Singular Integral Equation Method in the Analysis of Interaction between Rectangular Inclusions

Abstract

This paper deals with numerical solutions of singular integral equations in interaction problems of rectangular inclusions under various loading conditions. The body force method is used to formulate the problems as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknown functions are the densities of body forces distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. In order to analyze the problems accurately, the unknown functions are expressed as piecewise smooth functions using two types of fundamental densities and power series, where the fundamental densities are chosen to represent the symmetric stress singularity of 1/r^1-λ₁ and the skew-symmetric stress singularity of 1/r^1-λ₂. Then, newly defined stress intensity factors at the end of inclusions are systematically calculated for various shapes and spacings of two rectangular inclusions in a plate subjected to longitudinal tension, transverse tension, and in-plane shear. The present method is found to be effective for accurate and efficient analysis of rectangular inclusions.