Enhancement of Performances of the Simplex Finite Elements by Applying the Strain-Smoothed Element Method

Abstract

This paper presents the strain-smoothed element (SSE) method applied to the 4-node tetrahedral finite element. The unique characteristic of the SSE method represents constructing a smoothed strain field for the elements, rather than for the smoothing domains, whereby the constant strains of all adjacent elements are fully utilized for the strain smoothing of the target element. Consequently, a linear strain field within the 4-node tetrahedral finite element is constructed through four Gauss integration points. The method does not require any additional creation of the mesh, and a standard isoparametric formulation of the 4-node tetrahedral finite element is used to formulate it. A numerical example was used to demonstrate the stress prediction improvement achieved as regards the corrected element, as taken from Chaemin Lee and Phill-Seung Lee’s publication of the method itself, compared with the linear and quadratic tetrahedral finite elements, which are implemented within the PAK and Simcenter Nastran software packages. The numerical results show that stresses predicted by the strain-smoothed 4-node tetrahedral finite element are comparable to that of a 10-node tetrahedral finite element that incorporates an extrapolation process for the determination of nodal stress values.