Citation: | S.A.Eftekhari, A.A.Jafari. Mixed FE-DQM for Free and Forced Vibration, and Buckling Analysis of Rectangular Plates[J]. Applied Mathematics and Mechanics, 2012, 33(1): 76-93. doi: 10.3879/j.issn.1000-0887.2012.01.007 |
[1] |
Leissa A W. The free vibration of rectangular plates[J]. Journal of Sound and Vibration, 1973, 31(3): 257-293.
|
[2] |
Young D. Vibration of rectangular plates by the Ritz method[J]. American Society of Mechanical Engineers, Journal of Applied Mechanics, 1950, 17: 448-453.
|
[3] |
Bassily S F, Dickinson S M. On the use of beam functions for problems of plates involving free edges[J]. American Society of Mechanical Engineers, Journal of Applied Mechanics, 1975, 42(4): 858-864.
|
[4] |
Bhat R B. Natural frequencies of rectangular plates using characteristic orthogonal polynomials in the Rayleigh-Ritz method[J]. Journal of Sound and Vibration, 1985, 102(4): 493-499.
|
[5] |
Liew K M, Lam K Y. A set of orthogonal plate functions for flexural vibration analysis of regular polygonal plates[J]. American Society of Mechanical Engineers, Journal of Vibration and Acoustic, 1991, 113(2): 182-186.
|
[6] |
Fan S C, Cheung Y K. Flexural free vibrations of rectangular plates with complex support conditions[J]. Journal of Sound and Vibration, 1984, 93(1): 81-94.
|
[7] |
Leipholz H H E. On some developments in direct methods of the calculus of variations[J]. American Society of Mechanical Engineers, Applied Mechanics Reviews, 1987, 40(10): 1379-1392.
|
[8] |
Zitnan P. Vibration analysis of membranes and plates by a discrete least squares technique[J]. Journal of Sound and Vibration, 1996, 195(4): 595-605.
|
[9] |
Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering, 1994, 37(2): 229-256.
|
[10] |
Bert C W, Kang S K, Striz A G. Two new approximate methods for analyzing free vibration of structural components[J]. American Institute of Aeronautics and Astronautics Journal, 1988, 26: 612-618.
|
[11] |
Bert C W, Wang X, Striz A G. Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates[J]. Computers & Structures, 1993, 48(3): 473-479.
|
[12] |
Du H, Liew K M, Lim M K. Generalized differential quadrature method for buckling analysis[J]. American Society of Civil Engineers, Journal of Engineering Mechanics, 1996, 122(2): 95-100.
|
[13] |
TANG Yu-hua, WANG Xin-wei. Buckling of symmetrically laminated rectangular plates under parabolic edge compression[J]. International Journal of Mechanical Sciences, 2011, 53(2): 91-97.
|
[14] |
Sakata T, Takahashi K, Bhat R B. Natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation[J]. Journal of Sound and Vibration, 1996, 189(1): 89-101.
|
[15] |
Alipour M M, Shariyat M, Shaban M. A semi-analytical solution for free vibration and modal stress analyses of circular plates resting on two-parameter elastic foundations[J]. Journal of Solid Mechanics, 2010, 2(1): 63-78.
|
[16] |
Wei G W, Zhao Y B, Xiang Y. The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution[J]. International Journal of Mechanical Sciences, 2001, 43(8): 1731-1746.
|
[17] |
Ng C H W, Zhao Y B, Wei G W. Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(23/26): 2483-2506.
|
[18] |
Reddy J N. An Introduction to the Finite Element Method[M]. 2nd ed.New York: McGraw-Hill, 1993.
|
[19] |
Zienkiewicz O C, Taylor R L. The Finite Element Method[M]. 5th ed. New York: McGraw-Hill, 2000.
|
[20] |
Bellman R, Casti J. Differential quadrature and long term integration[J]. Journal of Mathematical Analysis and Applications, 1971, 34: 235-238.
|
[21] |
Bert C W, Malik M. Differential quadrature method in computational mechanics: a review[J]. American Society of Mechanical Engineers, Applied Mechanics Reviews, 1996, 49(1): 1-28.
|
[22] |
Shu C. Differential Quadrature and Its Application in Engineering[M]. New York: Springer Publication, 2000.
|
[23] |
Tanaka M, Chen W. Coupling dual reciprocity BEM and differential quadrature method for time-dependent diffusion problems[J]. Applied Mathematical Modeling, 2001, 25(3): 257-268.
|
[24] |
Fung T C. Stability and accuracy of differential quadrature method in solving dynamic problems[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(13/14):1311-1331.
|
[25] |
Shu C, Yao K S. Block-marching in time with DQ discretization: an efficient method for time-dependent problems[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(41/42): 4587-4597.
|
[26] |
Eftekhari S A, Farid M, Khani M. Dynamic analysis of laminated composite coated beams carrying multiple accelerating oscillators using a coupled finite element-differential quadrature method[J]. American Society of Mechanical Engineers, Journal of Applied Mechanics, 2009, 76(6), 061001:1-13.
|
[27] |
Eftekhari S A, Khani M. A coupled finite element-differential quadrature element method and its accuracy for moving load problem[J]. Applied Mathematical Modeling, 2010, 34(1): 228-237.
|
[28] |
Khalili S M R, Jafari A A, Eftekhari S A. A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads[J]. Composite Structures, 2010, 92(10): 2497-2511.
|
[29] |
Jafari A A, Eftekhari S A. A new mixed finite element-differential quadrature formulation for forced vibration of beams carrying moving loads[J]. American Society of Mechanical Engineers, Journal of Applied Mechanics, 2011, 78(1), 011020:1-16.
|
[30] |
Malik M, Bert C W. Implementing multiple boundary conditions in the DQ solution of higher-order PDE’s: application to free vibration of plates[J]. International Journal for Numerical Methods in Engineering, 1996, 39(7): 1237-1258.
|
[31] |
Shu C, Du H. A generalized approach for implementing general boundary conditions in the GDQ free vibration analyses of plates[J]. International Journal of Solids and Structures, 1997, 34(7): 837-846.
|
[32] |
Bert C W, Malik M. Semianalytical differential quadrature solution for free vibration analysis of rectangular plates[J]. American Institute of Aeronautics and Astronautics Journal, 1996, 34(3): 601-666.
|
[33] |
Bert C W, Malik M. Free vibration analysis of tapered rectangular plates by differential quadrature method: a semi-analytical approach[J]. Journal of Sound and Vibration, 1996, 190(1): 41-63.
|
[34] |
Malekzadeh P, Karami G, Farid M. A semi-analytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(45/47): 4781-4796.
|
[35] |
Yang J, Shen H S. Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions[J]. Composites: Part B, 2003, 34(2): 103-115.
|
[36] |
Malekzadeh P, Karami G. A mixed differential quadrature and finite element free vibration and buckling analysis of thick beams on two-parameter elastic foundations[J]. Applied Mathematical Modeling , 2008, 32(7): 1381-1394.
|
[37] |
Bathe K J, Wilson E L. Numerical Methods in Finite Element Analysis[M]. NJ: Prentic-Hall, Englewood Cliffs, 1976.
|
[38] |
Wang X, Gan L, Wang Y. A differential quadrature analysis of vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses[J]. Journal of Sound and Vibration, 2006, 298(1/2): 420-431.
|
[39] |
Timoshenko S P, Gere J M. Theory of Elastic Stability[M]. 2nd ed. New York: McGraw-Hill, 1963.
|
[40] |
Leissa A W, Kang J H. Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses[J]. International Journal of Mechanical Sciences, 2002, 44(9): 1925-1945.
|