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IssuesArchive of Issues2007-2pp.241-249

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I. G. Teregulov and S. N. Timergaliev, "Existence of solutions of boundary-value problems for thin elastic irregular shells," Mech. Solids. 42 (2), 241-249 (2007)
Year 2007 Volume 42 Number 2 Pages 241-249
Title Existence of solutions of boundary-value problems for thin elastic irregular shells
Author(s) I. G. Teregulov (Kazan State University of Architecture and Civil Engineering, Zelenaya 1, Kazan, 420043, Russia)
S. N. Timergaliev (Kama State Academy of Engineering and Economics, pr-t Mira 68/19, Naberezhnye Chelny, Tatarstan, 423810, Russia, samat_tim@mail.ru)
Abstract We study the solvability of a geometrically and physically nonlinear boundary-value problem for thin elastic anisotropic irregular shells with clamped edge. For this problem, we suggest a method based on solving the problem in some function space other than the space of displacements and stresses. This method is based on the integral representations of displacement components and strains in terms of auxiliary functions (conventional strains). This method permits obtaining, as the equilibrium equations, nonlinear singular integral equations over a bounded plane domain for the conventional strains. The solvability of these equations is studied by the contraction mapping principle.
References
1.  I. I. Vorovich, Mathematical Problems of Nonlinear Theory of Shallow Shells (Nauka, Moscow, 1989) [in Russian].
2.  I. G. Teregulov and S. N. Timergaliev, "Ritz Method for Approximate Solution of Boundary Value Problems in the Nonlinear Theory of Thin Shells," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 154-164 (2002) [Mech. Solids (Engl. Transl.)].
3.  N. F. Morozov, "Nonlinear Problems of the Theory of Thin Anisotropic Plates," Izv. Vyssh. Uchebn. Zaved. Mat., No. 6, 170-173 (1960).
4.  I. G. Teregulov, "Convergence of the Successive Approximation Method in a Problem on Nonlinear Theory of Shells," Izv. Vyssh. Uchebn. Zaved. Mat., No. 4, 168-177 (1959).
5.  I. G. Teregulov and S. N. Timergaliev, "On the Existence of a Solution of a Problem in Nonlinear Theory of Shallow Shells," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 21-29 (1998) [Mech. Solids (Engl. Transl.)].
6.  S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics (Nauka, Moscow, 1988) [in Russian].
7.  I. N. Vekua, Generalized Analytic Functions (Nauka, Moscow, 1988) [in Russian].
8.  M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations (Gostekhizdat, Moscow, 1956) [in Russian].
Received 16 December 2004
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