Regularized meshless method for antiplane shear problems with multiple inclusions

Abstract

In this paper, we employ the regularized meshless method to solve antiplane shear problems with multiple inclusions. The solution is represented by a distribution of double‐layer potentials. The singularities of kernels are regularized by using a subtracting and adding‐back technique. Therefore, the troublesome singularity in the method of fundamental solutions (MFS) is avoided and the diagonal terms of influence matrices are determined. An inclusion problem is decomposed into two parts: one is the exterior problem for a matrix with holes subjected to remote shear, the other is the interior problem for each inclusion. The two boundary densities, essential and natural data, along the interface between the inclusion and matrix satisfy the continuity and equilibrium conditions. A linear algebraic system is obtained by matching boundary conditions and interface conditions. Finally, numerical results demonstrate the accuracy of the present solution. Good agreements are obtained and compare well with analytical solutions and Gong's results.