A suitable low-order, tetrahedral finite element for solids

To use the all-tetrahedral mesh generation capabilities existing today, we have explored the creation of a computationally efficient eight-node tetrah edral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element's gradient opera tor, studies in obtaining a suitable mass lumping and the element's perform ance in applications are presented. In particular, we examine the eight-nod e tetrahedral finite element's behavior in longitudinal plane wave propagat ion, in transverse cylindrical wave propagation, and in simulating Taylor b ar impacts. The element samples only constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the eight -node, mean-quadrature hexahedral finite element. Comparisons with the resu lts obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, mean-quadrature tetrahedral finite element is a suitable replacement for the eight-node, mean-quadrature hexa hedral finite element and meshes requiring an inordinate amount of user int ervention and direction to generate. Copyright (C) 1999 John Wiley & Sons, Ltd. This paper was produced under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.