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

Hui Zheng, Xiaoling Lai, Anyu Hong () and Xing Wei
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Hui Zheng: School of Infrastructure Engineering, Nanchang University, Nanchang 330031, China
Xiaoling Lai: School of Infrastructure Engineering, 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

Mathematics, 2022, vol. 10, issue 19, 1-15

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.

Keywords: fictitious centre nodes; radial basis function; elasticity problems; shape parameter; modified Franke formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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