Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2001-2pp.120-126

Archive of Issues

Total articles in the database: 12854
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8044
In English (Mech. Solids): 4810

<< Previous article | Volume 36, Issue 2 / 2001 | Next article >>
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
<< Previous article | Volume 36, Issue 2 / 2001 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100