TY - JOUR
T1 - On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration
AU - Park, Kyoungsoo
AU - Chi, Heng
AU - Paulino, Glaucio H.
N1 - Funding 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.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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.
AB - 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.
KW - Elastodynamics
KW - Non-simply connected elements
KW - Nonconvex elements
KW - Stabilization
KW - Virtual element method (VEM)
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U2 - 10.1016/j.cma.2019.06.031
DO - 10.1016/j.cma.2019.06.031
M3 - Article
AN - SCOPUS:85070519311
SN - 0374-2830
VL - 356
SP - 669
EP - 684
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -