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 J. Sib. Fed. Univ. Math. Phys., 2021, Volume 14, Issue 1, Pages 28–41 (Mi jsfu888)

On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a Kirchhoff-Love plate with a crack

Nyurgun P. Lazarev, Galina M. Semenova, Natalya A. Romanova

North-Eastern Federal University, Yakutsk, Russian Federation

Abstract: The paper considers equilibrium models of Kirchhoff-Love plates with rigid inclusions of two types. The first type of inclusion is described by three-dimensional sets, the second one corresponds to a cylindrical rigid inclusion, which is perpendicular to the plate's median plane in the initial state. For both models, we suppose that there is a through crack along a fixed part of the inclusion's boundary. On the crack non-penetration conditions are prescribed which correspond to a certain known configuration bending near the crack. The uniqueness solvability of a new problems for a Kirchhoff-Love plate with a flat rigid inclusion is proved. It is proved that when a thickness parameter tends to zero, the problem for a flat rigid inclusion can be represented as a limiting task for a family of variational problems concerning the inclusions of the first type. A solvability of an optimal control problem with a control given by the size of inclusions is proved.

Keywords: variational problem, crack, limit passage, nonpenetration condition, optimal control problem.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-29-10007_ìê Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1543/1 The first author's work was supported by the Russian Foundation for Basic Research (grant no. 18-29-10007-mk), the 2nd author's work was supported the Ministry of science and higher education of the Russian Federation, supplementary agreement no. 075-02-2020-1543/1, April 29, 2020.

DOI: https://doi.org/10.17516/1997-1397-2021-14-1-28-41

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UDC: 517.9
Accepted: 20.09.2020
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Citation: Nyurgun P. Lazarev, Galina M. Semenova, Natalya A. Romanova, “On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a Kirchhoff-Love plate with a crack”, J. Sib. Fed. Univ. Math. Phys., 14:1 (2021), 28–41

Citation in format AMSBIB
\Bibitem{LazSemRom21} \by Nyurgun~P.~Lazarev, Galina~M.~Semenova, Natalya~A.~Romanova \paper On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a Kirchhoff-Love plate with a crack \jour J. Sib. Fed. Univ. Math. Phys. \yr 2021 \vol 14 \issue 1 \pages 28--41 \mathnet{http://mi.mathnet.ru/jsfu888} \crossref{https://doi.org/10.17516/1997-1397-2021-14-1-28-41} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000615268200004} 

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This publication is cited in the following articles:
1. N. P. Lazarev, E. F. Sharin, G. M. Semenova, “Optimalnoe upravlenie raspolozheniem tochki sharnirnogo soedineniya zhestkikh vklyuchenii v zadache o ravnovesii plastiny Timoshenko”, Chelyab. fiz.-matem. zhurn., 6:3 (2021), 278–288
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