Abstract:
We consider an equilibrium problem for a Kirchhoff–Love elastic plate with an inclined crack on the boundary of a rigid inclusion. The nonpenetration conditions are considered at the crack faces in the form of equalities and inequalities. On the boundary of the rigid inclusion, some identity holds describing the action of the external forces on the rigid part of the plate. The variational statement of the problem is studied, and an equivalent boundary value problem is formulated. For a family of problems about a plate with inclined crack on the boundary, we analyze the passage to the limit as the rigidity parameter of the inclusion tends to infinity.
Citation:
N. V. Neustroeva, “An equilibrium problem for an elastic plate with an inclined crack on the boundary of a rigid inclusion”, Sib. Zh. Ind. Mat., 18:2 (2015), 74–84; J. Appl. Industr. Math., 9:3 (2015), 402–411
\Bibitem{Neu15}
\by N.~V.~Neustroeva
\paper An equilibrium problem for an elastic plate with an inclined crack on the boundary of a~rigid inclusion
\jour Sib. Zh. Ind. Mat.
\yr 2015
\vol 18
\issue 2
\pages 74--84
\mathnet{http://mi.mathnet.ru/sjim884}
\crossref{https://doi.org/10.17377/sibjim.2015.18.208}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3549830}
\elib{https://elibrary.ru/item.asp?id=23598679}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 3
\pages 402--411
\crossref{https://doi.org/10.1134/S1990478915030114}
Linking options:
https://www.mathnet.ru/eng/sjim884
https://www.mathnet.ru/eng/sjim/v18/i2/p74
This publication is cited in the following 5 articles:
Nyurgun Lazarev, Galina Semenova, Evgenii Sharin, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 020002
R. V. Namm, G. I. Tsoi, “Solution of a contact elasticity problem with a rigid inclusion”, Comput. Math. Math. Phys., 59:4 (2019), 659–666
N. P. Lazarev, I. Khiromiti, P. V. Sivtsev, I. M. Tikhonova, “O regulyarnosti resheniya v zadache o ravnovesii plastiny Timoshenko, soderzhaschei naklonnuyu treschinu”, Matematicheskie zametki SVFU, 25:1 (2018), 38–49
N. P. Lazarev, V. V. Everstov, “Optimalnyi razmer vneshnego tonkogo zhestkogo vklyucheniya v nelineinoi zadache o ravnovesii tsilindricheskogo tela s treschinoi”, Matematicheskie zametki SVFU, 24:4 (2017), 37–51
N. P. Lazarev, “Optimalnoe upravlenie razmerom zhestkogo vklyucheniya v zadache o ravnovesii neodnorodnogo trekhmernogo tela s treschinoi”, Matematicheskie zametki SVFU, 23:2 (2016), 51–64
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