Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 117683 |
| Seitenumfang | 19 |
| Fachzeitschrift | Computer Methods in Applied Mechanics and Engineering |
| Jahrgang | 435 |
| Frühes Online-Datum | 23 Dez. 2024 |
| Publikationsstatus | Veröffentlicht - 15 Feb. 2025 |
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.
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in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 435, 117683, 15.02.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Space-time virtual element method for elastodynamics
T2 - Theory, applications, and code development
AU - Xu, Bing Bing
AU - Junker, Philipp
AU - Wriggers, Peter
N1 - Publisher Copyright: © 2024 The Authors
PY - 2025/2/15
Y1 - 2025/2/15
N2 - 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.
AB - 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.
KW - Dynamics
KW - Space time
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85212591866&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.117683
DO - 10.1016/j.cma.2024.117683
M3 - Article
AN - SCOPUS:85212591866
VL - 435
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 117683
ER -