Singular Integral Equation method in the Analysis of Interaction between Elliptical Inclusions

This paper deals with numerical solutions of singular integral equations of the body force method in interaction problems of elliptical inclusions under general loading conditions. The problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the densities of body forces distributed in the x- and y-directions of infinite plates having the same elastic constants of the matrix and the inclusions are unknown functions. In order to satisfy the boundary conditions along the inclusions, eight kinds of fundamental density functions proposed in our previous paper are used. Then the body force densities are approximated by a linear combination of the fundamental density functions and polynomials. The accuracy of the present analysis is verified by comparing with the results from previous research. The present method is found to give rapidly converging numerical results for stress distribution along the boundaries of both the matrix and the inclusions