On a limiting passage in the conjugation thin inclusions problem in elastic bodies.

In the paper, an equilibrium problem for an elastic body with a crack crossing a thin inclusion at some point is analyzed. As a result, the crack divides the inclusion of two parts. One part of the inclusion is a rigid and the other is an elastic. The elastic inclusion is modeled by a Bernoulli – Euler beam. The conjugation conditions of these inclusions at a given point are considered. To exclude a mutual penetration between inclusions, inequality type boundary conditions are imposed. Nonlinear boundary conditions are also considered at the crack faces.The main goal of the paper is to justify a passage to the limit as the rigidity parameter of the thin inclusion goes to infinity. [ABSTRACT FROM AUTHOR]