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

• Lazarev Nyurgun P., nyurgun@ngs.ru Северо-Восточный федеральный университет им. М. К. Аммосова, ул. Кулаковского, 48, Якутск 677000
• Sharin Evgenii F., ef.sharin@s-vfu.ru North-Eastern Federal University, 48 Kulakovsky Street, Yakutsk 677000, Russia
• Semenova Galina M., sgm.08@yandex.ru North-Eastern Federal University, 48 Kulakovsky Street, Yakutsk 677000, Russia
Keywords: variational inequality, crack, nonpenetration conditions, optimal control problem, rigid inclusion

### 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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How to Cite
Lazarev, N., Sharin, E. and Semenova, G. (2021) “Optimal location of a rigid inclusion for an equilibrium problem describing Kirchhoff-Love plate with nonpenetration conditions for known configurations of plate edges”, 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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Mathematics