A suitable low-order, tetrahedral finite element for solids

Abstract

SUMMARYTo use the all-tetrahedral mesh generation capabilities existing today, we have explored the creation of a computationally e cient eight-node tetrahedral ÿnite element (a four-node tetrahedral ÿnite element enriched with four mid-face nodal points). The derivation of the element's gradient operator, studies in obtaining a suitable mass lumping and the element's performance in applications are presented. In particular, we examine the eight-node tetrahedral ÿnite element's behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar 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 ÿnite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral ÿnite element and the four-node tetrahedral ÿnite element are included. Given automatic all-tetrahedral meshing, the eight-node, mean-quadrature tetrahedral ÿnite element is a suitable replacement for the eight-node, mean-quadrature hexahedral ÿnite element and meshes requiring an inordinate amount of user intervention and direction to generate.

Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes

“…The uniform strain elements are based on concepts developed for the quadrilateral and hexahedron [8] and extensions to other element types [9,10]. The elements do not require the introduction of additional degrees of freedom and their performance is shown to be signiÿcantly better than that of three-node triangular or four-node tetrahedral elements.…”

The generation of hexahedral meshes for assembly geometry: survey and progress

“…• Accurate tetrahedral mesh-based analyses: although the issue of hex versus tet accuracy for FEA is a controversial subject, it is still widely believed that hexahedra are preferable for some analyses; however there are limited data which show this to be true. Promising research is being done to develop more accurate tetrahedral elements for non-linear structural mechanics; these elements have eight nodes (four vertex nodes and four mid-face nodes), and are more e cient than the traditional 10-node tetrahedron [78]. It is not clear whether these are e cient enough to justify their use in place of hexahedra.…”