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Sibirskii Zhurnal Industrial'noi Matematiki, 2009, Volume 12, Number 3, Pages 151–156 (Mi sjim576)  
This article is cited in 1 scientific paper (total in 1 paper)

A Superposition of the Nadai and Prandtl Solutions to the Two-Dimensional Ideal Plasticity System

L. V. Yakhno

Siberian State Aerospace University, Krasnoyarsk
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Abstract: We give a general algorithm for transforming exact solutions to the flat ideal plasticity system of Mises using the superposition principle for solutions, which arises as a corollary to the original system admitting an infinite dimensional symmetry group. As an example we consider a relation between the known exact solutions: the Prandtl solution for a thin layer compressed by rough solid plates, and the Nadai solution for the radial distribution of stresses in a convergent channel in the shape of a flat wedge.
Keywords: flat ideal plasticity, exact solutions to differential equations, superposition principle for solutions, boundary value problem for hyperbolic systems.
Received: 08.12.2008
English version:
Journal of Applied and Industrial Mathematics, 2010, Volume 4, Issue 4, Pages 600–605
DOI: https://doi.org/10.1134/S1990478910040150
Bibliographic databases:
UDC: 539.374
Language: Russian
Citation: L. V. Yakhno, “A Superposition of the Nadai and Prandtl Solutions to the Two-Dimensional Ideal Plasticity System”, Sib. Zh. Ind. Mat., 12:3 (2009), 151–156; J. Appl. Industr. Math., 4:4 (2010), 600–605
Citation in format AMSBIB
\Bibitem{Yak09}
\by L.~V.~Yakhno
\paper A~Superposition of the Nadai and Prandtl Solutions to the Two-Dimensional Ideal Plasticity System
\jour Sib. Zh. Ind. Mat.
\yr 2009
\vol 12
\issue 3
\pages 151--156
\mathnet{http://mi.mathnet.ru/sjim576}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2668793}
\transl
\jour J. Appl. Industr. Math.
\yr 2010
\vol 4
\issue 4
\pages 600--605
\crossref{https://doi.org/10.1134/S1990478910040150}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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