Analysis of a row of elliptical inclusions in a plate using singular integral equations

Abstract

This paper deals with the interaction problem of a row of elliptical inclusions under uniaxial tension. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy--type and logarithmic singularities, where the unknowns are densities of body forces distributed in infinite plates that have the same elastic constants as those of the matrix and inclusion. In order to satisfy the boundary conditions along the elliptical boundaries, eight kinds of fundamental density functions, proposed in a previous paper, are applied. In the analysis, the number, shape, and position of inclusions are varied systematically; after which the magnitude and position of the maximum stress are examined. For any fixed shape and size of inclusions, the maximum stress is shown to be linear with the reciprocal of the number of inclusions. The present method is found to yield rapidly converging numerical results for various geometrical conditions of inclusions.