Stress analysis of arbitrarily distributed elliptical inclusions under longitudinal shear loading

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 inclusions. In order to satisfy the boundary conditions along the elliptical inclusions, four kinds of fundamental density functions are introduced in a similar way of previous papers treating plane stress problems. Then the body force densities are approximated by a linear combination of those fundamental density functions and polynomials. In the analysis, elastic constants of matrix and inclusion are varied systematically; then the magnitude and position of the maximum stress are shown in tables and the stress distributions along the boundary are shown in figures. For any fixed shape, size and elastic constant of inclusions, the relationships between number of inclusions and maximum stress are investigated for several arrangements.