A New Locking-Free Virtual Element Method for Linear Elasticity Problems

A New Locking-Free Virtual Element Method for Linear Elasticity Problems

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

Jianguo Huang

Sen Lin

Yue Yu

  1. 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]