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 Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 300–308 (Mi semr587)

Differentical equations, dynamical systems and optimal control

Optimal control of tilt angles in equilibrium problems for the Timoshenko plate with a oblique crack

N. P. Lazarev, N. V. Neustroeva, N. A. Nikolaeva

North-Eastern Federal University, Belinsky, 58, 677891, Yakutsk, Russia

Abstract: We consider an equilibrium problem of an elastic plate with a flat oblique crack (cut). Nonpenetration conditions on the crack faces are given in the form of inequalities. We investigate the dependence of the solution and energy functional with respect to variations of the crack's tilt angle. The existence of the solution to the optimal control problem is proved. For that problem the cost functional is defined by derivatives of a energy functional along the crack perturbation parameter and the crack's tilt angle is chosen as the control function.

Keywords: oblique crack, optimal control, plate, variational inequality.

DOI: https://doi.org/10.17377/semi.2015.12.024

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UDC: 517.977
MSC: 49J21
Received April 27, 2015, published May 20, 2015

Citation: N. P. Lazarev, N. V. Neustroeva, N. A. Nikolaeva, “Optimal control of tilt angles in equilibrium problems for the Timoshenko plate with a oblique crack”, Sib. Èlektron. Mat. Izv., 12 (2015), 300–308

Citation in format AMSBIB
\Bibitem{LazNeuNik15} \by N.~P.~Lazarev, N.~V.~Neustroeva, N.~A.~Nikolaeva \paper Optimal control of tilt angles in equilibrium problems for the Timoshenko plate with a oblique crack \jour Sib. \Elektron. Mat. Izv. \yr 2015 \vol 12 \pages 300--308 \mathnet{http://mi.mathnet.ru/semr587} \crossref{https://doi.org/10.17377/semi.2015.12.024} `

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This publication is cited in the following articles:
1. E. V. Pyatkina, “Optimal control of the shape of a layer shape in the equilibrium problem of elastic bodies with overlapping domains”, J. Appl. Industr. Math., 10:3 (2016), 435–443
2. E. V. Pyatkina, “On control problem for two-layers elastic body with a crack”, J. Math. Sci., 230:1 (2018), 159–166
3. I. V. Fankina, “Optimalnoe upravlenie razmerom zhestkogo sloya konstruktsii”, Sib. zhurn. chist. i prikl. matem., 17:3 (2017), 86–97
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