Three-component volume coordinate system for constructing high performance elements

Abstract

In finite element method (FEM), the volume-coordinate system (VCS) plays a very important role. To date, the number of coordinate components of all VCSs equals the number of faces of polyhedral elements (e.g. 4-component tetrahedral VCS or 6-component hexahedral VCS). To break the current situation, a 3-component VCS is established systematically based on hexahedron. The definition of the new 3-component VCS is still suitable for these degenerated solids from hexahedron, including tetrahedron and several 5-surface solids. In the proposed VCS, the number of coordinate components is unrelated to the number of faces of polyhedron. It is the very first shape-independent VCS in the history of FEM. The new 3-component VCS has both the superiorities of the local natural coordinate system and the simplicities of the Cartesian coordinate system. Based on the presented 3-component VCS, we construct a new incompatible eight-node hexahedral element, which is characterized by the high accuracy and the insensitivity to mesh distortion. This adequately demonstrates that the proposed 3-component VCS is a powerful tool for developing high-performance elements.