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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| Veröffentlicht in: | Computational mechanics Jg. 62; H. 1; S. 67 - 80 |
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| Sprache: | Englisch |
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Springer Berlin Heidelberg
01.07.2018
Springer Springer Nature B.V |
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| ISSN: | 0178-7675, 1432-0924 |
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| Abstract | 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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| AbstractList | 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. |
| Audience | Academic |
| Author | Cheng, Y. M. Chen, L. |
| Author_xml | – sequence: 1 givenname: L. surname: Chen fullname: Chen, L. organization: Department of Engineering Mechanics, Chang’an University – sequence: 2 givenname: Y. M. surname: Cheng fullname: Cheng, Y. M. email: ymcheng@shu.edu.cn organization: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University |
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| Keywords | Thin plate Elastic foundation Complex variable reproducing kernel particle method Winkler model Pasternak model Meshless method |
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| SubjectTerms | 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 |
| Title | The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations |
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