A four-node tetrahedral element with continuous nodal stress

Abstract

Formulation of a partition of unity (PU) based four-node tetrahedral element with continuous nodal stress (Tetr4-CNS) and its applications to the analysis of linear elasticity problems in three-dimension are presented in this paper. By simply using the same mesh as the classical tetrahedral element (Tetr4), Tetr4-CNS element is able to obtain continuous nodal stress without recourse to stress smoothing operation in the post-processing process, and to construct high order global approximation without adding extra nodes or nodal DOFs. Moreover, it is free from the linear dependence problem which cripples many of the PU-based methods. A series of numerical tests are carried out to evaluate the performance of the Tetr4-CNS element. The numerical results show that accuracy through the proposed element is superior to that through Tetr4 element and eight-node hexahedral element (Hexa8). More importantly, the proposed element has excellent mesh distortion tolerant capabilities.