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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2016, Volume 158, Book 3, Pages 322–335 (Mi uzku1371)  

Mixed finite element method for nonclassical boundary value problems of shallow shell theory

M. M. Karchevsky

Kazan Federal University, Kazan, 420008 Russia

Abstract: The necessary and sufficient conditions for the solvability of the variational problems of the geometrically and physically nonlinear shallow shell theory by nonclassical boundary conditions modeling the rigid contact of the shell boundary or the normal load in the tangent plane on the shell boundary are obtained. The mixed finite element schemes for approximate solving of these problems are constructed. The solvability conditions for the corresponding discrete problems are deduced. The convergence of the approximate solutions by refinement of the domain triangulation is proved.

Keywords: shallow shell, variational problem, solvability conditions, mixed finite element method, convergence of approximate solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-05686
15-41-02315
15-41-02569
This study was supported by the Russian Foundation for Basic Research (projects nos. 15-01-05686, 15-41-02315, 15-41-02569).


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Bibliographic databases:

Document Type: Article
UDC: 519.68
Received: 14.06.2016

Citation: M. M. Karchevsky, “Mixed finite element method for nonclassical boundary value problems of shallow shell theory”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 158, no. 3, Kazan University, Kazan, 2016, 322–335

Citation in format AMSBIB
\Bibitem{Kar16}
\by M.~M.~Karchevsky
\paper Mixed finite element method for nonclassical boundary value problems of shallow shell theory
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2016
\vol 158
\issue 3
\pages 322--335
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1371}
\elib{http://elibrary.ru/item.asp?id=27707612}


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