Numerical differential quadrature method for Reissner/Mindlin plates on two-parameter foundations

International Journal of Mechanical Sciences

Volumn 39, Issue 9, 1997, Pages 977-989

  Han, J B ^a   Liew, K M ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Bending; Differential quadrature method; Mindlin plates; Rectangular plates; Two parameter foundations

Indexed keywords

APPROXIMATION THEORY; BENDING (DEFORMATION); BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; DEFLECTION (STRUCTURES); DIFFERENTIAL EQUATIONS; FOUNDATIONS; LINEAR ALGEBRA; MATHEMATICAL TRANSFORMATIONS; SHEAR STRESS; STRUCTURAL ANALYSIS;

NUMERICAL DIFFERENTIAL QUADRATURE METHOD; REISSNER/MINDLIN PLATES; TWO PARAMETER FOUNDATIONS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0031237844     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-7403(97)00001-5     Document Type: Article

References (26)

1. Selvadurai, A. P. S., Elastic Analysis of Soil-Foundation Interaction. Elsevier, New York, 1979.
2. Kerr, A. D., Elastic and viscoelastic foundation models. ASME J. Appl. Mech., 1964, 31, 491-498.
3. Yang, T. Y., A finite element analysis on a two-parameter foundation model. Computers Struct., 1972, 2, 593-614.
4. Balas, J., Sladek, V. and Sladek, J., The boundary integral equation method for plates resting on a two-parameter foundation. ZAMM, 1984, 64, 137-146.
5. Katsikadelis, J. T. and Kallivokas, L. F., Clamped plates on Pasternak-type elastic foundation by the boundary element method. ASME J. Appl. Mech., 1986, 29, 1233-1239.
6. Puttonen, J. and Varpasuo, P., Boundary element analysis of plates on elastic foundations. Int. J. Numer. Meth. Engng, 1986, 23, 287-303.
7. Wang, J. G., Wang, X. X. and Huang, M. K., Fundamental solutions and boundary integral equations for Reissner's plates on two parameter foundations. Int. J. Solids Struct., 1992, 29, 1233-1239.
8. Fadhil, S. and El-Zafrany, A., Boundary element analysis of thick Reissner plates on two-parameter foundation. Int. J. Solids Struct., 1994, 21, 2901-2917.
9. Reissner, E., The effect of transverse shear deformation on the bending of elastic plates. ASME J. Appl Mech., 1945, 12, 69-77.
10. Mindlin, R. D., Influence of rotatory inertia and shear on flexural motion of isotropic, elastic plates. ASME J. Appl. Mech., 1951, 18, 31-38.
11. Bellman, R. E. and Casti, J., Differential quadrature and long term integration. J. Math. Anal. Appl., 1971, 34, 235-238.
12. Bellman, R. E., Kashef, B. G. and Casti, J., Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J. Computational Phys., 1972, 10, 40-52.
13. Bellman, R. E., Methods of Nonlinear Analysis, Vol. 2. Academic Press, New York, 1973, Chapter 16.
14. Civan, F. and Sliepcevich, C. M., Differential quadrature for multidimensional problems J. Math. Anal Appl., 1984, 101, 423-443.
15. Quan, J. R. and Chang, C. T., New insights in solving distributed system equations by the quadrature method - I. Analysis. Computers Chem. Engng, 1989, 13, 779-788.
16. Shu, C. and Richards, B. E., Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids, 1992, 15, 791-798.
17. Bert, C. W., Jang, S. K. and Striz, A. G., Two new approximate methods for analyzing free vibration of structural components. AIAA J., 1988, 26, 612-618.
18. Sherbourne, A. N. and Pandey, M. D., Differential quadrature method in the buckling analysis of beams and composite plates. Computers Struct., 1991, 40, 903-913.
19. Kukreti, A. R., Farsa, J. and Bert, C. W., Fundamental frequency of tapered plates by differential quadrature. ASCE J. Engng Mech., 1992, 118, 1221-1237.
20. Gutierrez, R. H., Laura, P. A. A. and Rossi, R. E., The method of differential quadrature and its application to the approximate solution of ocean engineering problems. Ocean Engng, 1994, 21, 57-66.
21. Liew, K. M., Han, J.-B., Xiao, Z. M. and Du, H., Differential quadrature method for Mindlin plates on Winkler foundations. Int. J. Mech. Sci., 1996, 38, 405-421.
22. Liew, K. M., Han, J.-B. and Xiao, Z. M., Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility. Int. J. Solids Struct., 1996, 33, 2647-2658.
23. Liew, K. M. and Han, J.-B., Bending analysis of simply supported shear deformable skew plates. ASCE J. Engng Mech., 1997, 123, 214-221.
24. Liew, K. M. and Han, J.-B., A four-node differential quadrature method for straight-sided quadrilateral Reissner-Mindlin plates. Commun. Numer. Meth. Engng, 1997, 13, 73-81.
25. Han, J.-B. and Liew, K. M., An eight-node curvilinear differential quadrature formulation for Reissner/Mindlin plates. Computer Meth. Appl. Mech. Engng, 1997, 141, 265-280.
26. Kobayashi, H. and Sonoda, K., Rectangular Mindlin plates on elastic foundations. Int. J. Mech. Sci., 1989, 31, 679-692.