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A Novel RBF Collocation Method Using Fictitious Centre Nodes for Elasticity Problems

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  • Hui Zheng

    (School of Infrastructure Engineering, Nanchang University, Nanchang 330031, China
    Institute of Aerospace, Nanchang University, Nanchang 330031, China)

  • Xiaoling Lai

    (School of Infrastructure Engineering, Nanchang University, Nanchang 330031, China
    Institute of Aerospace, Nanchang University, Nanchang 330031, China)

  • Anyu Hong

    (School of Infrastructure Engineering, Nanchang University, Nanchang 330031, China)

  • Xing Wei

    (School of Civil Engineering & Architecture, East China Jiaotong University, Nanchang 330013, China)

Abstract

The traditional radial basis function collocation method (RBFCM) has poor stability when solving two-dimensional elastic problems, and the numerical results are very sensitive to shape parameters, especially in solving elastic problems. In this paper, a novel radial basis function collocation method (RBFCM) using fictitious centre nodes is applied to the elastic problem. The proposed RBFCM employs fictitious centre nodes to interpolate the unknown coefficients, and is much less sensitive to the shape parameter compared with the traditional RBFCM. The details of the shape parameters are discussed for the novel RBFCM in elastic problems. Elastic problems with and without analytical solutions are given to show the effectiveness of the improved RBFCM.

Suggested Citation

  • Hui Zheng & Xiaoling Lai & Anyu Hong & Xing Wei, 2022. "A Novel RBF Collocation Method Using Fictitious Centre Nodes for Elasticity Problems," Mathematics, MDPI, vol. 10(19), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3711-:d:938159
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    References listed on IDEAS

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    1. Wu, Hui-Yuan & Duan, Yong, 2016. "Multi-quadric quasi-interpolation method coupled with FDM for the Degasperis–Procesi equation," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 83-92.
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