Virtual element method: Theory and applications

LIU Chuanqi; XU Guangtao; WEI Yujie

doi:10.6052/1000-0992-22-037

Volume 52 Issue 4

Dec. 2022

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Article Navigation > Advances in Mechanics > 2022 > 52(4): 874-913

Liu C Q, Xu G T, Wei Y J. Virtual element method: Theory and applications. Advances in Mechanics, 2022, 52(4): 874-913 doi: 10.6052/1000-0992-22-037

Citation:

Liu C Q, Xu G T, Wei Y J. Virtual element method: Theory and applications. Advances in Mechanics, 2022, 52(4): 874-913 doi: 10.6052/1000-0992-22-037

Liu C Q, Xu G T, Wei Y J. Virtual element method: Theory and applications. Advances in Mechanics, 2022, 52(4): 874-913 doi: 10.6052/1000-0992-22-037

Citation:

Liu C Q, Xu G T, Wei Y J. Virtual element method: Theory and applications. Advances in Mechanics, 2022, 52(4): 874-913 doi: 10.6052/1000-0992-22-037

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Virtual element method: Theory and applications

doi: 10.6052/1000-0992-22-037

LIU Chuanqi^1
,,
XU Guangtao^{1, 2},
WEI Yujie^{1, 2, 3
,
,}

1.
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China
3.
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

More Information

Corresponding author: yujie_wei@lnm.imech.ac.cn
Received Date: 2022-07-04
Accepted Date: 2022-08-19

Available Online: 2022-08-19

Publish Date: 2022-12-29

Abstract

Abstract

Virtual Element Method (VEM) is a recently-developed numerical method suitable for arbitrarily convex or concave cells. This benefits the VEM to handle hanging nodes, contacts and polycrystalline deformations. We here illustrate the theory of the VEM via the Poisson equation and the elastic problem, and summarize its applications to non-linear problems. Compared to the Finite Element Method (FEM), the characteristics of the VEM are explained in details. The VEM has demonstrated potentials to model contacts, cracks, coupling of multiple physics, and etc. We hope that this review can provides an alternative means for software developers in computational mechanics.
- virtual element method,
- non-polynomial function,
- computational mechanics,
- convexity and concavity

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References(58)

References

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