Differential cubature method for static solutions of arbitrarily shaped thick plates

International Journal of Solids and Structures

Volumn 35, Issue 28-29, 1998, Pages 3655-3674

  Liu, F L ^a   Liew, K M ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

BENDING MOMENTS; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; LINEAR EQUATIONS; SHEAR DEFORMATION;

DIFFERENTIAL CUBATURE METHOD; FIRST ORDER SHEAR DEFORMATION THEORY; LINEAR ALGEBRAIC EQUATIONS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0032184172     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(97)00215-1     Document Type: Article

References (23)

1. Bellman, R. E. and Casti, J. (1971) Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications 34, 235-238.
2. Bellman, R. E. and Casti, J. (1972) Differential quadrature : a technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics 10, 40-52.
3. Bert, C. W., Jang, S. K. and Striz, A. G. (1988) Two new approximate methods for analyzing free vibration of structural components. AIAA Journal 26, 612-618.
4. Bert, C. W., Jang, S. K. and Striz, A. G. (1989) Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature. Computational Mechanics 5, 217-226.
5. Butalia, T. S., Kant, T. and Dixit, V.D. (1990) Performance of heteosis element for bending of skew rhombic plates. Computers and Structures 34, 23-49.
6. Civan, F. and Sliepcevich, C. M. (1984) Differential quadrature for multidimensional problems. Journal of Mathematical Analysis and Applications 101, 423-443.
7. Civan, F. (1994) Solving multivariable mathematical models by the quadrature and cubature methods. Numerical Methods for Partial Differential Equations 10, 545-567.
8. Han, J.-B. and Liew, K. M. (1997) An eight-node curvilinear differential quadrature formulation for Reissner/ Mindlin plates. Computer Methods in Applied Mechanics and Engineering 141, 265-280.
9. Iyengar, K. F. S. R., Chadrashekhara, K. and Sebastian, V. K. (1974) On the analysis of thick rectangular plates. Ing. Arch. 43, 317-330.
10. Kobayashi, H. and Sonoda, K. (1989) Rectangular Mindlin plates on elastic foundations. International Journal of Mechanical Sciences 31, 679-692.
11. Kobayashi, H., Isshikawa, K. and Tuvey, G. J. (1995) On bending of rhombic plates. Journal of Structural Engineering. JSCE 41A, 41-48.
12. Liew, K. M., Han, J.-B., Xiao, Z. M. and Du, H. (1996) Differential quadrature method for Mindlin plates on Winkler foundations. International Journal of Mechanical Sciences 38, 405-421.
13. Liew, K. M. and Han, J.-B. (1997) A four-node differential quadrature method for straight-sided quadrilateral Reissner/Mindlin plates. Communications in Numerical Methods in Engineering 13, 73-81.
14. Liew, K. M. and Liu, F.-L. (1997) Differential cubature method : a solution technique for Kirchhoff plates of arbitrary shape. Computer Methods in Applied Mechanics and Engineering 145, 1-10.
15. Mindlin, R. D. (1951) Influence of rotatory inertia and shear in flexural motion of isotropic, elastic plates. Trans. ASME Journal of Applied Mechanics 18, 1031-1036.
16. Pandya, M. D. and Sherbourne, A. N. (1991) Buckling of anisotropic composite plates under stress gradient. ASCE Journal of Engineering Mechanics 117, 260-275.
17. Reissner, E. (1945) The effect of transverse shear deformation on the bending of elastic plate. Trans. ASME Journal of Applied Mechanics 12, 69-76.
18. Sengupta, D. (1995) Performance study of a simple finite element in the analysis of skew rhombic plates. Computers and Structures 54, 1173-1182.
19. Senthilnathan, N. R. (1989) A simple higher-order shear deformation plate theory. PhD. thesis, The National University of Singapore, Singapore.
20. Shu, C. and Chew, Y. T. (1994) Application of GDQ scheme to solve incompressible Navier-Stokes Equations in the curvilinear coordinate system. Int. Pacific Air and Space Technology Conf. Proceedings, Singapore, 205-211.
21. Srinivas, S., Rao, A. K. and Rao, C. V. (1969) Flexure of simply-supported thick homogeneous and laminated rectangular plates. ZAMM 49, 449-458.
22. Striz, A. G., Chen, W. L. and Bert, C. W. (1994) Static analysis of structures by the quadrature element method (QEM). International Journal of Solids and Structures 31, 2807-2818.
23. Timoshenko, S. P. and Woinowsky-Krieger, S. (1959) Theory of Plates and Shells. McGraw-Hill, New York.