Details
| Original language | English |
|---|---|
| Article number | 116826 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 421 |
| Early online date | 2 Feb 2024 |
| Publication status | Published - 1 Mar 2024 |
Abstract
We present a first-order stabilization-free virtual element method (VEM) for three-dimensional linear elastic problems in this paper. VEM has been increasingly used in various fields of engineering, but the need of stabilization yields a method that cannot be used without care, e.g. in nonlinear engineering applications. In this work, by increasing the order of the strain model, a new virtual element formulation is constructed for three-dimensional problems that does not require any stabilization term. The core concept involves adapting the virtual element space to enable the computation of a higher-order L2 projection operator, guaranteeing an accurate representation of the element energy in terms of strain and stress. This work describes the calculation process of the original H1 projection operator and the higher-order L2 projection operator for three-dimensional problems. Eigenvalue analysis allows to derive an approximate relation between the polynomial order and the number of element vertices. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional linear elastic problems.
Keywords
- Nonmatching Mesh, Stabilization-free, Virtual element method
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 421, 116826, 01.03.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - 3D stabilization-free virtual element method for linear elastic analysis
AU - Xu, Bing Bing
AU - Wriggers, Peter
N1 - Funding Information: The authors are grateful for the support provided by the Alexander von Humboldt Foundation, Germany . The first author thanks Dr. Jian Meng and Professor Alessandro Russo for discussions on the enhancement space.
PY - 2024/3/1
Y1 - 2024/3/1
N2 - We present a first-order stabilization-free virtual element method (VEM) for three-dimensional linear elastic problems in this paper. VEM has been increasingly used in various fields of engineering, but the need of stabilization yields a method that cannot be used without care, e.g. in nonlinear engineering applications. In this work, by increasing the order of the strain model, a new virtual element formulation is constructed for three-dimensional problems that does not require any stabilization term. The core concept involves adapting the virtual element space to enable the computation of a higher-order L2 projection operator, guaranteeing an accurate representation of the element energy in terms of strain and stress. This work describes the calculation process of the original H1 projection operator and the higher-order L2 projection operator for three-dimensional problems. Eigenvalue analysis allows to derive an approximate relation between the polynomial order and the number of element vertices. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional linear elastic problems.
AB - We present a first-order stabilization-free virtual element method (VEM) for three-dimensional linear elastic problems in this paper. VEM has been increasingly used in various fields of engineering, but the need of stabilization yields a method that cannot be used without care, e.g. in nonlinear engineering applications. In this work, by increasing the order of the strain model, a new virtual element formulation is constructed for three-dimensional problems that does not require any stabilization term. The core concept involves adapting the virtual element space to enable the computation of a higher-order L2 projection operator, guaranteeing an accurate representation of the element energy in terms of strain and stress. This work describes the calculation process of the original H1 projection operator and the higher-order L2 projection operator for three-dimensional problems. Eigenvalue analysis allows to derive an approximate relation between the polynomial order and the number of element vertices. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional linear elastic problems.
KW - Nonmatching Mesh
KW - Stabilization-free
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85183941783&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.116826
DO - 10.1016/j.cma.2024.116826
M3 - Article
AN - SCOPUS:85183941783
VL - 421
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 116826
ER -