 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| E.A. Lopanitsyn and E.A. Matveev, "Stability of Cylindrical Shells with Initial Imperfections under the Action of External Pressure," Mech. Solids. 46 (2), 170-178 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
2 |
Pages |
170-178 |
| DOI |
10.3103/S0025654411020038 |
| Title |
Stability of Cylindrical Shells with Initial Imperfections under the Action of External Pressure |
| Author(s) |
E.A. Lopanitsyn (Moscow State Technical University "MAMI," Bol'shaya Semyonovskaya 38, Moscow, 107023 Russia, eal@mami.ru, eal54@mail.ru)
E.A. Matveev (Moscow State Technical University "MAMI," Bol'shaya Semyonovskaya 38, Moscow, 107023 Russia, zed-math@yandex.ru) |
| Abstract |
We use the equations of nonlinear theory of shallow shells to solve the problem of stability of thin elastic isotropic cylindrical shells, with small initial shape imperfections, that are under the action of external uniform pressure. The problem solution is constructed by the Rayleigh-Ritz method with the approximation of the shell midsurface displacement by double functional sums in trigonometric and beam functions. The system of nonlinear algebraic equations is solved by using the methods of continuation with respect to a close-to-best parameter. For the initial imperfections of the shells, we use their normalized deflections from the limit points of overcritical branches of the loading trajectories. We consider various cases of the shell fixation and support under loading by lateral and hydrostatic uniform pressure. We also construct the range of values of the critical pressure, which, with the maximal deviation of the shell shape from the cylindrical shape up to 30%, covers practically all known experimental data. |
| Keywords |
thin isotropic cylindrical shells, external pressure, initial imperfections of shape, finite deflections, stability, continuation methods |
| References |
| 1. | E. I. Grigolyuk and V. V. Kabanov,
Stability of Shells
(Nauka, Moscow, 1978)
[in Russian]. |
| 2. | E. I. Grigolyuk and V. V. Kabanov,
Stability of Circular Cylindrical Shells,
in Itogi Nauki i Tekhniki, Mekhanika Deformiruemogo Tverdogo Tela
(VINITI, Moscow, 1969)
[in Russian]. |
| 3. | A. S. Vol'mir,
Stability of Deformable Systems
(Nauka, Moscow, 1967)
[in Russian]. |
| 4. | V. Z. Vlasov,
General Theory of Shells and Its Application in Technology
(Gostekhizdat, Moscow-Leningrad, 1949);
V. Z. Vlasov,
Selected Works, Vol. 1
(Izd-vo AN SSSR, Moscow, 1962)
[in Russian]. |
| 5. | Kh. M. Mushtari and K. Z. Galimov,
Nonlinear Theory of Thin Elastic Shells
(Tatknigoizdat, Kazan, 1957; Program for Scientific Translations, Israel, 1961). |
| 6. | E. A. Lopanitsyn and A. B. Frolov,
"Stability of Circular Cylindrical Shells under the Action of Uniform Compression,"
in Selected Strength Problems in Modern Mechanical Engineering,
Collection of Papers on the Occasion of E. I. Grigolyuk's Eighty-Fifth Birthday
(Nauka, Moscow, 2008),
pp. 176-189
[in Russian]. |
| 7. | S. G. Mikhlin,
Variational Methods in Mathematical Physics
(Pergamon, New York, 1964; Nauka, Moscow, 1970). |
| 8. | E. I. Grigolyuk and E. A. Lopanitsyn,
Finite Deflections, Stability, and Postbuckling
Behavior of Thin Shallow Shells
(MGTU "MAMI", Moscow, 2004)
[in Russian]. |
| 9. | M. Yamada and S. Yamada,
"Agreement between Theory and Experiment on Large-Deflection Behavior
of Clamped Shallow Spherical Shells under External Pressure,"
in Collapse, Ed. by J. M. T. Tompson and J. W. Hant
(Cambridge Univ. Press, Cambridge, 1983),
pp. 431-441. |
|
| Received |
08 December 2010 |
| Link to Fulltext |
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