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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Volume 62, Issue 5, Pages 208–216
DOI: https://doi.org/10.15372/PMTF20210520 (Mi pmtf123) 		 
Group analysis of the ideal plasticity equations

S. I. Senashova, O. V. Gomonovaa, O. N. Cherepanovab

a Reshetnev Siberian State University of Science and Technology, 660037, Krasnoyarsk, Russia
b Siberian Federal University, Krasnoyarsk, 660041, Krasnoyarsk, Russia
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DOI: https://doi.org/10.15372/PMTF20210520
Abstract: The problem of constructing exact solutions of the von Mises three-dimensional plasticity equations based on the group of continuous transformations admitted by the equations (Annin's problem). New classes of solutions of the three-dimensional plasticity equations are given. The problem of compression of an elastoplastic material layer by rigid plates is solved. In this case, the material obeys the exponential plasticity condition, proposed by Annin.
Keywords: ideal plasticity, exact solutions, conservation laws, elastoplastic problem.
Funding agency Grant number
Krasnoyarsk Mathematical Center 075-02-2021-1384
Received: 23.06.2021
Revised: 23.06.2021
Accepted: 28.06.2021
English version:
Journal of Applied Mechanics and Technical Physics, 2021, Volume 62, Issue 5, Pages 882–889
DOI: https://doi.org/10.1134/S0021894421050205
Bibliographic databases:
Document Type: Article
UDC: 539.374
Language: Russian
Citation: S. I. Senashov, O. V. Gomonova, O. N. Cherepanova, “Group analysis of the ideal plasticity equations”, Prikl. Mekh. Tekh. Fiz., 62:5 (2021), 208–216; J. Appl. Mech. Tech. Phys., 62:5 (2021), 882–889
Citation in format AMSBIB
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\by S.~I.~Senashov, O.~V.~Gomonova, O.~N.~Cherepanova
\paper Group analysis of the ideal plasticity equations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2021
\vol 62
\issue 5
\pages 208--216
\mathnet{http://mi.mathnet.ru/pmtf123}
\crossref{https://doi.org/10.15372/PMTF20210520}
\elib{https://elibrary.ru/item.asp?id=46709913}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2021
\vol 62
\issue 5
\pages 882--889
\crossref{https://doi.org/10.1134/S0021894421050205}
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