Interaction Effect among a Row of Ellipsoidal Cavities in an Infinite Body under Uniaxial Tension.

Abstract

This paper deals with the numerical solution of singular integral equations of the body force method in the interaction problem for a row of ellipsoidal cavities under uniaxial tension. The problem is solved by the superposition of two auxiliary loads: (i)biaxial tension and (ii)plane state of pure shear. These problems are formulated as a system of singular integral equations with Cauchy-type singularities, where the densities of body forces distributed in the r, θ and z directions are unknown functions. In order to satisfy the boundary conditions along the ellipsoidal boundaries, eight kinds of fundamental density functions proposed in our previous paper are applied. In the analysis, the number, shape, and distance of cavities are varied systematically; then the magunitude and position of the maximum stress are examined. For any fixed shape and size of cavities, the maximum stress is shown to be linear with the reciprocal of the squared number of cavities.