On the Stress Fluctuation in the Smoothed Finite Element Method for 2D Elastoplastic Problems

Abstract

In this study, the unusual stress fluctuation in the smoothed finite element method (SFEM) for 2D elastoplastic problems is investigated. The governing equation of the 2D elastoplastic problem based on SFEM is presented. The mysterious stress fluctuations from different SFEM approaches are explored. It is demonstrated that conventional finite element method might experience the same symptom. It is found that the stress noises only occur for cases consisting of elements with linear shape functions. Three strategies, including use of higher-order elements, modification of interpolation techniques, and evenly distributed mesh division are proposed to prevent mysterious stress fluctuations. All of them could considerably minimize the strange stress noises.