Inverse problem for elastic body with thin elastic inclusion

An inverse problem for an elastic body with a thin elastic inclusion is investigated. It is assumed that the inclusion crosses the external boundary of the elastic body. A connection between the inclusion and the elastic body is characterized by the damage parameter. We study a dependence of the solutions on the damage parameter. In particular, passages to infinity and to zero of the damage parameter are investigated. Limit models are analyzed. Assuming that the damage and rigidity parameters of the model are unknown, inverse problems are formulated. Sufficient conditions for the inverse problems to have solutions are found. Estimates concerning solutions of the inverse problem are established.

The boundary value problem for piezo-electric half space with thin elastic inclusion

The problem of finding mechanical and electric fields in a piezo-elastic half-space with elastic inclusion is considered. The inclusion is loaded with forces of constant intensity. The tangential contact stresses along the contact surface are determined and the behavior of the contact stresses in the neighborhood of singular points is established. By using methods of the theory of analytic functions, the problem is reduced to a singular integro-differential equation in a finite interval. Using an integral transformation a Riemann problem is obtained, and the solution is presented in its explicit form.