While the literature on numerical methods (e.g. finite elements and, to a certain extent, virtual elements) concentrates on convex elements, there is a need to probe beyond this limiting constraint so that the field can be further explored and developed. Thus, in this paper, we employ the virtual element method for non-convex discretizations of elastodynamic problems in 2D and 3D using an explicit time integration scheme. In the formulation, a diagonal matrix-based stabilization scheme is proposed to improve performance and accuracy. To address efficiency, a critical time step is approximated and verified using the maximum eigenvalue of the local (rather than global) system. The computational results demonstrate that the virtual element method is able to consistently handle general nonconvex elements and even non-simply connected elements, which can lead to convenient modeling of arbitrarily-shaped inclusions in composites.
|Number of pages||16|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - 2019 Nov 1|
Bibliographical noteFunding Information:
KP acknowledges the supports from the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning, South Korea (Grant Number: 2018R1A2B6007054 ), and from the Korea Institute of Energy Technology Evaluation and Planning (KETEP) funded by the Ministry of Trade, Industry & Energy, South Korea (Grant Number: 20174030201480 ). HC and GHP acknowledge support from the US National Science Foundation (NSF) under grant #1624232 (formerly #1437535 ), and the support from the Raymond Allen Jones Chair at the Georgia Institute of Technology, United States . The authors thank Prof. Beirao da Veiga for suggesting investigation of the diagonal matrix-based stabilization.
© 2019 Elsevier B.V.
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications