Virtual elements on agglomerated finite elements to increase the critical time step in elastodynamic simulations

In this article, we use the first-order virtual element method (VEM) to investigate effect of shape quality polyhedra in estimation critical time step for explicit three-dimensional elastodynamic finite (FE) simulations. Low-quality FEs are common when meshing realistic complex components, and while tetrahedral technology is generally robust, algorithms cannot guarantee high-quality meshes arbitrary geometries or non-water-tight computer-aided design models. For reliable simulations on such meshes, consider FE with prismatic elements that have badly shaped elements—tetrahedra dihedral angles close 0 ∘ $$ {0}^{\circ } 18 18{0}^{\circ , slender prisms triangular faces short edges—and agglomerate “bad” neighboring form a larger polyhedral element. On each element, element-eigenvalue inequality used estimate step. suite illustrative ϵ \epsilon being mesh-coordinate parameter leads poor mesh quality, show adopting VEM agglomerated yield steps insensitive as → \to . The significant reduction solution vis-à-vis demonstrated through dynamics tapered beam.