Year: 2025
Author: Zhentian Huang, Dong Lei, Zi Han, Heping Xie, Jianbo Zhu
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 350–372
Abstract
An innovative meshless method is proposed in this paper for the bending problem of arbitrary Kirchhoff plates subjected to external force with various shapes and different boundary conditions. Without using a numerical integral, the deflection of the thin plate is approximated by using the boundary mapped collocation approach. Moreover, the computational domain discretization is just dependent on discretized nodes on the axis, while tensor product nodes have been mapped in the domain automatically. Hence, in the boundary mapped collocation implementation, the approximation functions are derived by employing the one-dimensional moving least squares technique for two-dimensional and higher-dimensional problems. Further, the virtual boundary technique is introduced to enforce the boundary conditions in the proposed method. Additionally, four numerical experiments are presented to illustrate the excellent convergence and high precision of the proposed approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0166
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 350–372
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Boundary mapped collocation method moving least squares Kirchhoff plate meshless method.