DSC analysis for buckling and vibration of rectangular plates with elastically restrained edges and linearly varying in-plane loading

International Journal of Structural Stability and Dynamics

Volumn 9, Issue 3, 2009, Pages 511-531

  Lai, S K ^a   Xiang, Y ^a  

^a UNIVERSITY OF WESTERN SYDNEY   (Australia)

Author keywords

Buckling; DSC method; Elastic rotational restraint; Thin plate; Vibration

Indexed keywords

COMPARISON STUDY; DISCRETE SINGULAR CONVOLUTION; DSC METHOD; ELASTIC ROTATIONAL RESTRAINT; ELASTICALLY RESTRAINED EDGES; INPLANE LOADING; NUMERICAL STABILITIES; OPPOSITE EDGES; PLATE EDGES; RECTANGULAR PLATES; ROTATIONAL SPRING; THIN PLATE; VIBRATION; VIBRATION PROBLEM;

BUCKLING; CONVERGENCE OF NUMERICAL METHODS; SANDWICH STRUCTURES; STRUCTURAL ANALYSIS;

PLATES (STRUCTURAL COMPONENTS);

EID: 68449092209     PISSN: 02194554     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219455409003119     Document Type: Article

References (54)

1. A. W. Leissa and J. H. Kang, Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses, Int. J. Mech. Sci. 44 (2002) 1925-1945.
2. C. W. Bert and K. K. Devarakonda, Buckling of rectangular plates subjected to non-linearly distributed in-plane loading, Int. J. Solids Struct. 40 (2003) 4097-4106.
3. J. H. Kang and H. J. Shim, Exact solutions for the free vibrations of rectangular plates having in-plane moments acting on two opposite simply supported edges, J. Sound Vib. 273 (2004) 933-948.
4. J. H. Kang and A. W. Leissa, Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges, Int. J. Solids Struct. 42 (2005) 4220-4238.
5. K. K. V. Devarakonda and C. W. Bert, Flexural vibration of rectangular plates subjected to sinusoidally distributed compressive loading on two opposite sides, J. Sound Vib. 283 (2005) 749-763.
6. S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability (McGraw-Hill, New York, 1961).
7. A. W. Leissa, Vibration of Plates (US Government Printing Office, Washington, D.C., 1969).
8. A. W. Leissa, Vibration of Shells (US Government Printing Office, Washington, D.C., 1973).
9. J. N. Reddy, An Introduction to the Finite Element Method (McGraw-Hill, New York, 1984).
10. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method (McGraw-Hill, London, 1989).
11. M. S. Cheung, Finite Strip Analysis of Structures, PhD Thesis, University of Calgary (1971).
12. Y. K. Cheung, Finite Strip Method in Structural Analysis (Pergamon Press, Oxford, 1976).
13. K. M. Liew and C. M. Wang, pb-2 Rayleigh-Ritz method for general plate analysis, Eng. Struct. 15 (1993) 55-60.
14. K. M. Liew, C. M. Wang, Y. Xiang and S. Kitipornchai, Vibration of Mindlin Plates, Programming the p-Version Ritz Method (Elsevier, Amsterdam, 1998).
15. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming and P. Krysl, Meshless methods: an overview and recent developments, Comput. Meth. Appl. Mech. Eng. 139 (1996) 3-47.
16. B. M. Donning and W. K. Liu, Meshless methods for shear-deformable beams and plates, Comput. Meth. Appl. Mech. Eng. 152 (1998) 47-71.
17. R. Bellman, B. G. Kashef and J. Casti, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, J. Comput. Phys. 10 (1972) 40-52.
18. X. Wang, C. W. Bert and A. G. Striz, Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates, Comput. Struct. 48 (1993) 473-479.
19. C. Shu, Differential Quadrature and Its Application in Engineering (Springer, London, 2000).
20. X. Wang, L. Gan and Y. Wang, A differential quadrature analysis of vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses, J. Sound Vib. 298 (2006) 420-431.
21. G. W. Wei, Discrete singular convolution for the solution of the Fokker-Planck equation, J. Chem. Phys. 110 (1999) 8930-8942.
22. G. W. Wei, A unified approach for the solution of the Fokker-Planck equation, J. Phys. A-Math. Gen. 33 (2000) 4935-4953.
23. D. S. Zhang, G. W. Wei, D. J. Kouri and D. K. Hoffman, Lagrange distributed approximating functional method for the solution of the Schrödinger equation, Chem. Phys. Lett. 284 (1998) 56-62.
24. G. W. Wei, A unified method for solving Maxwell's equation, in Proceedings of 1999 Asia-Pacific Microwave Conference Singapore (1999), pp. 562-565.
25. G. W. Wei, Discrete singular convolution for the sine-Gordon equation, Physica D 137 (2000) 247-259.
26. G. W. Wei, Discrete singular convolution for beam analysis, Eng. Struct. 23 (2001) 1045-1053.
27. G. W. Wei, Vibration analysis by discrete singular convolution, J. Sound Vib. 244 (2001) 535-553.
28. G. W. Wei, A new algorithm for solving some mechanical problems, Comput. Meth. Appl. Mech. Eng. 190 (2001) 2017-2030.
29. G. W. Wei, Y. B. Zhao and Y. Xiang, The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution, Int. J. Mech. Sci. 43 (2001) 1731-1746.
30. Y. B. Zhao and G. W. Wei, DSC analysis of rectangular plates with non-uniform boundary conditions, J. Sound Vib. 255 (2002) 203-228.
31. G. W. Wei, Y. B. Zhao and Y. Xiang, Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm, Int. J. Numer. Methods Eng. 55 (2002) 913-946.
32. Y. Xiang, Y. B. Zhao and G. W. Wei, Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications, Int. J. Numer. Methods Eng. 55 (2002) 947-971.
33. Y. B. Zhao, G. W. Wei and Y. Xiang, Plate vibration under irregular internal supports, Int. J. Solids Struct. 39 (2002) 1361-1383.
34. Y. B. Zhao, G. W. Wei and Y. Xiang, Discrete singular convolution for the prediction of high frequency vibration of plates, Int. J. Solids Struct. 39 (2002) 65-88.
35. G. W. Wei, Y. B. Zhao and Y. Xiang, A novel approach for the analysis of high-frequency vibrations, J. Sound Vib. 257 (2002) 207-246.
36. C. H. W. Ng, Y. B. Zhao and G. W. Wei, Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates, Comput. Meth. Appl. Mech. Eng. 193 (2004) 2483-2506.
37. C. W. Lim, Z. R. Li and G. W. Wei, DSC-Ritz method for high-mode frequency analysis of thick shallow shells, Int. J. Numer. Methods Eng. 62 (2005) 205-232.
38. Y. Hou, G. W. Wei and Y. Xiang, DSC-Ritz method for the free vibration analysis of Mindlin plates, Int. J. Numer. Methods Eng. 62 (2005) 262-288.
39. C. W. Lim, Z. R. Li, Y. Xiang, G. W. Wei and C. M. Wang, On the missing modes when using the exact frequency relationship between Kirchhoff and Mindlin plates, Advances in Vibration Engineering 4 (2005) 221-248.
40. S. Zhao, G. W. Wei and Y. Xiang, DSC analysis of free-edged beams by an iteratively matched boundary method, J. Sound Vib. 284 (2005) 487-493.
41. Ö. Civalek, Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: Discrete singular convolution (DSC) approach, J. Comput. Appl. Math. 205 (2007) 251-271.
42. Ö. Civalek, An effcient method for free vibration analysis of rotating truncated conical shells, Int. J. Pressure Vessels Pip. 83 (2006) 1 - 12.
43. Ö. Civalek, A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution, Thin-Walled Struct. 45 (2007) 692-698.
44. Ö. Civalek, Free vibration and buckling analyses of composite plates with straight-sided quadrilateral domain based on DSC approach, Finite Elem. Anal. Des. 43 (2007) 1013-1022.
45. A. Seçgin and A. Saide Sarigül, Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: Algorithm and verification, J. Sound Vib. 315 (2008) 197-211.
46. C. M. Wang, K. M. Liew and W. A. M. Alwis, Buckling of skew plates and corner condition for simply supported edges, J. Eng. Mech. ASCE 118 (1992) 651-662.
47. P. A. A. Laura, R. O. Grossi and G. I. Carneiro, Transverse vibrations of rectangular plates with thickness varying in two directions and with edges elastically restrained against rotation, J. Sound Vib. 63 (1979) 499-505.
48. P. A. A. Laura and R. H. Gutiérrez, A note on transverse vibrations of stiffened rectangular plates with edges elastically restrained against rotation, J. Sound Vib. 78 (1981) 139-144.
49. T. Mizusawa and T. Kajita, Vibration and buckling of skew plates with edges elastically restrained against rotation, Comput. Struct. 22 (1986) 987-994.
50. R. O. Grossi and R. B. Bhat, Natural frequencies of edge restrained tapered rectangular plates, J. Sound Vib. 185 (1995) 335-343.
51. K. M. Liew, Y. Xiang and S. Kitipornchai, Vibration of laminated plates having elastic edge flexibilities, J. Eng. Mech. ASCE 123 (1997) 1012-1019.
52. F. Bleich, Buckling Strength of Metal Structures (McGraw-Hill, New York, 1952).
53. M. Mukhopadhyay, Buckling analysis of rectangular ship plating, International Shipbuilding Progress 26 (1979) 89-91.
54. M. Mukhopadhyay, Vibration and buckling of rectangular plates with varying degrees of rotational restraint along the edges, Comput. Struct. 32 (1989) 341-346.