A Novel Triangular Prism Element Based on Smoothed Finite Element Method

Abstract

In this paper, a novel triangular prism element based on smoothed finite element method (SFEM) is proposed for three-dimensional static and dynamic mechanics problems. The accuracy of the proposed element is comparable to that of the hexahedral element while keeping good adaptability as the tetrahedral element on a surface dimension. In the process of constructing the proposed element, one triangular prism element is further divided into two smoothing cells. Very simple shape functions and a constant smoothing function are used in the construction of the smoothed strains and the smoothed nominal stresses. The divergence theorem is applied to convert the volume integral to the integrals of all the surrounding surfaces of a smoothing cell. Thus, no gradient of shape function and no mapping or coordinate transformation are involved in the process of creating the discretized system equations. Afterwards, several numerical examples include elastic-static and free vibration problems are provided to demonstrate the accuracy and efficiency of the proposed element. Meanwhile, an explicit scheme of the proposed element is given for dynamic large-deformation analysis of elastic-plastic materials, and the numerical results show good agreement with the experimental data.