Development of a Software Package of Smoothed Finite Element Method (S-FEM) for Solid Mechanics Problems

Abstract

This paper reports a work to develop a general solver of smoothed finite element methods (S-FEMs) for stress analysis of 2D and 3D solid mechanics problems. In the solver, several efficient algorithms are proposed to construct the real smoothing domains and calculate all the connectivity for later computation. The present implementation of S-FEM distinguishes from the existing published implementation of S-FEM in terms of computing the smoothed strains. The existing implementation uses the volume/area-weighted average method to compute the smoothed strains for the smoothing domain. The present algorithm uses surface/line integrals to compute the smoothed strains strictly following the general [Formula: see text] formulation of S-FEM. Therefore, the present solver is the most general, applicable to any polygon elements, and even to higher order interpolation including using radial basis functions. Numerical experiments for a number of 2D and 3D solid mechanics examples are carried out to demonstrate the effectiveness and reliability of our solver.