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 J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 1, Pages 53–62 (Mi jsfu288)

An equilibrium problem for the Timoshenko-type plate containing a crack on the boundary of a rigid inclusion

Nyurgun P. Lazarevab

a Institute of Hydrodynamics, SB RAS, Novosibirsk, Russia
b North-Eastern Federal University, Yakutsk, Russia

Abstract: An equilibrium problem for an elastic Timoshenko type plate containing a rigid inclusion is considered. On the interface between the elastic plate and the rigid inclusion, there is a vertical crack. It is assumed that at both crack faces, boundary conditions of inequality type are considered describing a mutual non-penetration of the faces. A solvability of the problem is proved, and a complete system of boundary conditions is found. It is also shown that the problem is the limit one for a family of other problems posed for a wider domain and describing an equilibrium of elastic plates with a vertical crack as the rigidity parameter goes to infinity.

Keywords: crack, Timoshenko-type plate, rigid inclusion, energy functional, mutual non-penetration condition.

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UDC: 539.311
Accepted: 20.09.2012
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Citation: Nyurgun P. Lazarev, “An equilibrium problem for the Timoshenko-type plate containing a crack on the boundary of a rigid inclusion”, J. Sib. Fed. Univ. Math. Phys., 6:1 (2013), 53–62

Citation in format AMSBIB
\Bibitem{Laz13} \by Nyurgun~P.~Lazarev \paper An equilibrium problem for the Timoshenko-type plate containing a~crack on the boundary of a~rigid inclusion \jour J. Sib. Fed. Univ. Math. Phys. \yr 2013 \vol 6 \issue 1 \pages 53--62 \mathnet{http://mi.mathnet.ru/jsfu288} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. V. Shcherbakov, “Existence of an optimal shape for thin rigid inclusions in the Kirchhoff–Love plate”, J. Appl. Industr. Math., 8:1 (2014), 97–105
2. N. P. Lazarev, N. V. Neustroeva, N. A. Nikolaeva, “Optimalnoe upravlenie uglom naklona treschiny v zadache o ravnovesii plastiny Timoshenko”, Sib. elektron. matem. izv., 12 (2015), 300–308
3. N. V. Neustroeva, “An equilibrium problem for an elastic plate with an inclined crack on the boundary of a rigid inclusion”, J. Appl. Industr. Math., 9:3 (2015), 402–411
4. N. P. Lazarev, “Optimal control of the size of rigid inclusion in equilibrium problem for inhomogeneous Timoshenko-type plate with crack”, J. Math. Sci., 228:4 (2018), 409–420
5. V. A. Puris, “The conjugation problem for thin elastic and rigid inclusions in an elastic body”, J. Appl. Industr. Math., 11:3 (2017), 444–452
6. N. Lazarev, N. Neustroeva, “Optimal control of rigidity parameter of elastic inclusions in composite plate with a crack”, Mathematics and Computing (ICMC 2018), Springer Proceedings in Mathematics & Statistics, 253, eds. D. Ghosh, D. Giri, R. Mohapatra, K. Sakurai, E. Savas, T. Som, Springer, 2018, 67–77
7. N. A. Nikolaeva, “O ravnovesii uprugikh tel s treschinami, peresekayuschimi tonkie vklyucheniya”, Sib. zhurn. industr. matem., 22:4 (2019), 68–80
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