Stress Analysis Of Elliptical And EllipsoidalInclusions Using Singular Integral Equations

Abstract

This paper deals with stress analysis of elliptical and ellipsoidal inclusions using singular integral equations of the body force method. The stress and displacement fields due to a point force in an infinite plate and a ring force in an infinite body are used as fundamental solutions. On the idea of the body force method, the problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknown functions are densities of body forces distributed in the x- and y-directions of infinite plates or in the r- and z-directions of infinite bodies having the same elastic constants of the matrix and inclusions. 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 present method is found to give rapidly converging numerical results for the problems. The calculations are carried out systematically for various shape, distance and elastic constant of inclusions and the stress distributions along the boundaries of both the matrix and inclusions are shown in figures. Then the interaction effects are discussed through the comparison between the elliptical inclusions and ellipsoidal inclusions.