 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 44, Issue 4 / 2009 | Next article >> |
| S. N. Kukudzhanov, "On the Stability of Nearly Cylindrical Long Shells of Revolution," Mech. Solids. 44 (4), 543-551 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
4 |
Pages |
543-551 |
| DOI |
10.3103/S0025654409040062 |
| Title |
On the Stability of Nearly Cylindrical Long Shells of Revolution |
| Author(s) |
S. N. Kukudzhanov (Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze 1, Tbilisi, 0193 Georgia, sergo@rmi.acnet.ge) |
| Abstract |
In contrast to [1-4], where the stability problem was studied for shells of medium length, in the present paper we study the stability problem for nearly cylindrical long shells under the action of meridian forces uniformly distributed over their ends and under the action of the normal pressure distributed over the entire lateral surface of the shell. We consider the shells whose generating midsurface shape is determined by a parabolic function. The study is performed for nonaxisymmetric buckling modes by using an equation refined as compared with the equation given in [1]. We consider shells of both positive and negative Gaussian curvature. We assume that the shell ends are freely supported and obtain formulas for the critical load under both separate and joint action of the meridian forces and the pressure. In the specific case of a cylindrical shell under the action of longitudinal compression, the formulas thus obtained imply both the Euler formula and the Southwell-Timoshenko formula [5]. When solving the problem, we use the Bubnov-Galerkin method combined with the optimal approximation method [6]. |
| Keywords |
stability, Bubnov-Galerkin optimal approximation, analytic formulas for critical loads |
| References |
| 1. | V. M. Darevskii,
"Stability of Nearly Cylindrical Shell,"
in Problems of Computation of Spatial Constructions
(MISI, Moscow, 1980),
pp. 35-45
[in Russian]. |
| 2. | P. E. Tovstik,
Stability of Thin Shells
(Nauka, Fizmatlit, Moscow, 1995)
[in Russian]. |
| 3. | S. S. Kan,
"Stability of Shells of Revolution with Curvilinear Generators in Axial Compression,"
Prikl. Mekh.
2 (1), 59-68 (1966)
[Soviet Appl. Mech. (Engl. Transl.)
2 (1), 35-39 (1966)]. |
| 4. | G. M. Tusheva,
"Stability of Nearly Cylindrical Shells of Curvature of Two Kinds under Common Action of Radial Pressure and Meridian Force,"
Izv. Vyssh. Uchebn. Zaved. Mashinostr.,
No. 5, 10-14 (1970). |
| 5. | E. I. Grigolyuk and V. V. Kabanov,
Stability of Shells
(Nauka, Moscow, 1978)
[in Russian]. |
| 6. | S. N. Kukudzhanov,
"On Optimal Approximations in the Eigenvalue Problem
for the Riesz and Bubnov-Galerkin Methods,"
Zh. Vychisl. Mat. Mat. Fiz.
23 (5), 1230-1233 (1983). |
|
| Received |
21 June 2006 |
| Link to Fulltext |
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