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 Issues2005-3pp.134-142

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 40, Issue 3 / 2005 | Next article >>
V. A. Ivanov, V. N. Paimushin, and V. I. Shalashilin, "Refined geometrically nonlinear theory and buckling modes of sandwich shells with transversely-soft core," Mech. Solids. 40 (3), 134-142 (2005)
Year 2005 Volume 40 Number 3 Pages 134-142
Title Refined geometrically nonlinear theory and buckling modes of sandwich shells with transversely-soft core
Author(s) V. A. Ivanov (Kazan)
V. N. Paimushin (Kazan)
V. I. Shalashilin (Moscow)
Abstract The studies on the mechanics of laminated structural elements carried out before 1996 were reviewed in [1], while the current state of the buckling theory of sandwich plates and shells, analysis of its main development stages and prospects for further research were presented in [2]. This work was preceded by the papers [3, 4] where a refined classification of the buckling modes of statically loaded sandwich structural elements, analyzed then in [2], was proposed. According to this classification, of all possible buckling modes in sandwich structures, the shear buckling mode is distinguished. From the analysis of the buckling equations derived in [4], it was concluded that the shear buckling modes may potentially occur at zero subcritical stresses in the face (load-carrying) layers and non-zero subcritical transverse tangential stresses in the core.

The results obtained in [5] led to the essential revision of the conclusions drawn in [2-4] with respect to the classification proposed in [3, 4]. These conclusions were based on the possibility of purely shear buckling of a circular sandwich ring subjected to uniform external pressure, in which case, in the subcritical state, non-zero tangential stresses occur in the face layers, and zero transverse tangential stresses develop in the core.

The current paper is mainly aimed at the elimination of the contradictions and inconsistencies which surfaced in more thorough further studies on the problem of shear buckling of a sandwich ring subjected to uniform external pressure formulated in [5]. It is shown that the buckling equations derived in [4, 6] and used in [5], as well as other similar equations, involve only less important parametric terms which are used for the description and analysis of the shear buckling modes, whereas the main cause of the occurrence of these buckling modes in the absence of subcritical tangential stresses in the core is that subcritical compressive transverse stresses develop in it. In this respect, refined geometrically non-linear equations are derived for thin sandwich shells with transversely-soft core, these equations are based on the relationships of the classical moderate bending theory for the face layers, and the linear approximation for the transverse displacements in the core. This approach differs from all similar sandwich shell theories known from literature in that the equations derived admit finite transverse shear strains in the core, which are caused by the possibility of substantial relative tangential displacements of the face layers subjected to moderate bending.

With the parametric strain terms omitted, linearized buckling equations are derived and applied to obtaining a refined solution to the problem of shear buckling of a sandwich ring subjected to external pressure. It is shown that this buckling mode may equally occur under internal pressure, the critical value of which coincides with that of the external pressure. Moreover, it is established that, with appropriate edge conditions, shear buckling of a cylindrical sandwich shell subjected to internal or external pressure may occur in the axial direction as well.
References
1.  A. K. Norr, W. S. Burton, and Ch. W. Bert, "Computational models for sandwich panels and shells," Appl. Mech. Rev-s., Vol. 49, No. 3, pp. 155-199, 1996.
2.  V. N. Paimushin, "Theory of stability for three-layer plates and shells: stages of development, state-of-the-art, and prospects," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 148-162, 2001.
3.  V. N. Paimushin, "Buckling theory for sandwich structural elements. Analysis of modern state and refined classification of buckling modes," Mekhanika Kompositnykh Materialov, Vol. 35, No. 6, pp. 706-716, 1999.
4.  V. N. Paimushin, and S. N. Bobrov, "Refined geometrically nonlinear theory of sandwich shells with transversely-soft core of medium thickness for studying mixed buckling modes," Mekhanika Kompositnykh Materialov, Vol. 36, No. 1, pp. 95-108, 2000.
5.  V. N. Paimushin, "Shear buckling mode of a sandwich circular ring subjected to uniform external pressure," Doklady AN, Vol. 378, No. 1, pp. 58-60, 2001.
6.  V. A. Ivanov, and V. N. Paimushin, "Refined buckling theory of sandwich structures (non-linear equations of subcritical equilibrium of shells with transversely-soft core,)" Izv. Vuzov, Matematika, No. 11, pp. 29-42, 1994.
7.  V. V. Bolotin, and Yu. N. Novichkov, Mechanics of Multilayer Structures [in Russian], Mashinostroenie, Moscow, 1980.
8.  K. Z. Galimov, V. N. Paimushin, and I. G. Teregulov, Foundations of the Non-linear Shell Theory [in Russian], Fen, Kazan, 1996.
9.  V. N. Paimushin, V. A. Ivanov, S. N. Bobrov, and T. V. Polyakova, "Buckling of a circular sandwich ring subjected to uniform external pressure," Mekhanika Kompositnykh Materialov, Vol. 36, No. 3, pp. 317-328, 2000.
10.  V. N. Paimushin, "Classical and non-classical problems of dynamics of sandwich shells with transversely-soft core," Mekhanika Kompositnykh Materialov, Vol. 37, No. 3, pp. 289-306, 2001.
Received 29 April 2003
<< Previous article | Volume 40, Issue 3 / 2005 | 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