Mechanics of Solids (about journal) Mechanics of Solids
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IssuesArchive of Issues2011-6pp.877-887

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S.N. Kukudzhanov, "On Stability of Orthotropic Cylindrical Shells," Mech. Solids. 46 (6), 877-887 (2011)
Year 2011 Volume 46 Number 6 Pages 877-887
DOI 10.3103/S0025654411060070
Title On Stability of Orthotropic Cylindrical Shells
Author(s) S.N. Kukudzhanov (Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze 1, Tbilisi, 0193 Georgia,
Abstract In contrast to [1-3], the present paper obtains a system of stability equations and the corresponding resolving equation for orthotropic cylindrical shells of any but very short length in the case where the precritical stress state cannot be treated as the zero-moment state. These equations are a generalization of the results obtained in [4]. On the basis of these equations, one can obtain both the well-known formulas [1-3] and, for medium-length shells, some new expressions of the critical load in longitudinal compression and that under the joint action of torsional moments, normal pressure, and longitudinal compression. Some estimates are performed and the determination of the domain of application of some formulas given in [2] and in the present paper is attempted. For an orthotropic shell, a relationship between the elastic parameters and the shear modulus is established for axisymmetric and nonaxisymmetric buckling mode shapes in longitudinal compression.
Keywords stress state, cylindrical shell, shear modulus, orthotropy, stability, critical load
1.  S. A. Ambartsumyan, General Theory of Anisotropic Shells (Nauka, Moscow, 1974) [in Russian].
2.  Kh. M. Mushtari, "Some Generalizations of the Theory of Thin Shells," Izv. Fiz.-Mat. Obshch. Kazan Univ. 11, Ser. 3, 71-150 (1938).
3.  V. M. Darevskii and S. N. Kukudzhanov, "Stability of a Cylindrical Orthotropic Shell under Torsion and Normal Pressure," in Strength of Cylindrical Shells (Oborongiz, Moscow, 1959), pp. 95-108 [in Russian].
4.  V. M. Darevskii, "Equations of Stability of Cylindrical Shells," Inzh. Zh. 3 (4), 658-664 (1963).
5.  V. M. Darevskii, "On Basic Relations in the Theory of Thin Shells," Prikl. Mat. Mekh. 25 (3), 519-535 (1961) [J. Appl. Math. Mech. (Engl. Transl.) 25 (3), 768-790 (1961)].
6.  A. Love, Mathematical Theory of Elasticity (ONTI, Moscow, 1935) [in Russian].
7.  S. P. Timoshenko, Stability of Elastic Systems (Gostekhizdat, Moscow-Leningrad, 1946) [in Russian].
8.  E. I. Grigolyuk and V. V. Kabanov, Stability of Shells (Nauka, Moscow, 1978) [in Russian].
Received 23 April 2008
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