A new approach to solve the anti-plane crack problems by the method of fundamental solutions

Abstract

This paper expands the method of fundamental solutions (MFS) to solve the anti-plane crack problems based on the traditional fundamental solution by the conformal mapping technique without using the domain decomposition technique and/or the crack Green's function. Based on the complex analysis and the conformal mapping technique, the approximate solution of the complex analytic function is derived for the MFS. The modified boundary conditions are deduced to construct the interpolation equations of the MFS. The conformal mapping technique naturally introduces singularities of the stress fields and the stress intensity factors (SIFs) for the anti-plane crack problems without using the crack Green's function and the domain-decomposition technique. The obtained numerical examples illustrate the validity and accuracy for the anti-plane crack problems. The proposed method is an expansion of the traditional MFS, and can be applied for many anti-plane elastic problems with the simple concept and the easy numerical implementation.