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Sib. Zh. Ind. Mat., 2020, Volume 23, Number 1, Pages 11–15 (Mi sjim1073)  

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

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.

DOI: https://doi.org/10.33048/SIBJIM.2020.23.102

Full text: PDF file (459 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 539.3
Received: 26.08.2019
Revised: 26.08.2019
Accepted:05.09.2019

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

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}


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