 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 42, Issue 2 / 2007 | Next article >> |
| 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 |
| Link to Fulltext |
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