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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 5, Pages 49–61 (Mi ivm8999)  
This article is cited in 7 scientific papers (total in 7 papers)

Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges

S. N. Timergaliev, A. N. Uglov, L. S. Kharasova

Chair of Mathematics, Naberezhnye Chelny Branch of Kazan Federal University, 68/19 Mira Ave., Naberezhnye Chelny, 423810 Russia
Full-text PDF (241 kB) Citations (7)
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Abstract: We study the solvability of a geometrically nonlinear, physically linear boundary-value problems for elastic shallow homogeneous isotropic shells with pivotally supported edges in the framework of S. P. Timoshenko's shear model. The purpose of work is the proof of the theorem on existence of solutions. Research method consists in reducing the original system of equilibrium equations to one nonlinear differential equation for the deflection. The method is based on integral representations for displacements, which are built with the help of the general solutions of the nonhomogeneous Cauchy–Riemann equation. The solvability of equation relative to deflection is established with the use of principle of contraction mappings.
Keywords: Timoshenko type shell, equilibrium equations system, boundary-value problem, generalized shifts, generalized problem solution, integral images, Sobolev spaces, operator, integral equations, holomorphic functions existence theorem.
Received: 28.11.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 5, Pages 41–51
DOI: https://doi.org/10.3103/S1066369X15050060
Bibliographic databases:
Document Type: Article
UDC: 517.958+539.3
Language: Russian
Citation: S. N. Timergaliev, A. N. Uglov, L. S. Kharasova, “Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 5, 49–61; Russian Math. (Iz. VUZ), 59:5 (2015), 41–51
Citation in format AMSBIB
\Bibitem{TimUglKha15}
\by S.~N.~Timergaliev, A.~N.~Uglov, L.~S.~Kharasova
\paper Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 5
\pages 49--61
\mathnet{http://mi.mathnet.ru/ivm8999}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 5
\pages 41--51
\crossref{https://doi.org/10.3103/S1066369X15050060}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928646399}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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