Space-time virtual element method for elastodynamics

Theory, applications, and code development

verfasst von

Bing Bing Xu, Philipp Junker, Peter Wriggers

Abstract

In this work, a space-time virtual element method is presented for the discretization of the two-dimensional elastodynamics in a space-time cylinder. The basic idea of the space-time scheme is to treat time as an additional dimension. This approach has been extensively applied to numerous initial value problems based on the finite element method and virtual element method. However, there has been no report on the application of the space-time virtual element method in elastodynamics. The variational formulation and space-time bilinear format are derived based on Hamilton's principle to achieve this. The discretization space is obtained by the virtual element method in space and the upwind finite element method in time. The space-time mesh is obtained as a tensor product of space and time meshes, then the element stiffness matrix for the elastodynamic problem can be obtained based on the Kronecker product directly. Some two-dimensional examples solved by the developed space-time virtual element method are given to demonstrate the accuracy and stabilization. MATLAB codes for the space-time virtual element and finite element methods can be downloaded from github.com/Qinxiaoye/VEM-spcae-time-dynamic.

Organisationseinheit(en)

Institut für Kontinuumsmechanik

Typ

Artikel

Journal

Computer Methods in Applied Mechanics and Engineering

Band

435

Anzahl der Seiten

ISSN

0045-7825

Publikationsdatum

15.02.2025

Publikationsstatus

Veröffentlicht

Peer-reviewed

ASJC Scopus Sachgebiete

Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Allgemeine Physik und Astronomie, Angewandte Informatik

Elektronische Version(en)

https://doi.org/10.1016/j.cma.2024.117683 (Zugang: Offen)

BibTeX

@article{f52fa8137f734fd1b5f883b00c04b5ed,
title = "Space-time virtual element method for elastodynamics: Theory, applications, and code development",
abstract = "In this work, a space-time virtual element method is presented for the discretization of the two-dimensional elastodynamics in a space-time cylinder. The basic idea of the space-time scheme is to treat time as an additional dimension. This approach has been extensively applied to numerous initial value problems based on the finite element method and virtual element method. However, there has been no report on the application of the space-time virtual element method in elastodynamics. The variational formulation and space-time bilinear format are derived based on Hamilton's principle to achieve this. The discretization space is obtained by the virtual element method in space and the upwind finite element method in time. The space-time mesh is obtained as a tensor product of space and time meshes, then the element stiffness matrix for the elastodynamic problem can be obtained based on the Kronecker product directly. Some two-dimensional examples solved by the developed space-time virtual element method are given to demonstrate the accuracy and stabilization. MATLAB codes for the space-time virtual element and finite element methods can be downloaded from https://github.com/Qinxiaoye/VEM-spcae-time-dynamic.",
keywords = "Dynamics, Space time, Virtual element method",
author = "Xu, {Bing Bing} and Philipp Junker and Peter Wriggers",
note = "Publisher Copyright: {\textcopyright} 2024 The Authors",
year = "2025",
month = feb,
day = "15",
doi = "10.1016/j.cma.2024.117683",
language = "English",
volume = "435",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}