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Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 4, Pages 89–94
DOI: https://doi.org/10.33048/sibjim.2019.22.409 (Mi sjim1068) 		 
This article is cited in 4 scientific papers (total in 4 papers)

New solutions of dynamic equations of ideal plasticity

S. I. Senashov, I. L. Savostyanova

Reshetnev Siberian State University of Science and Technology, pr. Krasnoyarskii rabochii 31, 660037 Krasnoyarsk
Full-text PDF (277 kB) Citations (4)
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DOI: https://doi.org/10.33048/sibjim.2019.22.409
Abstract: Point symmetries allowed by plasticity equations in the dynamical case are used to construct solutions for the dynamical equations of ideal plasticity. These symmetries make it possible to convert the exact solutions of stationary dynamical equations to nonstationary solutions. The so-constructed solutions include arbitrary functions of time. The solutions allow us to describe the plastic flow between the plates changing their shape under the action of dynamical loads. Some new spatial self-similar solution is also presented.
Keywords: ideal plasticity, exact solution, symmetry.
Received: 12.07.2019
Revised: 12.07.2019
Accepted: 05.09.2019
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 4, Pages 740–745
DOI: https://doi.org/10.1134/S199047891904015X
Document Type: Article
UDC: 539.374
Language: Russian
Citation: S. I. Senashov, I. L. Savostyanova, “New solutions of dynamic equations of ideal plasticity”, Sib. Zh. Ind. Mat., 22:4 (2019), 89–94; J. Appl. Industr. Math., 13:4 (2019), 740–745
Citation in format AMSBIB
\Bibitem{SenSav19}
\by S.~I.~Senashov, I.~L.~Savostyanova
\paper New solutions of dynamic equations of ideal plasticity
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 4
\pages 89--94
\mathnet{http://mi.mathnet.ru/sjim1068}
\crossref{https://doi.org/10.33048/sibjim.2019.22.409}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 4
\pages 740--745
\crossref{https://doi.org/10.1134/S199047891904015X}
Linking options:
  • https://www.mathnet.ru/eng/sjim1068
  • https://www.mathnet.ru/eng/sjim/v22/i4/p89
    • This publication is cited in the following 4 articles:
    1. Sergey I. Senashov, Alexander Yakhno, “Dissimilar subalgebras of symmetry algebra of plasticity equations”, Journal of Symbolic Computation, 127 (2025), 102358  crossref
    2. I. M. Tsvetkov, “Dynamic Regimes of Biaxial Stretching of a Thin Ideally Rigid-Plastic Rectangular Plate”, Mech. Solids, 58:7 (2023), 2656  crossref
    3. I. M. Tsvetkov, “Dynamic Regimes of Biaxial Stretching of a Thin Ideally Rigid-Plastic Rectangular Plate”, Prikladnaya matematika i mekhanika, 87:4 (2023), 684  crossref
    4. S. I. Senashov, O. V. Gomonova, O. N. Cherepanova, I. L. Savostyanova, “New Classes of Solutions of Dynamical Problems of Plasticity”, J. Sib. Fed. Univ.-Math. Phys., 13:6 (2020), 792–796  mathnet  crossref  mathscinet  zmath  isi  scopus
    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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