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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 227, Pages 51–60
DOI: https://doi.org/10.36535/0233-6723-2023-227-51-60 (Mi into1217) 		 
Problem of the equilibrium of a two-dimensional elastic body with two contacting thin rigid inclusions

N. P. Lazareva, V. A. Kovtunenkob

a North-Eastern Federal University named after M. K. Ammosov, Yakutsk
b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.36535/0233-6723-2023-227-51-60
Abstract: A new nonlinear mathematical model is proposed that describes the equilibrium of a two-dimensional elastic body with two thin rigid inclusions. The problem is formulated as a minimizing problem for the energy functional over a nonconvex set of possible displacements defined in a suitable Sobolev space. The existence of a variational solution to the problem is proved. Optimality conditions and differential relations are obtained that characterize the properties of the solution in the domain and on the inclusion; these conditions are satisfied for sufficiently smooth solutions.
Keywords: crack, rigid inclusion, nonpenetration condition, variational problem
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-881
FSRG-2023-0025
This work was supported by the Ministry of Education and Science of the Russian Federation (project Nos. 075-02-2022-881 and FSRG-2023-0025).
Document Type: Article
UDC: 51-72, 517.97
MSC: 35A15, 74B99
Language: Russian
Citation: N. P. Lazarev, V. A. Kovtunenko, “Problem of the equilibrium of a two-dimensional elastic body with two contacting thin rigid inclusions”, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 227, VINITI, Moscow, 2023, 51–60
Citation in format AMSBIB
\Bibitem{LazKov23}
\by N.~P.~Lazarev, V.~A.~Kovtunenko
\paper Problem of the equilibrium of a two-dimensional elastic body with two contacting thin rigid inclusions
\inbook Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 227
\pages 51--60
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1217}
\crossref{https://doi.org/10.36535/0233-6723-2023-227-51-60}
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