The state of stress of bi-material plate with an elliptic hole

Abstract

Problems of elasticity for composite materials with holes, cracks and inclusions have a great practical significance for mechanics, physics and other fields of science. The plane problem (plane strain or plane stress) for bi-material plate with elliptic hole is considered. On the boundary of the hole an external load is applied. At infinity constant stresses are given. The proximity of the hole to interface renders essential influence on the magnitude of stresses near the hole and on the interface. For engineering applications it is important to know fields of stresses and displacements. The method of Kolosov-Muskhelishvili complex potentials and the method of superposition are used for the solution of the problem. As a special case of the considered problem the solution of problem of an elliptic hole in a halfplane is represented.