Details
| Original language | English |
|---|---|
| Pages (from-to) | 963-977 |
| Number of pages | 15 |
| Journal | Computational Mechanics |
| Volume | 66 |
| Issue number | 4 |
| Early online date | 13 Aug 2020 |
| Publication status | Published - Oct 2020 |
Abstract
The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations that introduce curved element edges. These virtual elements allow for specific geometrical forms of the course of the curve at the edges. In this contribution a new methodology is proposed that allows to use general mappings for virtual elements which can model arbitrary geometries.
Keywords
- Bezier splines, Isoparametric maps, Stabilization, Virtual element method
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, Vol. 66, No. 4, 10.2020, p. 963-977.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A virtual element formulation for general element shapes
AU - Wriggers, Peter
AU - Hudobivnik, Blaz
AU - Aldakheel, Fadi
N1 - Funding Information: Open Access funding provided by Projekt DEAL. The first author gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the collaborative research center CRC 1153 “Process chain for the production of hybrid high-performance components through tailored forming” while the third author acknowledges support for this research by the Priority Program SPP 2020 under the project WR 19/58-2.
PY - 2020/10
Y1 - 2020/10
N2 - The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations that introduce curved element edges. These virtual elements allow for specific geometrical forms of the course of the curve at the edges. In this contribution a new methodology is proposed that allows to use general mappings for virtual elements which can model arbitrary geometries.
AB - The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations that introduce curved element edges. These virtual elements allow for specific geometrical forms of the course of the curve at the edges. In this contribution a new methodology is proposed that allows to use general mappings for virtual elements which can model arbitrary geometries.
KW - Bezier splines
KW - Isoparametric maps
KW - Stabilization
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85089399805&partnerID=8YFLogxK
U2 - 10.1007/s00466-020-01891-5
DO - 10.1007/s00466-020-01891-5
M3 - Article
AN - SCOPUS:85089399805
VL - 66
SP - 963
EP - 977
JO - Computational Mechanics
JF - Computational Mechanics
SN - 0178-7675
IS - 4
ER -