Improvement of the performance of a tetrahedral element with rotational DOFs using strain smoothing techniques

Abstract

In this paper, the performance of a 4-node tetrahedral element with rotational DOFs is improved using strain smoothing techniques. A partition-of-unity based approximation is used to construct the tetrahedral element with rotational DOFs. To overcome the stiff behavior of the tetrahedral element with rotational DOFs, a face-based strain smoothing technique is used. The stiffness matrix is expressed explicitly and the element performance is evaluated through numerical examples, which demonstrate that the proposed strain smoothed tetrahedral elements with rotational DOFs satisfy the patch test and have a better performance than other tetrahedral elements with rotational DOFs.