Year: 2023
Author: Jianguo Huang, Sen Lin, Yue Yu
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 3 : pp. 352–384
Abstract
This paper devises a new lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one $\widetilde{K}$ with additional vertices consisting of interior points on edges of $K$, so that the discrete admissible space is taken as the $V_1$ type virtual element space related to the partition $\{\widetilde{K}\}$ instead of $\{K\}$. The method is proved to converge with optimal convergence order both in $H^1$ and $L^2$ norms and uniformly with respect to the Lamé constant $\lambda$. Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2023-0024
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 3 : pp. 352–384
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Virtual element method linear elasticity locking-free numerical tests.
Author Details
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A locking-free virtual element method for 3D linear elasticity problems
Huang, Jianguo
Wang, Wenxuan
Applied Mathematics Letters, Vol. 160 (2025), Iss. P.109333
https://doi.org/10.1016/j.aml.2024.109333 [Citations: 0]