Details
| Original language | English |
|---|---|
| Number of pages | 15 |
| Journal | Computational mechanics |
| Early online date | 15 Nov 2024 |
| Publication status | E-pub ahead of print - 15 Nov 2024 |
Abstract
The virtual element method (VEM) was developed not too long ago, starting with the paper (Beirão-da-Veiga et al. in SIAM J Numer Anal 51:794–812, 2013) related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements, however has so far not applied to space-time formulations for one-dimensional structural elements like strings, trusses and beams. Here we study several VEM elements suitable for space-time formulations that are build upon the Hamilton’s principle. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same number of unknowns. Furthermore, we show that the property of VEM to deal with non-conforming meshes is of special interest for holistic space time formulation: VEM formulations allow locally varying time discretizations (time increments) in a natural and efficient way.
Keywords
- Hamilton’s principle, Space-time formulations, Strings, Trusses, Virtual element method (VEM)
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, 15.11.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On a space-time implementation of the wave equation using virtual elements
AU - Wriggers, P.
AU - Junker, Ph
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/11/15
Y1 - 2024/11/15
N2 - The virtual element method (VEM) was developed not too long ago, starting with the paper (Beirão-da-Veiga et al. in SIAM J Numer Anal 51:794–812, 2013) related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements, however has so far not applied to space-time formulations for one-dimensional structural elements like strings, trusses and beams. Here we study several VEM elements suitable for space-time formulations that are build upon the Hamilton’s principle. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same number of unknowns. Furthermore, we show that the property of VEM to deal with non-conforming meshes is of special interest for holistic space time formulation: VEM formulations allow locally varying time discretizations (time increments) in a natural and efficient way.
AB - The virtual element method (VEM) was developed not too long ago, starting with the paper (Beirão-da-Veiga et al. in SIAM J Numer Anal 51:794–812, 2013) related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements, however has so far not applied to space-time formulations for one-dimensional structural elements like strings, trusses and beams. Here we study several VEM elements suitable for space-time formulations that are build upon the Hamilton’s principle. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same number of unknowns. Furthermore, we show that the property of VEM to deal with non-conforming meshes is of special interest for holistic space time formulation: VEM formulations allow locally varying time discretizations (time increments) in a natural and efficient way.
KW - Hamilton’s principle
KW - Space-time formulations
KW - Strings
KW - Trusses
KW - Virtual element method (VEM)
UR - http://www.scopus.com/inward/record.url?scp=85209145247&partnerID=8YFLogxK
U2 - 10.1007/s00466-024-02556-3
DO - 10.1007/s00466-024-02556-3
M3 - Article
AN - SCOPUS:85209145247
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
ER -