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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 1, Pages 11–15
DOI: https://doi.org/10.33048/SIBJIM.2020.23.102 (Mi sjim1073) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Group analysis and exact solutions of the dynamic equations of plane strain of an incompressible nonlinearly elastic body

B. D. Annina, V. D. Bondar'b, S. I. Senashovc

a Lavrentyev Institute of Hydrodynamics SB RAS, pr. Akad. Lavrentieva 15, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
c Reshetnev Siberian State University of Science and Technology, pr. Krasnoyarskii rabochii 31, Krasnoyarsk 660037, Russia
Full-text PDF (459 kB) Citations (4)
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.102
Abstract: Under study is the plane strain dynamics of an incompressible body in the framework of a nonlinear model of elasticity which uses the actual state variables. We obtain some system of nonlinear equations for displacement and pressure, give the exact solutions of the equations by using group analysis, and indicate the area of the possible application of these solutions.
Keywords: nonlinear elasticity model, group analysis, invariant solutions.
Received: 26.08.2019
Revised: 26.08.2019
Accepted: 05.09.2019
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 1, Pages 6–8
DOI: https://doi.org/10.1134/S1990478920010020
Document Type: Article
UDC: 539.3
Language: Russian
Citation: B. D. Annin, V. D. Bondar', S. I. Senashov, “Group analysis and exact solutions of the dynamic equations of plane strain of an incompressible nonlinearly elastic body”, Sib. Zh. Ind. Mat., 23:1 (2020), 11–15; J. Appl. Industr. Math., 14:1 (2020), 6–8
Citation in format AMSBIB
\Bibitem{AnnBonSen20}
\by B.~D.~Annin, V.~D.~Bondar', S.~I.~Senashov
\paper Group analysis and exact solutions of the dynamic equations of plane strain of an incompressible nonlinearly elastic body
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 1
\pages 11--15
\mathnet{http://mi.mathnet.ru/sjim1073}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.102}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 1
\pages 6--8
\crossref{https://doi.org/10.1134/S1990478920010020}
Linking options:
  • https://www.mathnet.ru/eng/sjim1073
  • https://www.mathnet.ru/eng/sjim/v23/i1/p11
    • This publication is cited in the following 4 articles:
    1. Sergei I. Senashov, Irina L. Savostyanova, Olga N. Cherepanova, “Solving cauchy problem for elasticity equations in a plane dynamic case”, Zhurn. SFU. Ser. Matem. i fiz., 18:1 (2025), 71–80  mathnet
    2. S. I. Senashov, I. L. Savostyanova, “Solution of the problem of compression of a two-layer nonlinear material”, J. Appl. Mech. Tech. Phys., 64:4 (2023), 712–714  mathnet  crossref  crossref  elib
    3. S. I. Senashov, I. L. Savostyanova, “Ispolzovanie zakonov sokhraneniya dlya resheniya kraevykh zadach sistemy Moisila — Teodoresku”, Sib. zhurn. industr. matem., 25:2 (2022), 101–109  mathnet  crossref  mathscinet
    4. S. I. Senashov, I. L. Savostyanova, “Using Conservation Laws to Solve Boundary Value Problems for the Moisil–Theodoresco System”, J. Appl. Ind. Math., 16:2 (2022), 349  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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