A Novel Alpha Smoothed Finite Element Method for Ultra-Accurate Solution Using Quadrilateral Elements

Abstract

Smoothed finite element method (S-FEM) based on triangular elements has recently been widely used for solving solid mechanics problems. In this paper, a novel [Formula: see text]S-FEM using quadrilateral elements ([Formula: see text]SFEM-Q4) is proposed to obtain ultra-accurate solutions in the displacement and strain energy for solid mechanics problems. This method combines node-based S-FEM (NS-FEM), edge-based S-FEM (ES-FEM) and cell-based S-FEM (CS-FEM) equipped with a scale factor [Formula: see text] that controls contribution from each of these three different S-FEM models. This novel combination makes the best use of the upper bound property of the NS-FEM and the lower bound property of the CS-FEM (with 4 or more sub-smoothing domains for each element), and establishes a continuous strain-energy function of a scale factor [Formula: see text] for obtaining close-to-exact solutions. Our [Formula: see text]SFEM-Q4 also ensures the variational consistence and the compatibility of the displacement field, and hence guarantees to reproduce linear field exactly. Various solid mechanics problems are presented to validate the stability, effectiveness and ultra-accuracy of the proposed method.