The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations

In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used t...

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Bibliographic Details
Published in:Computational mechanics Vol. 62; no. 1; pp. 67 - 80
Main Authors: Chen, L., Cheng, Y. M.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2018
Springer
Springer Nature B.V
Subjects:
Basis functions
Classical and Continuum Physics
Complex variables
Computational Science and Engineering
Dynamic programming
Elastic foundations
Engineering
Galerkin method
Mathematical analysis
Mathematical models
Original Paper
Product design
Shape functions
Theoretical and Applied Mechanics
Thin plates
Thin plate
Elastic foundation
Complex variable reproducing kernel particle method
Winkler model
Pasternak model
Meshless method
ISSN:0178-7675, 1432-0924
Online Access:Get full text
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Summary:In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-017-1484-2