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

This article is cited in 7 scientific papers (total in 7 papers)

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.

Full text: PDF file (186 kB)
References: PDF file   HTML file
UDC: 539.311
Received: 29.02.2012
Received in revised form: 10.06.2012
Accepted: 20.09.2012
Language:

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
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  mathscinet
    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  mathnet  crossref
    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  mathnet  crossref  crossref  mathscinet  elib
    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  mathnet  crossref  crossref
    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  mathnet  crossref  crossref  elib
    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  crossref  mathscinet  isi  scopus
    7. N. A. Nikolaeva, “O ravnovesii uprugikh tel s treschinami, peresekayuschimi tonkie vklyucheniya”, Sib. zhurn. industr. matem., 22:4 (2019), 68–80  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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