# Optimal control of the crack angle in the equilibrium problem for a Timoshenko plate with elastic inclusion

• Neustroeva Natalia V., nnataliav@mail.ru North-Eastern Federal University, Institute of Mathematics and Informatics, 48 Kulakovsky Street, Yakutsk 677000, Russia
• Lazarev Nyurgun P., nyurgun@ngs.ru North-Eastern Federal University, Scientific Research Institute of Mathematics, 58 Belinsky Street, Yakutsk 677891, Russia
Keywords: inclined crack, elastic inclusion, plate, optimal control, Tymoshenko model

### Abstract

Mathematical modeling and research of problems on the deformation of inhomogeneous bodies containing cracks along elastic inclusions involves setting the conjugation conditions at the interface between different materials. Difficulties are associated with the possibility of large stress values appearing near the inclusions. Determining the inhomogeneous bodies with the most optimal parameters is one of the most popular areas of theoretical and experimental research. In this paper, we study the problem of optimal control of the angle of the crack inclination to the median plane in the equilibrium problem for an elastic Timoshenko plate containing an oblique crack at the boundary of an elastic inclusion. The complexity of the problem is due to the fact that the non-penetration condition on the crack faces is given in the form of inequality. The quality functional characterizes the deviation from the specified displacements. We prove solvability of the optimal control problem and establish continuous dependence of the solutions on the value of the crack inclination angle.

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How to Cite
Neustroeva, N. and Lazarev, N. (2022) “Optimal control of the crack angle in the equilibrium problem for a Timoshenko plate with elastic inclusion”, Mathematical notes of NEFU, 28(4), pp. 58-70. doi: https://doi.org/10.25587/SVFU.2021.71.81.005.
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Mathematics