 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| S. N. Timergaliev, "Solvability of boundary value problems in the geometrically and physically nonlinear theory of shallow shells of Timoshenko type," Mech. Solids. 44 (3), 435-444 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
3 |
Pages |
435-444 |
| DOI |
10.3103/S0025654409030121 |
| Title |
Solvability of boundary value problems in the geometrically and physically nonlinear theory of shallow shells of Timoshenko type |
| Author(s) |
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 |
This paper deals with the proof of the existence of solutions of a geometrically and physically nonlinear boundary value problem for shallow Timoshenko shells with the transverse shear strains taken into account. The shell edge is assumed to be partly fixed. It is proposed to study the problem by a variational method based on searching the points of minimum of the total energy functional for the shell-load system in the space of generalized displacements. We show that there exists a generalized solution of the problem on which the total energy functional attains its minimum on a weakly closed subset of the space of generalized displacements. |
| References |
| 1. | I.I. Vorovich,
Mathematical Problems of Nonlinear Theory of Shallow Shells
(Nauka, Moscow, 1989) [in Russian]. |
| 2. | N.F. Morozov,
"To Nonlinear Theory of Thin Shells,"
Dokl. Akad. Nauk SSSR 114 (5), 968-971 (1957). |
| 3. | M.M. Karchevskii,
"Nonlinear Problems of Theory of Plates and Shells and Their Grid Approximations,"
Izv. Vyssh. Uchebn. Zaved. Mat., No. 10, 17-30 (1985)
[Soviet Math. (Iz VUZ) (Engl. Transl.)]. |
| 4. | 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.) 33 (3), 15-21 (1998)]. |
| 5. | 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.) 37 (1), 129-137 (2002)]. |
| 6. | K.Z. Galimov,
Foundations of Nonlinear Theory of Thin Shells
(Izd-vo Kazan Univ., Kazan, 1975) [in Russian]. |
| 7. | K. Washizu,
Variational Methods in Elasticity and Plasticity
(Pergamon Press, New York, 1972; Mir, Moscow, 1987). |
| 8. | A.I. Lurie,
The Theory of Elasticity
(Nauka, Moscow, 1970) [in Russian]. |
| 9. | M.A. Krasnosel'skii,
Topological Methods in the Theory of Nonlinear Integral Equations
(Gostekhizdat, Moscow, 1956; Pergamon, London, 1964; Macmillan, New York, 1964). |
| 10. | M.M. Vainberg,
Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations
(Nauka, Moscow, 1972; Wiley, New York, 1973). |
| 11. | L.V. Kantorovich and G.P. Akilov,
Approximate Methods of Higher Analysis
(Gostekhizdat, Leningrad-Moscow, 1949) [in Russian]. |
| 12. | I.N. Vekua,
Generalized Analytic Functions
(Nauka, Moscow, 1988) [in Russian]. |
| 13. | Mathematical Encyclopaedia, Vol. 3
(Idz-vo "Sov. Entsiklopedia", Moscow, 1982) [in Russian]. |
| 14. | O.A. Ladyzhenskaya,
The Boundary Value Problems of Mathematical Physics
(Nauka, Moscow, 1973; Springer, New York, 1985). |
|
| Received |
13 July 2006 |
| Link to Fulltext |
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