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.
Citation:
N. P. Lazarev, G. M. Semenova, “Optimal control of the location of a thin rigid inclusion in the equilibrium problem of an inhomogeneous two-dimensional body with a crack”, Sib. Zh. Ind. Mat., 22:1 (2019), 53–62; J. Appl. Industr. Math., 13:1 (2019), 76–84
\Bibitem{LazSem19}
\by N.~P.~Lazarev, G.~M.~Semenova
\paper Optimal control of the location of a thin rigid inclusion in the equilibrium problem of an inhomogeneous two-dimensional body with a crack
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 1
\pages 53--62
\mathnet{http://mi.mathnet.ru/sjim1032}
\crossref{https://doi.org/10.33048/sibjim.2019.22.106}
\elib{https://elibrary.ru/item.asp?id=38692166}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 1
\pages 76--84
\crossref{https://doi.org/10.1134/S1990478919010095}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064949494}
Linking options:
https://www.mathnet.ru/eng/sjim1032
https://www.mathnet.ru/eng/sjim/v22/i1/p53
This publication is cited in the following 2 articles:
N. P. Lazarev, G. M. Semenova, “Equilibrium problem for a Timoshenko plate
with a geometrically nonlinear condition of nonpenetration
for a vertical crack”, J. Appl. Industr. Math., 14:3 (2020), 532–540
N. Lazarev, N. Romanova, G. Semenova, “Optimal location of a thin rigid inclusion for a problem describing equilibrium of a composite timoshenko plate with a crack”, J. Inequal. Appl., 2020:1 (2020), 29
Citation in format AMSBIB
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