3D stabilization-free virtual element method for linear elastic analysis

authored by: Bing Bing Xu, Peter Wriggers
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.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 421
ISSN: 0045-7825
Publication date: 01.03.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2024.116826 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{170cf83cbdce443c99f6501853a9ec68,
title = "3D stabilization-free virtual element method for linear elastic analysis",
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",
author = "Xu, {Bing Bing} and Peter Wriggers",
note = "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.",
year = "2024",
month = mar,
day = "1",
doi = "10.1016/j.cma.2024.116826",
language = "English",
volume = "421",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}