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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 188, Pages 43–53
DOI: https://doi.org/10.36535/0233-6723-2020-188-43-53 (Mi into739) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Method of asymptotic splitting in dynamical problems of the spatial theory of elasticity

S. K. Golushkoab, G. L. Goryninc, A. G. Gorynina

a Novosibirsk State University
b Institute of Computational Technologies, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Surgut State University
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DOI: https://doi.org/10.36535/0233-6723-2020-188-43-53
Abstract: In this paper, we apply the method of asymptotic splitting to dynamical problems of the spatial theory of elasticity, whose equations contain a small parameter, and obtain asymptotic solutions. Two-dimensional and one-dimensional boundary-value problems arising in the process of asymptotic splitting allow obtaining analytical solutions in some special cases. In the general case, they can be solved numerically by the collocation method, the method of least squares, and the finite-element method.
Keywords: spatial theory of elasticity, dynamical problem, method of asymptotic splitting, collocation method, method of least squares, finite element method, layered beam, free oscillations.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-18029
This work was supported by the Russian Foundation for Basic Research (project No. 18-29-18029).
Document Type: Article
UDC: 517.955.8, 539.3
MSC: 35Q74, 74H10
Language: Russian
Citation: S. K. Golushko, G. L. Gorynin, A. G. Gorynin, “Method of asymptotic splitting in dynamical problems of the spatial theory of elasticity”, Differential Equations and Mathematical Modeling, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 188, VINITI, Moscow, 2020, 43–53
Citation in format AMSBIB
\Bibitem{GolGorGor20}
\by S.~K.~Golushko, G.~L.~Gorynin, A.~G.~Gorynin
\paper Method of asymptotic splitting in dynamical problems of the spatial theory of elasticity
\inbook Differential Equations and Mathematical Modeling
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 188
\pages 43--53
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into739}
\crossref{https://doi.org/10.36535/0233-6723-2020-188-43-53}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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