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The Method of Fundamental Solutions with Dual Reciprocity for thin Plates on Winkler Foundations with Arbitrary Loadings

Published online by Cambridge University Press:  05 May 2011

C. C. Tsai
C. C. Tsai*
Affiliation:
Department of Information Technology, Toko University, Chia-Yi County, Taiwan 61363, R.O.C.
*
* Assistant Professor
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Abstract

This paper describes the combination of the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method to solve problems of thin plates resting on Winkler foundations under arbitrary loadings, where the DRM is based on the augmented polyharmonic splines constructed by splines and monomials. In the solution procedure, the arbitrary distributed loading is first approximated by the augmented polyharmonic splines (APS) and thus the desired particular solution can be represented by the corresponding analytical particular solutions of the APS. Thereafter, the complementary solution is solved formally by the MFS. In the mathematical derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators. In other words, the solutions obtained by the MFS-DRM are first treated in terms of these complex coefficient operators and then converted to real numbers in suitable ways. Furthermore, the boundary conditions of lateral displacement, slope, normal moment, and effective shear force are all given explicitly for the particular solutions of APS as well as the kernels of MFS. Finally, numerical experiments are carried out to validate these analytical formulas.

Keywords

Method of fundamental solutionsDual reciprocity methodKirchhoff platesWinkler foundation
Type
Articles
Information
Journal of Mechanics , Volume 24 , Issue 2 , June 2008 , pp. 163 - 171
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

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