Abstract
This paper deals with an interaction problem of arbitrarily distributed elliptical inclusions under longitudinal shear loading. The problem is formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknown functions are the densities of body forces distributed in the longitudinal directions of infinite bodies having the same elastic constants as those of the matrix and the inclusions. In order to satisfy the boundary conditions along the inclusions, four kinds of new fundamental density functions are applied. Then the body force densities are approximated by a linear combination of the fundamental density functions and polynomials. The calculations are carried out for several arrangement of the inclusions, and it is found that the present method yields rapidly converging numerical results for arbitrarily distributed elliptical inclusions.
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