuan, H.; Dai, K. Y.; Lam, K. Y., On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM), Int. J. Numer. Meth. Engrg., 77, 1863-1869, (2009) · Zbl 1181.74137
[28] Liu, G. R.; Nguyen-Thoi, T.; Nguyen-Xuan, 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)
[29] Nguyen-Thoi, T.; Liu, G. R.; Nguyen-Xuan, H.; Nguyen-Tran, C., Adaptive analysis using the node-based smoothed finite element method (NS-FEM), Commun. Numer. Methods Engrg., 27, 2, 198-218, (2011) · Zbl 1370.74144
[30] Nguyen-Thoi, T.; Liu, G. R.; Nguyen-Xuan, H., Additional properties of the node-based smoothed finite element method (NS-FEM) for solid mechanics problems, Int. J. Comput. Methods, 6, 4, 633-666, (2009) · Zbl 1267.74115
[31] Liu, G. R.; Nguyen-Thoi, T.; Lam, K. Y., An edge-based smoothed finite element method (ES-FEM) for static and dynamic problems of solid mechanics, J. Sound Vib., 320, 1100-1130, (2009)
[32] Nguyen-Thoi, T.; Liu, G. R.; Nguyen-Xuan, H., An n-sided polygonal edge-based smoothed finite element method (nES-FEM) for solid mechanics, Commun. Numer. Methods Engrg., 27, 9, 1446-1472, (2011) · Zbl 1248.74043
[33] Nguyen-Thoi, T.; Liu, G. R.; Lam, K. Y.; Zhang, G. Y., A face-based smoothed finite element method (FS-FEM) for 3D linear and nonlinear solid mechanics problems using 4-node tetrahedral elements, Int. J. Numer. Meth. Engrg., 78, 324-353, (2009) · Zbl 1183.74299
[34] Liu, G. R.; Nguyen-Thoi, T.; Lam, K. Y., A novel alpha finite element method (FEM) for exact solution to mechanics problems using triangular and tetrahedral elements, Comput. Methods Appl. Mech. Engrg., 197, 3883-3897, (2008) · Zbl 1194.74433
[35] Liu, G. R.; Nguyen-Thoi, T.; Lam, K. Y., A novel FEM by scaling the gradient of strains with factor (FEM), Comput. Mech., 43, 369-391, (2009) · Zbl 1162.74469
[36] Liu, G. R.; Nguyen-Xuan, H.; Nguyen-Thoi, T.; Xu, X., A novel Galerkin-like weakform and a superconvergent alpha finite element method (SFEM) for mechanics problems using triangular meshes, J. Comput. Phys., 228, 4055-4087, (2009) · Zbl 1273.74542
[37] Liu, G. R.; Nguyen-Xuan, H.; Nguyen-Thoi, T., A variationally consistent FEM (VCFEM) for solid mechanics problems, Int. J. Numer. Meth. Engrg., 85, 461-497, (2011) · Zbl 1217.74126
[38] Liu, G. R.; Nguyen-Thoi, T.; Dai, K. Y.; Lam, K. Y., Theoretical aspects of the smoothed finite element method (SFEM), Int. J. Numer. Meth. Engrg., 71, 902-930, (2007) · Zbl 1194.74432
[39] Liu, G. R.; Nguyen-Xuan, H.; Nguyen-Thoi, T., A theoretical study on NS/ES-FEM: properties, accuracy and convergence rates, Int. J. Numer. Meth. Engrg., 84, 1222-1256, (2010) · Zbl 1202.74180
[40] Nguyen-Xuan, H.; Liu, G. R.; Thai-Hoang, C.; Nguyen-Thoi, T., An edge-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates, Comput. Methods Appl. Mech. Engrg., 199, 471-489, (2009) · Zbl 1227.74083
[41] Phung-Van, P.; Nguyen-Thoi, T.; Luong-Van, H.; Lieu-Xuan, Q., Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C0-HSDT, Comput. Methods Appl. Mech. Engrg., (2013) · Zbl 1296.74124
[42] Nguyen-Xuan, H.; Rabczuk, T.; Nguyen-Thanh, N.; Nguyen-Thoi, T.; Bordas, S., A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates, Comput. Mech., 46, 5, 679-701, (2010) · Zbl 1260.74029
[43] Nguyen-Xuan, H.; Tran-Vinh, L.; Nguyen-Thoi, T.; Vu-Do, H. C., Analysis of functionally graded plates using an edge-based smoothed finite element method, Compos. Struct., 93, 11, 3019-3039, (2011)
[44] Thai-Hoang, C.; Tran-Vinh, Loc; Than-Trung, D.; Nguyen-Thoi, T.; Nguyen-Thoi, H., Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method, Appl. Math. Model., 36, 5657-5677, (2012) · Zbl 1254.74079
[45] Phan-Dao, H. H.; Nguyen-Xuan, H.; Thai-Hoang, C.; Nguyen-Thoi, T.; Rabczuk, T., An edge-based smoothed finite element method for analysis of laminated composite plates, Int. J. Comput. Methods, 10, 1, 1340005, (2013) · Zbl 1359.74434
[46] T. Nguyen-Thoi, T. Bui-Xuan, P. Phung-Van, S. Nguyen-Hoang, H. Nguyen-Xuan, An edge-based smoothed three-node Mindlin plate element (ES-MIN3) for static and free vibration analyses of plates, KSCE J. Civil Engrg. (2013), in press. · Zbl 1294.74064
[47] Phung-Van, P.; Nguyen-Thoi, T.; Loc Tran, V.; Nguyen-Xuan, H., A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) based on the C0-type higher-order shear deformation theory for static and free vibration analyses of functionally graded plates, Comput. Mater. Sci., 79, 857-872, (2013)
[48] Nguyen-Thoi, T.; Phung-Van, P.; Luong-Van, H.; Nguyen-Van, H.; Nguyen-Xuan, H., A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates, Comput. Mech., 50, 1, 65-81, (2013) · Zbl 1294.74064
[49] Nguyen-Xuan, H.; Rabczuk, T.; Bordas, S.; Debongnie, J. F., A smoothed finite element method for plate analysis, Comput. Methods Appl. Mech. Engrg., 197, 13-16, 1184-1203, (2008) · Zbl 1159.74434
[50] Wu, C. T.; Wang, H. P., An enhanced cell-based smoothed finite element method for the analysis of Reissner-Mindlin plate bending problems involving distorted mesh, Int. J. Numer. Meth. Engrg., 95, 288-312, (2013) · Zbl 1352.74452
[51] Luong-Van, H.; Nguyen-Thoi, T.; Liu, G. R.; Phung-Van, P., A cell-based smoothed finite element method using three-node shear-locking free Mindlin plate element (CS-FEM-MIN3) for dynamic response of laminated composite plates on viscoelastic foundation, Engrg. Anal. Bound. Elem., (2013) · Zbl 1297.74122
[52] Nguyen-Thoi, T.; Bui-Xuan, T.; Phung-Van, P.; Nguyen-Xuan, H.; Ngo-Thanh, P., Static, free vibration and buckling analyses of stiffened plates by CS-FEM-DSG3 using triangular elements, Comput. Struct., 125, 100-113, (2013)
[53] H. Nguyen-Xuan, V. Loc Tran, H. Chien Thai, T. Nguyen-Thoi, Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing, Thin-Walled Struct. 54 (2012) 1-18.
[54] Nguyen-Thoi, T.; Phung-Van, P.; Thai-Hoang, C.; Nguyen-Xuan, H., A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using triangular elements for static and free vibration analyses of shell structures, Int. J. Mech. Sci., 74, 32-45, (2013)
[55] Nguyen-Xuan, H.; Liu, G. R.; Nguyen-Thoi, T.; Nguyen-Tran, C., An edge-based smoothed finite element method (ES-FEM) for analysis of two-dimensional piezoelectric structures, Smart Mater. Struct., 18, 1-12, (2009)
[56] Phung-Van, P.; Nguyen-Thoi, T.; Le-Dinh, T.; Nguyen-Xuan, H., Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3), Smart Mater. Struct., 22, 095026, (2013)
[57] Liu, G. R.; Chen, L.; Nguyen-Thoi, T.; Zeng, K.; Zhang, G. Y., A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of cracks, Int. J. Numer. Methods Engrg., 83, 11, 1466-1497, (2010) · Zbl 1202.74179
[58] Nguyen-Thoi, T.; Liu, G. R.; Vu-Do, H. C.; Nguyen-Xuan, H., An edge-based smoothed finite element method (ES-FEM) for visco-elastoplastic analyses of 2D solids using triangular mesh, Comput. Mech., 45, 23-44, (2009) · Zbl 1398.74382
[59] Nguyen-Thoi, T.; Vu-Do, H. C.; Rabczuk, T.; Nguyen-Xuan, H., A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes, Comput. Methods Appl. Mech. Engrg., 199, 3005-3027, (2010) · Zbl 1231.74432
[60] Nguyen-Thoi, T.; Liu, G. R.; Vu-Do, H. C.; Nguyen-Xuan, H., A face-based smoothed finite element method (FS-FEM) for visco-elastoplastic analyses of 3D solids using tetrahedral mesh, Comput. Methods Appl. Mech. Engrg., 198, 3479-3498, (2009) · Zbl 1230.74193
[61] Tran, T. N.; Liu, G. R.; Nguyen-Xuan, H.; Nguyen-Thoi, T., An edge-based smoothed finite element method for primal-dual shakedown analysis of structures, Int. J. Numer. Methods Engrg., 82, 7, 917-938, (2010) · Zbl 1188.74073
[62] Nguyen-Xuan, H.; Rabczuk, T.; Nguyen-Thoi, T.; Tran, T. N.; Nguyen-Thanh, N., Computation of limit and shakedown loads using a node-based smoothed finite element method, Int. J. Numer. Methods Engrg., 90, 3, 287-310, (2012) · Zbl 1242.74142
[63] Nguyen-Thoi, T.; Phung-Van, P.; Rabczuk, T.; Nguyen-Xuan, H.; Le-Van, C., Free and forced vibration analysis using the n-sided polygonal cell-based smoothed finite element method (nCS-FEM), Int. J. Comput. Methods, 10, 1, 1340008, (2013) · Zbl 1359.74433
[64] Nguyen-Thoi, T.; Phung-Van, P.; Rabczuk, T.; Nguyen-Xuan, H.; Le-Van, C., An application of the ES-FEM in solid domain for dynamic analysis of 2D fluid-solid interaction problems, Int. J. Comput. Methods, 10, 1, 1340003, (2013) · Zbl 1359.74432
[65] Nguyen-Thoi, T.; Phung-Van, P.; Nguyen-Xuan, H.; Thai-Hoang, C., A cell-based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner-Mindlin plates, Int. J. Numer. Meth. Engrg., 91, 7, 705-741, (2012) · Zbl 1253.74111
[66] 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)
[67] Zhuang, X. Y.; Huang, R. Q.; Zhu, H. H.; Askes, H.; Mathisen, K., A new and simple locking-free triangular thick plate element using independent shear degrees of freedom, Finite Elem. Anal. Des., 75, 1-7, (2013) · Zbl 1368.74038
[68] Nguyen-Thanh, N.; Kiendl, J.; Nguyen-Xuan, H.; Wüchner, R.; Bletzinger, K. U.; Bazilevs, Y.; Rabczuk, T., Rotation free isogeometric thin shell analysis using PHT-splines, Comput. Methods Appl. Mech. Engrg., 200, 47-48, 3410-3424, (2011) · Zbl 1230.74230
[69] Areias, P.; Rabczuk, T.; Dias-da-Costa, D., Assumed-metric spherically interpolated quadrilateral shell element, Finite Elem. Anal. Des., 66, 53-67, (2013) · Zbl 1282.74057
[70] Rabczuk, T.; Areias, P. M.A., A meshfree thin shell for arbitrary evolving cracks based on an external enrichment, CMES-Comput. Model. Engrg. Sci., 16, 2, 115-130, (2006)
[71] Rabczuk, T.; Areias, P. M.A.; Belytschko, T., A meshfree thin shell method for nonlinear dynamic fracture, Int. J. Numer. Methods Engrg., 72, 5, 524-548, (2007) · Zbl 1194.74537
[72] Chau-Dinh, T.; Zi, G.; Lee, P. S.; Song, J. H.; Rabczuk, T., Phantom-node method for shell models with arbitrary cracks, Comput. Struct., 92-93, 242-256, (2012)
[73] Natarajan, S.; Chakraborty, S.; Thangavel, M.; Bordas, S.; Rabczuk, T., Size-dependent free flexural vibration behavior of functionally graded nanoplates, Comput. Mater. Sci., 65, 74-80, (2012)
[74] Reddy, J. N., Mechanics of laminated composite plates - theory and analysis, (1997), CRC Press New York · Zbl 0899.73002
[75] Lyly, M.; Stenberg, R.; Vihinen, T., A stable bilinear element for the Reissner-Mindlin plate model, Comput. Methods Appl. Mech. Engrg., 110, 343-357, (1993) · Zbl 0846.73065
[76] Bischoff, M.; Bletzinger, K. U., Improving stability and accuracy of Reissner-Mindlin plate finite elements via algebraic subgrid scale stabilization, Comput. Methods Appl. Mech. Engrg., 193, 1517-1528, (2004) · Zbl 1079.74633
[77] Reddy, J. N., A simply higher-order theory for laminated composite plates, J. Appl. Mech., 51, 745-752, (1984) · Zbl 0549.73062
[78] Newmark, N. M., A method of computation for structural dynamics, J. Engrg. Mech. Div. ASCE, 85, 67-94, (1959)
[79] Ferreira, A. J.M.; Luís, M. S.C.; Silvia, B., A high order collocation method for the static and vibration analysis of composite plates using a first-order theory, Compos. Struct., 89, 3, 424-432, (2009)
[80] Ferreira, A. J.M.; Roque, C. M.C.; Martins, P. A.L. S., Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method, Compos. B: Engrg., 34, 627-636, (2003)
[81] Akhras, G.; Cheung, M. S.; Li, W., Finite strip analysis for anisotropic laminated composite plates using higher-order deflection theory, Comput. Struct., 52, 3, 471-477, (1994) · Zbl 0872.73074
[82] G. Akhras, M.S. Cheung, W. Li, Static and vibration analysis of anitropic laminated plates by finite strip method, Int. J. Solids Struct. 30 (22) (1993) 3129-3137. · Zbl 0790.73078
[83] Pagano, N. J., Exact solutions for rectangular bidirectional composites and sandwich plates, J. Compos. Mater., 4, 20-34, (1970)
[84] Srinivas, S., A refined analysis of composite laminates, J. Sounds Vib., 30, 495-507, (1973) · Zbl 0267.73050
[85] Pandya, B. N.; Kant, T., Higher-order shear deformable theories for flexure of sandwich plates - finite element evaluations, Int. J. Solids Struct., 24, 419-451, (1988) · Zbl 0676.73044
[86] Ferreira, A. J.M.; Barbosa, J. T., Buckling behaviour of composites and sandwich plates, J. Compos. Mater., 4, 20-34, (1970)
[87] Srinivas, S.; Rao, C. V.J.; Rao, A. K., An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates, J. Sound Vib., 12, 2, 187-199, (1970) · Zbl 0212.57801
[88] A. Noiser, R.P. Kapania, J.N. Reddy, Free vibration analysis of laminated plates using a layerwise theory, AIAA J. 31 (2) (1993) 2335-2346. · Zbl 0793.73052
[89] S. Wang, Y. Zhang, Vibration analysis of rectangular composite laminated plates using layerwise B-spline finite strip method, Compos. Struct. 68 (3) (2005) 349-358.
[90] Zhen, W.; Wanji, C., Free vibration of laminated composite and sandwich plates using global-local higher-order theory, J. Sound Vib., 298, 333-349, (2006)
[91] Liew, K. M., Solving the vibration of thick symmetric laminates by Reissner/Mindlin plate theory and the p-titz method, J. Sound Vib., 198, 343-360, (1996)
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