 | | 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 |
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| 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 |
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