This article is cited in 2 papers

Optimal control of the location of a thin rigid inclusion in the equilibrium problem of an inhomogeneous two-dimensional body with a crack

N. P. Lazarev, G. M. Semenova

North-Eastern Federal University, ul. Kulakovskogo 48, 677000 Yakutsk

Abstract: Under study is some two-dimensional model describing equilibrium of a composite solid with a thin rigid inclusion and a crack. A boundary condition of Signorini's type is prescribed on the crack curve. For a family of corresponding variational problems, the dependence is analyzed of their solutions on the parameter characterizing the location of the rigid inclusion. The existence of solution of the optimal control problem is proved. For this problem, the quality functional is defined with the help of an arbitrary continuous functional on the solution space, while the location of the inclusion is chosen as the control parameter.

Keywords: variational inequality, optimal control problem, nonpenetration condition, nonlinear boundary conditions, crack, rigid inclusion.

UDC: 517.97

Received: 12.09.2018
Revised: 12.09.2018
Accepted: 15.12.2018

DOI: 10.33048/sibjim.2019.22.106

 English version: Journal of Applied and Industrial Mathematics, 2019, 13:1, 76–84

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