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Optimal Control of the Location of a Thin Rigid Inclusion in the Equilibrium Problem of an Inhomogeneous Two-Dimensional Body with a Crack

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Abstract

Under study is some two-dimensional model describing equilibriumof 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.

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Authors and Affiliations

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

    N. P. Lazarev & G. M. Semenova

Authors
  1. N. P. Lazarev
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  2. G. M. Semenova
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Correspondence to N. P. Lazarev or G. M. Semenova.

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Russian Text © N.P. Lazarev, G.M. Semenova, 2019, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2019, Vol. XXII, No. 1, pp. 53–62.

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Lazarev, N.P., Semenova, G.M. Optimal Control of the Location of a Thin Rigid Inclusion in the Equilibrium Problem of an Inhomogeneous Two-Dimensional Body with a Crack. J. Appl. Ind. Math. 13, 76–84 (2019). https://doi.org/10.1134/S1990478919010095

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  • DOI: https://doi.org/10.1134/S1990478919010095

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