Stress analysis of arbitrarily distributed elliptical inclusions under longitudinal shear loading

This paper deals with an interaction problem of arbitrarily distributed ell iptical inclusions under longitudinal shear loading. The problem is formula ted as a system of singular integral equations with Cauchy-type or logarith mic-type singularities, where unknown functions are the densities of body f orces 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 ki nds of fundamental density functions are introduced in a similar way of pre vious papers treating plane stress problems. Then the body force densities are approximated by a linear combination of those fundamental density funct ions and polynomials. In the analysis, elastic constants of matrix and incl usion are varied systematically; then the magnitude and position of the max imum stress are shown in tables and the stress distributions along the boun dary are shown in figures. For any fixed shape, size and elastic constant o f inclusions, the relationships between number of inclusions and maximum st ress are investigated for several arrangements.