On an approach to the solution of the problem for elastic plane with infinite piece homogeneous inclusion

The problem is solved for an elastic plane containing an infinite piecewise homogeneous elastic inclusion of a sufficiently small constant thickness. The inclusion consists of two semi-infinite and one finite pieces with different elastic properties. The problem is reduced to solving a system of Fredholm integral equations of the second kind with respect to tangential stresses acting on the finite and semi-infinite sections of the contact between the inclusion and the plane. It is shown that for almost all possible values of elastic and geometric characteristics, the solution of the problem can be obtained by the method of successive approximations.