Interaction among a row of ellipsoidal inclusions

摘要

In this paper the interaction among a row of N ellipsoidal inclusions of revolution is considered. Inclusions in a body under both (A) asymmetric uniaxial tension in the x-direction and (B) axisymmetric uniaxial tension in the z-direction are treated in terms of singular integral equations resulting from the body force method. These problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r. #theta#, z directions. In order to satisfy the boundary conditions along the ellipsoidal boundaries, the unknown functions are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for interface stresses. When the elastic ratio E_1 ? E_I/EM > 1, the primary feature of the interaction is a large compressive or tensile stress #sigma#_n on the interface #theta#= 0. When E_1 ? E_I/EM > 1, a large tensile stress #sigma#_(#theta#) or #sigma#_t on the interface #theta#=1/2#pi# is of interest. If the spacing h/d and the elastic ratio El/EM are fixed, the interaction effects are dominant when the shape ratio a/b is large. For any fixed shape and spacing of inclusions, the maximum stress is shown to be linear with the reciprocal of the squared number of inclusions.