Stress analysis of bi-material plane with an elliptic hole by analytical and numerical methods

The problems of elasticity for composite materials with holes and inclusions have a great practical significance for mechanics, physics and other areas of science. In this work the analytic solution of a plane problem (plane strain and plane stress) for bi-material plate with an elliptic hole is obtained. A hole is located entirely in a lower half-plane. The constant stresses are given at infinity and on the boundary of the hole an external load is applied. The methods of Kolosov-Muskhelishvili complex potentials, conformal mapping and superposition are used for the solution of the problem. The affinity of a hole to an interface makes essential influence on value of stresses in a vicinity of a hole and on value of stresses at an interface. For engineering applications it is important to know the fields of the stresses and displacements in order to estimate influence of a hole on strength of structure. From considered problems as special cases follow the solutions of problems about a half-plane with an elliptic hole, about an inclined crack in a bi-material plane and half-plane.