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Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 4, Pages 107–120
DOI: https://doi.org/10.33048/sibjim.2019.22.411
(Mi sjim1070)
 

This article is cited in 4 scientific papers (total in 4 papers)

On the equilibrium of a two-layer elastic structure with a crack

I. V. Frankina

Lavrentyev Institute of Hydrodynamics SB RAS, pr. Akad. Lavrentyeva 15, 630090 Novosibirsk
Full-text PDF (332 kB) Citations (4)
References:
Abstract: Under study is some problem concerning the equilibrium of a two-layer structure whose layers are some elastic plates. The upper layer is glued to the lower one along a part of the edge. The behavior of the plates is modelled in the framework of the plane theory of elasticity. Along the gluing line in the lower layer, there is a crack crossing the external boundary at zero angle. On the crack faces, the nonlinear boundary conditions are imposed that exclude their mutual penetration. The solvability of the equilibrium problem is considered as well as the behavior of the solution in the case when the elasticity moduli of upper plate tend to zero or to infinity.
Keywords: two-layer structure, crack, nonpenetration condition, fictitious domain method, variational inequality.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10007_мк
The author is supported by the Russian Foundation for Basic Research (project no. 18-29-10007).
Received: 10.07.2019
Revised: 10.07.2019
Accepted: 05.09.2019
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 4, Pages 629–641
DOI: https://doi.org/10.1134/S1990478919040069
Document Type: Article
UDC: 539.311:517.958
Language: Russian
Citation: I. V. Frankina, “On the equilibrium of a two-layer elastic structure with a crack”, Sib. Zh. Ind. Mat., 22:4 (2019), 107–120; J. Appl. Industr. Math., 13:4 (2019), 629–641
Citation in format AMSBIB
\Bibitem{Fan19}
\by I.~V.~Frankina
\paper On the equilibrium of a two-layer elastic structure with a crack
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 4
\pages 107--120
\mathnet{http://mi.mathnet.ru/sjim1070}
\crossref{https://doi.org/10.33048/sibjim.2019.22.411}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 4
\pages 629--641
\crossref{https://doi.org/10.1134/S1990478919040069}
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  • https://www.mathnet.ru/eng/sjim/v22/i4/p107
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский журнал индустриальной математики
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