Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2012, Number 6, Pages 26–32 (Mi vmumm542)  
This article is cited in 5 scientific papers (total in 5 papers)

Mechanics

General solutions of weakened equations in terms of stresses in the theory of elasticity

D. V. Georgievskii

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (254 kB) Citations (5)
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Abstract: The general solutions of some weakened systems of equations in terms of stresses in isotropic elasticity are analyzed. These systems which are not equivalent to the classic one, involve (besides the equilibrium equations) only three of six compatibility equations, namely either diagonal or off-diagonal ones. An equivalence of the formulations of quasistatic boundary-value problems in elasticity in terms of stresses based on such systems is discussed.
Key words: elasticity, problem in terms of stresses, compatibility equations, Kröner tensor, equivalence, general solution, parametrization.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00020а
11-01-00181а
12-01-00789а
Received: 15.02.2012
English version:
Moscow University Mechanics Bulletin, 2013, Volume 68, Issue 1, Pages 1–7
DOI: https://doi.org/10.3103/S0027133013010019
Bibliographic databases:
Document Type: Article
UDC: 539.3
Language: Russian
Citation: D. V. Georgievskii, “General solutions of weakened equations in terms of stresses in the theory of elasticity”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 6, 26–32; Moscow University Mechanics Bulletin, 68:1 (2013), 1–7
Citation in format AMSBIB
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\by D.~V.~Georgievskii
\paper General solutions of weakened equations in terms of stresses in the theory of elasticity
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 6
\pages 26--32
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\transl
\jour Moscow University Mechanics Bulletin
\yr 2013
\vol 68
\issue 1
\pages 1--7
\crossref{https://doi.org/10.3103/S0027133013010019}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874900608}
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