Interaction of an elliptic hole with interface of two bonded half-planes

Abstract

The problems of elasticity for composite materials with the holes and inclusions have a great practical significance for mechanics, physics and other fields of science. The analytic solution of a plane problem (plane strain or plane stress) for a bi-material plate with elliptic hole is obtained. A hole is located entirely in the lower half-plane. The stresses and the angles of rotation are given at infinity, on the boundary of the hole where an external load is applied. The methods of Kolosov–Muskhelishvili complex potentials, conformal mapping and superposition were used for solution to the problem. The affinity of a hole to an interface makes essential influence on value of stresses in a vicinity of a hole and also on value of stresses at an interface. For engineering applications it is important to know the fields of the stresses and displacements so as to estimate influence of a hole on strength of bonding. Special cases of these problems follow the solutions of problems on an elliptic hole in a half-plane, about an inclined crack in a bi-material plane and half-plane and a some others. Refs 19. Figs 2.