We present a general framework to solve elastodynamic problems by means of the virtual element method (VEM) with explicit time integration. In particular, the VEM is extended to analyze nearly incompressible solids using the B-bar method. We show that, to establish a B-bar formulation in the VEM setting, one simply needs to modify the stability term to stabilize only the deviatoric part of the stiffness matrix, which requires no additional computational effort. Convergence of the numerical solution is addressed in relation to stability, mass lumping scheme, element size, and distortion of arbitrary elements, either convex or nonconvex. For the estimation of the critical time step, two approaches are presented, ie, the maximum eigenvalue of a system of mass and stiffness matrices and an effective element length. Computational results demonstrate that small edges on convex polygonal elements do not significantly affect the critical time step, whereas convergence of the VEM solution is observed regardless of the stability term and the element shape in both two and three dimensions. This extensive investigation provides numerical recipes for elastodynamic VEMs with explicit time integration and related problems.
|Number of pages||31|
|Journal||International Journal for Numerical Methods in Engineering|
|Publication status||Published - 2020 Jan 15|
Bibliographical noteFunding Information:
KP acknowledges support from the National Research Foundation of Korea through the Basic Science Research Program funded by the Ministry of Science, ICT and Future Planning under grant 2018R1A2B6007054 and from the Korea Institute of Energy Technology Evaluation and Planning funded by the Ministry of Trade, Industry and Energy under grant 20171510101910. HC and GHP acknowledge support from the National Science Foundation under grant 1624232 (formerly grant 1437535) and from the Raymond Allen Jones Chair at the Georgia Institute of Technology.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Applied Mathematics