Optimal control of thin elastic inclusion in an elastic body

The article deals with the inverse problem of the location of a thin elastic inclusion in an elastic body. A thin inclusion is considered to be soldered. The body is fixed on one part of the outer border, while external surface forces act on the other part. The inverse problem of identification of the inclusion is considered as the problem of minimizing the target functional. The existence of a solution to the inverse problem is proved. The first variations of the solution of the direct problem with respect to the shape of the domain and the derivative of the functional with respect to the shape are calculated. A numerical algorithm for solving this problem is proposed and numerical results are presented.