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Sibirskii Zhurnal Industrial'noi Matematiki, 2018, Volume 21, Number 2, Pages 66–78
DOI: https://doi.org/10.17377/sibjim.2018.21.206
(Mi sjim1000)
 

This article is cited in 8 scientific papers (total in 8 papers)

Problems on thin inclusions in a two-dimensional viscoelastic body

T. S. Popova

North-Eastern Federal University, 58 Belinskogo str., 677000 Yakutsk
Full-text PDF (258 kB) Citations (8)
References:
Abstract: Under study are the equilibrium problems for a two-dimensional viscoelastic body with delaminated thin inclusions in the cases of elastic and rigid inclusions. Both variational and differential formulations of the problems with nonlinear boundary conditions are presented; their unique solvability is substantiated. For the case of a thin elastic inclusion modelled as a Bernoulli–Euler beam, we consider the passage to the limit as the rigidity parameter of the inclusion tends to infinity. In the limit it is the problem about a thin rigid inclusion. Relationship is established between the problems about thin rigid inclusions and the previously considered problems about volume rigid inclusions. The corresponding passage to the limit is justified in the case of inclusions without delamination.
Keywords: variational inequality, viscoelasticity, nonpenetration conditions, elastic inclusion, rigid inclusion, thin inclusion, nonlinear boundary conditions.
Received: 23.11.2017
English version:
Journal of Applied and Industrial Mathematics, 2018, Volume 12, Issue 2, Pages 313–324
DOI: https://doi.org/10.1134/S1990478918020114
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: T. S. Popova, “Problems on thin inclusions in a two-dimensional viscoelastic body”, Sib. Zh. Ind. Mat., 21:2 (2018), 66–78; J. Appl. Industr. Math., 12:2 (2018), 313–324
Citation in format AMSBIB
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\by T.~S.~Popova
\paper Problems on thin inclusions in a~two-dimensional viscoelastic body
\jour Sib. Zh. Ind. Mat.
\yr 2018
\vol 21
\issue 2
\pages 66--78
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\crossref{https://doi.org/10.17377/sibjim.2018.21.206}
\elib{https://elibrary.ru/item.asp?id=35459102}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 2
\pages 313--324
\crossref{https://doi.org/10.1134/S1990478918020114}
\elib{https://elibrary.ru/item.asp?id=35484260}
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Linking options:
  • https://www.mathnet.ru/eng/sjim1000
  • https://www.mathnet.ru/eng/sjim/v21/i2/p66
  • This publication is cited in the following 8 articles:
    1. Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal, “Well-posedness of the governing equations for a quasi-linear viscoelastic model with pressure-dependent moduli in which both stress and strain appear linearly”, Z. Angew. Math. Phys., 75:1 (2024)  crossref
    2. 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
    3. N. A. Nikolaeva, “Plastina Kirkhgofa — Lyava s ploskim zhestkim vklyucheniem”, Chelyab. fiz.-matem. zhurn., 8:1 (2023), 29–46  mathnet  crossref
    4. T. S. Popova, “On Numerical Solving of Junction Problem for the Thin Rigid and Elastic Inclusions in Elastic Body”, Lobachevskii J Math, 44:10 (2023), 4143  crossref
    5. Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal, “A generalization of the Kelvin–Voigt model with pressure‐dependent moduli in which both stress and strain appear linearly”, Math Methods in App Sciences, 46:14 (2023), 15641  crossref
    6. Natalia Nikolaeva, “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, 020030  crossref
    7. T. S. Popova, “on Equilibrium of a Two-Dimensional Viscoelastic Body With a Thin Timoshenko Inclusion”, Sib. Electron. Math. Rep., 17 (2020), 1463–1477  mathnet  crossref  mathscinet  zmath  isi  scopus
    8. Tatiana S. Popova, “On numerical solving of junction problem for semirigid and Timoshenko inclusions in elastic body”, Procedia Structural Integrity, 30 (2020), 113  crossref
    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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