1. On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration
- Author
-
Kyoungsoo Park, Heng Chi, and Glaucio H. Paulino
- Subjects
Computer science ,Mechanical Engineering ,Numerical analysis ,Constraint (computer-aided design) ,Computational Mechanics ,Regular polygon ,General Physics and Astronomy ,Field (mathematics) ,010103 numerical & computational mathematics ,01 natural sciences ,Finite element method ,Computer Science Applications ,010101 applied mathematics ,Mechanics of Materials ,Diagonal matrix ,Applied mathematics ,Polygon mesh ,0101 mathematics ,Element (category theory) - Abstract
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.
- Published
- 2019