# Optimal location of a rigid inclusion for an equilibrium problem describing Kirchhoff-Love plate with nonpenetration conditions for known configurations of plate edges

### Abstract

A nonlinear model describing equilibrium of a cracked plate with a volume rigid inclusion is studied. It is assumed that under the action of certain given loads, plates have deformations with a certain predetermined configuration of edges near the crack. On the crack curve we impose a nonlinear boundary condition as a system of inequalities and an equality describing the nonpenetration of the opposite crack faces. For a family of variational problems, we study the dependence of their solutions on the location of the inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on a suitable Sobolev space. For this problem, the location parameter of the inclusion serves as a control parameter. We prove continuous dependence of the solutions on the location parameter and the existence of a solution to the optimal control problem.

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*Mathematical notes of NEFU*, 28(2), pp. 16-33. Available at: https://mzsvfu.ru/index.php/mz/article/view/optimal-location-of-arigid-inclusion (Accessed: 13August2024).

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