任意分布だ円形介在物の干渉効果の解析法

Abstract

This paper deals with the numerical solutions of singular integral equations of the body force method in an interaction problem of arbitrarily distributed elliptical inclusions under general loading conditions. The problem is 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 as those of the matrix and the inclutions 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 calculations are carried out for several arrangement of the inclusions, and it is found that the present method yields rapidly conversing numerical results for arbitrarily distributed elliptical inclusions. The numerical results of weight functions and stress distributions along the boundaries are shown in figures to demonstrate the present solution.