Singularity analysis of linear hardening V-notch by asymptotic expansion coupled BEM

Abstract

In this paper, a general numerical method by the asymptotic expansion coupled the boundary element method (CBEM), considering the singular term and the higher order terms, is developed to analyze the complete singular stress field of linear hardening elastic–plastic material with a V-notch. The method firstly transforms the singularity analysis for the governing equation of the V-notch tip into an ordinary differential eigenvalue equation, which is then solved by the interpolating matrix method. Then, the complete singular stress field and the notch stress intensity factors (SIFs) can be obtained by coupling the asymptotic expansion of the elastic–plastic singular stresses at the V-notch tip with the conventional boundary elements method for the remaining region of the structure. Two types of examples are analyzed for the V-notch problem of linear hardening material. It is shown that the elastic–plastic singular stress field can be evaluated by the equivalent Young’s modulus and Poisson’s ratio. The proposed new approach is found to be accurate and effective in evaluating singular stress fields in a V-notch structure with linear hardening material.