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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 11, Pages 12–22 (Mi ivm8390)  
This article is cited in 4 scientific papers (total in 4 papers)

Mathematical modeling of the stress state of a transverse plastic layer in a round rod

T. V. Eroshkina, V. L. Dil'man

Chair of Higher Mathematics, Southern Ural State University, Chelyabinsk, Russia
Full-text PDF (247 kB) Citations (4)
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Abstract: We construct mathematical models of the plastic deformation of a continuous round rod containing a transverse (less strong) inhomogeneous layer under an axial load. We study the obtained models by analytical and numerical methods. We thoroughly study the local strengthening of such layers by involving the base material of the rod in the plastic deformation process. We obtain explicit formulas for the critical stress states in the layer and the critical axial load on the rod.
Keywords: less strong layer, plastic deformation, local strengthening, system of hyperbolic partial differential equations.
Received: 08.09.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 11, Pages 9–17
DOI: https://doi.org/10.3103/S1066369X11110028
Bibliographic databases:
Document Type: Article
UDC: 517.958+539.4
Language: Russian
Citation: T. V. Eroshkina, V. L. Dil'man, “Mathematical modeling of the stress state of a transverse plastic layer in a round rod”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 11, 12–22; Russian Math. (Iz. VUZ), 55:11 (2011), 9–17
Citation in format AMSBIB
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\by T.~V.~Eroshkina, V.~L.~Dil'man
\paper Mathematical modeling of the stress state of a~transverse plastic layer in a~round rod
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 11
\pages 12--22
\mathnet{http://mi.mathnet.ru/ivm8390}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2963175}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 11
\pages 9--17
\crossref{https://doi.org/10.3103/S1066369X11110028}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84856251167}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:24
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