A coordinate transformation based barycentric interpolation collocation method and its application in bending, free vibration and buckling analysis of irregular Kirchhoff plates

In this article, a meshless barycentric interpolation collocation method (BICM) with coordinate transformation is proposed to solve the governing partial differential equations (PDEs) for bending, free vibration and buckling problems of irregular plates. First, the coordinate transformation equation...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2023-11, Vol.124 (22), p.5069-5101
Main Authors: Huang, Z. M., Peng, L. X.
Format: Article
Language:English
Subjects:
Bending
Boundary conditions
Buckling
Collocation methods
Coordinate transformations
Finite element method
Free vibration
Interpolation
Mathematical analysis
Partial differential equations
Plates
Transformations (mathematics)
Vibration analysis
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Summary:In this article, a meshless barycentric interpolation collocation method (BICM) with coordinate transformation is proposed to solve the governing partial differential equations (PDEs) for bending, free vibration and buckling problems of irregular plates. First, the coordinate transformation equations for first to fourth derivatives are introduced. Then the PDEs and boundary conditions defined in a physical domain are transformed into a rectangular domain (reference domain) with the derived differential interpolation matrices. The presented BICM can solve the PDEs based on the reference domain and is adaptive to irregular problem domains. Finally, the bending, free vibration and buckling problems of Kirchhoff plates with irregular shapes are studied with the proposed method. To illustrate the effectiveness of the proposed method, the results are compared with those given by theoretical solutions, finite element methods and literature.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.7338