Tension of a Wide Plate Containing a Row of Elliptical Inclusions

Abstract

This paper deals with a row of equally spaced equal elliptical inclusions in a plate subjected to transverse and longitudinal tensions. Based on the concepts of the body force method, 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 an infinite plate having the same elastic constants of the matrix and inclusions are unknown functions. In order to satisfy the boundary conditions along the inclusions, eight kinds of fundamental density function 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. In the analysis, elastic constants of matrix and inclusion are varied systematically ; then, the magnitude and position of the maximum stress are examined. For any fixed shape, size and elastic constant of inclusions, the maximum stress is shown to be linear with the reciprocal of the number of inclusions.