Details
| Original language | English |
|---|---|
| Pages (from-to) | 1151-1180 |
| Number of pages | 30 |
| Journal | CMES - Computer Modeling in Engineering and Sciences |
| Volume | 129 |
| Issue number | 3 |
| Early online date | 12 Aug 2021 |
| Publication status | Published - 2021 |
Abstract
The virtual element method (VEM) can be seen as an extension of the classical finite element method (FEM) based on Galerkin projection. It allows meshes with highly irregular shaped elements, including concave shapes. So far the virtual element method has been applied to various engineering problems such as elasto-plasticity, multiphysics, damage and fracture mechanics. This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations. Within this framework, we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape. The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior. Generally the construction of a virtual element is based on a projection part and a stabilization part. While the stiffness matrix needs a suitable stabilization, the mass matrix can be calculated using only the projection part. For the implicit time integration scheme, Newmark-Method is used. To show the performance of the method, various two- and three-dimensional numerical examples in are presented.
Keywords
- Dynamics, Finite strains, Three-dimensional, Virtual element method
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Modelling and Simulation
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In: CMES - Computer Modeling in Engineering and Sciences, Vol. 129, No. 3, 2021, p. 1151-1180.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Virtual Element Formulation For Finite Strain Elastodynamics
T2 - Dedicated to Professor Karl Stark Pister for his 95th birthday
AU - Cihan, Mertcan
AU - Aldakheel, Fadi
AU - Hudobivnik, Blaz
AU - Wriggers, Peter
N1 - Funding Information: Funding Statement: The authors gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in (i) the Collaborative Research Center CRC 1153 and (ii) the Priority Program SPP 2020.
PY - 2021
Y1 - 2021
N2 - The virtual element method (VEM) can be seen as an extension of the classical finite element method (FEM) based on Galerkin projection. It allows meshes with highly irregular shaped elements, including concave shapes. So far the virtual element method has been applied to various engineering problems such as elasto-plasticity, multiphysics, damage and fracture mechanics. This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations. Within this framework, we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape. The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior. Generally the construction of a virtual element is based on a projection part and a stabilization part. While the stiffness matrix needs a suitable stabilization, the mass matrix can be calculated using only the projection part. For the implicit time integration scheme, Newmark-Method is used. To show the performance of the method, various two- and three-dimensional numerical examples in are presented.
AB - The virtual element method (VEM) can be seen as an extension of the classical finite element method (FEM) based on Galerkin projection. It allows meshes with highly irregular shaped elements, including concave shapes. So far the virtual element method has been applied to various engineering problems such as elasto-plasticity, multiphysics, damage and fracture mechanics. This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations. Within this framework, we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape. The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior. Generally the construction of a virtual element is based on a projection part and a stabilization part. While the stiffness matrix needs a suitable stabilization, the mass matrix can be calculated using only the projection part. For the implicit time integration scheme, Newmark-Method is used. To show the performance of the method, various two- and three-dimensional numerical examples in are presented.
KW - Dynamics
KW - Finite strains
KW - Three-dimensional
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85115806244&partnerID=8YFLogxK
U2 - 10.32604/cmes.2021.016851
DO - 10.32604/cmes.2021.016851
M3 - Article
VL - 129
SP - 1151
EP - 1180
JO - CMES - Computer Modeling in Engineering and Sciences
JF - CMES - Computer Modeling in Engineering and Sciences
SN - 1526-1492
IS - 3
ER -