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

• Published in: arXiv.org 2022-05
• Main Authors: Sukumar, N, Tupek, Michael R
• Format: Article
• Language: English
• Subjects: Agglomeration; Algorithms; Angles (geometry); CAD; Computer aided design; Computer simulation; Eigenvalues; Elastodynamics; Finite element method; Meshing; Polyhedra; Prisms; Shape effects; Simulation; Tetrahedra
• ISSN: 2331-8422

In this paper, we use the first-order virtual element method (VEM) to investigate the effect of shape quality of polyhedra in the estimation of the critical time step for explicit three-dimensional elastodynamic finite element (FE) simulations. Low-quality finite elements are common when meshing realistic complex components, and while tetrahedral meshing technology is generally robust, meshing algorithms cannot guarantee high-quality meshes for arbitrary geometries or for non-water-tight computer-aided design models. For reliable simulations on such meshes, we consider FE meshes with tetrahedral and prismatic elements that have badly-shaped elements\(-\)tetrahedra with dihedral angles close to \(0^\circ\) and \(180^\circ\), and slender prisms with triangular faces that have short edges\(-\)and agglomerate such `bad' elements with neighboring elements to form a larger polyhedral virtual element. On each element, the element-eigenvalue inequality is used to estimate the critical time step. For a suite of illustrative finite element meshes with \(\epsilon\) being a mesh-coordinate parameter that leads to poor mesh quality, we show that adopting VEM on the agglomerated polyhedra yield critical time steps that are insensitive as \(\epsilon \rightarrow 0\). The significant reduction in solution time on meshes with agglomerated virtual elements vis-\(à\)-vis tetrahedral meshes is demonstrated through explicit dynamics simulations on a tapered beam.