SINGULAR INTEGRAL-EQUATION METHOD FOR INTERACTION BETWEEN ELLIPTIC INCLUSIONS

This paper deals with numerical solutions of singular integral equatio ns in interaction problems of elliptical inclusions under general load ing conditions. The stress and displacement fields due to a point forc e in infinite plates are used as fundamental solutions. Then, the prob lems are formulated as a system of singular integral equations with Ca uchy-type or logarithmic-type singularities, where the unknowns are th e body force densities distributed in infinite plates having the same elastic constants as those of the man-it and inclusions. To determine the unknown body force densities to satisfy the boundary conditions, f our auxiliary unknown functions are derived from each body force densi ty. It is found that determining these four auxiliary functions in the range 0 less than or equal to phi(k) less than or equal to pi/2 is eq uivalent to determining an original unknown density in the range 0 les s than or equal to phi(k) less than or equal to 2 pi. Then these auxil iary unknowns are approximated by using fundamental densities and poly nomials. Initially, the convergence of the results such as unknown den sities and interface stresses are confirmed with increasing Collocatio n points. Also, the accuracy is verified by examining the boundary con ditions and relations between interface stresses and displacements. Ra ndomly or regularly distributed elliptical inclusions can be treated b y combining both solutions for remote tension and shear shown in this study.