Interaction between elliptical and ellipsoidal inclusions under bending stress fields

This paper deals with interaction problems of elliptical and ellipsoidal in clusions under bending, using singular integral equations of the body force method. The problems are formulated as a system of singular integral equat ions with Cauchy-type or logarithmic-type singularities, where unknown func tions are densities of body forces distributed in the x,y and r, theta, z d irections in infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy the boundary conditions alon g the elliptical and the ellipsoidal boundaries, the unknown functions are approximated by a linear combination of fundamental density functions and p olynomials. The present method is found to yield the exact solutions for a single elliptical or spherical inclusion under a bending stress field. It y ields rapidly converging numerical results for interface stresses in the in teraction of inclusions.