Modelling three dimensional dynamic problems using the four-node tetrahedral element with continuous nodal stress

Abstract

A partition of unity (PU) based four-node tetrahedral element with continuous nodal stress (Tetr4-CNS) was recently proposed for static analysis of three-dimensional solids. By simply using the same mesh as the classical four-node tetrahedral (Tetr4) element, high order global approximation function in the Tetr4-CNS element can be easily constructed without extra nodes or nodal DOFs. In this paper, the Tetr4-CNS element is further applied in the analysis of three dimensional dynamic problems. A series of free vibration and forced vibration problems are solved using the Tetr4-CNS element. The numerical results show that, for regular meshes, accuracy obtained using the Tetr4-CNS element is superior to that obtained using the Tetr4 and eight-node hexahedral (Hexa8) elements. For distorted meshes, the Tetr4-CNS element has better mesh-distortion tolerance than both the Tetr4 and Hexa8 elements.