 | | 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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| L. M. Zubov, "Nonlinear theory of elastic shells with continuously distributed dislocations," Mech. Solids. 36 (2), 120-126 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
2 |
Pages |
120-126 |
| Title |
Nonlinear theory of elastic shells with continuously distributed dislocations |
| Author(s) |
L. M. Zubov (Rostov-on-Don) |
| Abstract |
A nonlinear theory for elastic shells is constructed in the case of large
deformations and continuously distributed translational dislocations.
First, we formulate a variational problem of equilibrium for a
multiply connected shell of Cosserat type with isolated dislocations.
The variational principle proposed here allows for an easy transition from
the case of isolated defects to that of continuously distributed
dislocations. An analogy is established between the boundary value
problem describing the equilibrium of an unloaded shell with continuously
distributed dislocations and the boundary value problem for a shell
subjected to distributed loads and having no dislocations.
An exposition of the linear theory of continuously distributed defects in
elastic shells can be found in [1]. |
| References |
| 1. | L. M. Zubov, "Continuously distributed dislocations and
disclinations in elastic shells," Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 102-110, 1996. |
| 2. | P. A. Zhilin, "Basic equations of the nonclassical theory of
elastic shells', Trudy Leningrad. Politekhn. In-ta, No. 386, pp. 29-46,
1982. |
| 3. | J. G. Simmonds and D. A. Danielson, "Nonlinear shell theory with
a finite rotation vector," Kon. Nederland. Akad. Wetesch, B-73, No. 5,
pp. 460-478, 1970. |
| 4. | W. Pietraszkiewicz, "Geometrically nonlinear theories of thin
elastic shells," Advances in Mechanics, Vol. 12, No. 1, pp. 51-130, 1989. |
| 5. | L. M. Zubov, Methods of the Nonlinear Elasticity and the Theory of
Shells [in Russian], Izd-vo Rostov. Un-ta, Rostov-on-Don, 1982. |
| 6. | L. M. Zubov, "Nonlinear theory of isolated dislocations and
disclinations in elastic shells" Izv. AN SSSR. MTT [Mechanics of Solids],
No. 4, pp. 139-145, 1989. |
| 7. | A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow,
1980. |
| 8. | L. M. Zubov, "A static geometrical analogy and variational
principles in the nonlinear membrane shell theory," in Proc. 12th
All-Union Conference on Shells and Plates [in Russian], pp. 171-176,
Izd-vo Erevan. Gos. Un-ta, Erevan, 1980. |
| 9. | L. M. Zubov, "Variational principles and invariant integrals for
nonlinearly elastic bodies with moment stresses," Izv. AN SSSR. MTT
[Mechanics of Solids], No. 6, pp. 10-16, 1990. |
| 10. | E. Kröner, General Theory of Continuous Dislocations and Proper
Stresses [Russian translation], Mir, Moscow, 1965. |
| 11. | A. A. Vakulenko, "Relations between macro and micro properties of
elastic-plastic materials," in Achievements in Science and Technology.
Ser. Mechanics of Solids [in Russian], Vol. 22, pp. 3-54, VINITI, Moscow, 1991. |
| 12. | A. L. Goldenveizer, Theory of Thin Elastic Shells [in Russian], Nauka,
Moscow, 1976. |
|
| Received |
30 October 1997 |
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