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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 10, Pages 1714–1727
DOI: https://doi.org/10.31857/S004446690003590-0 (Mi zvmmf10797) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Equilibrium of an elastic body with closely spaced thin inclusions

A. M. Khludnevab

a Lavrentiev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Citations (2)
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DOI: https://doi.org/10.31857/S004446690003590-0
Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.
Key words: thin inclusion, crack, boundary conditions of mutual nonpenetration, stiffness of inclusion, limiting models.
Received: 13.02.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 10, Pages 1660–1672
DOI: https://doi.org/10.1134/S096554251810007X
Bibliographic databases:
Document Type: Article
UDC: 517.958+539.3
Language: Russian
Citation: A. M. Khludnev, “Equilibrium of an elastic body with closely spaced thin inclusions”, Zh. Vychisl. Mat. Mat. Fiz., 58:10 (2018), 1714–1727; Comput. Math. Math. Phys., 58:10 (2018), 1660–1672
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf10797
  • https://www.mathnet.ru/eng/zvmmf/v58/i10/p1714
    • This publication is cited in the following 2 articles:
    1. N. A. Nikolaeva, “Zadacha o ravnovesii uprugogo tela s treschinoi i tonkimi vklyucheniyami, kotorye sopryazheny mezhdu soboi”, Dalnevost. matem. zhurn., 24:1 (2024), 73–95  mathnet  crossref
    2. A. M. Khludnev, “Inverse problems for elastic body with closely located thin inclusions”, Z. Angew. Math. Phys., 70:5 (2019), 134  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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