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IssuesArchive of Issues2009-4pp.552-564

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P. E. Tovstik, "Stability of a Transversally Isotropic Cylindrical Shell under Axial Compression," Mech. Solids. 44 (4), 552-564 (2009)
Year 2009 Volume 44 Number 4 Pages 552-564
DOI 10.3103/S0025654409040074
Title Stability of a Transversally Isotropic Cylindrical Shell under Axial Compression
Author(s) P. E. Tovstik (Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, peter.tovstik@mail.ru)
Abstract We consider the stability of a thin transversally isotropic circular cylindrical shell under axial compression. We use a local approach according to which the buckling deflection is sought in the form of a doubly periodic function of curvilinear coordinates and the boundary conditions are ignored. We compare the solutions obtained according to the two-dimensional Kirchhoff-Love (KL) and Timoshenko-Reissner (TR) models with the solutions constructed according to the three-dimensional theory. Attention is mainly paid to the case of very small shear stiffness in the transverse direction.
Keywords surface vibrations and waves, plate, elastic basement, anisotropy, initial stresses, stability
References
1.  E. I. Grigolyuk and V. V. Kabanov, "Stability of Circular Cylindrical Shells," in Mechanics of Strained Bodies (Itogi Nauki, VINITI, Moscow, 1967) [in Russian].
2.  E. I. Grigolyuk and V. V. Kabanov, Stability of Shells (Nauka, Moscow, 1978) [in Russian].
3.  D. Bushnell, "Buckling of Shells - Pitfall for Designers," AIAA Journal 19 (9), 1183-1226 (1981).
4.  W. Nachbar and N. J. Hoff, "The Buckling of Free Edge of an Axially Compressed Circular Cylindrical Shell," Quart. Appl. Math. 20 (3), 267-277 (1962).
5.  N. A. Kil'chevskii and S. N. Nikulinskaya, "An Axisymmetric Bulking Mode of a Circular Cylindrical Shell," Prikl. Mekh. 1 (11), 1-6 (1965).
6.  P. E. Tovstik, tability of Thin Shells. Asymptotic Methods (Nauka, Fizmatlit, Moscow, 1995) [in Russian].
7.  J. Arbocz and C. D. Babcock, "The Effect of General Imperfections on the Buckling of Cylindrical Shells," Trans. ASME. Ser. E. J. Appl. Mech. 36 (1), 28-38 (1969).
8.  P. E. Tovstik and S. P. Chernyaev, "Nonlinear Deformation of Thin Shells with the Middle Surface Imperfections," Vestnik St. Petersburg. Univ., No. 3, 88-95 (2004).
9.  A. S. Vol'mir, Stability of Deformable Systems (Nauka, Moscow, 1967) [in Russian].
10.  A. V. Pogorelov, Geometric Theory of Stability of Shells (Nauka, Moscow, 1966) [in Russian].
11.  Yu. N. Rabotnov, "Local Stability of Shells," Dokl. Akad. Nauk SSSR 52 (2), 111-112 (1946).
12.  P. E. Tovstik, "Local Buckling of Plates and Shallow Shells on an Elastic Foundation," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 147-160 (2005) [Mech. Solids (Engl. Transl.) 40 (1), 120-131 (2005)].
13.  R. Lorenz, "Die Nicht Achsensymmetrische Knickung Dunnwandiger Hohlzylinder," Phyz. Z. 12 (7), 241-260 (1911).
14.  S. P. Timoshenko, "To the Strain Problem and Stability of Cylindrical Shell," Vestnik Obshch. Tekhnol. 21, 785-792 (1914); [Stability of Rods, Plates, and Shells (Nauka, Moscow, 1971)].
15.  S. A. Ambartsumyan, General Theory of Anisotropic Shells (Nauka, Moscow, 1974) [in Russian].
16.  V. Ts. Gnuni, "Analysis of the Transverse Shear Influence on the Characteristics of Rigidity, Stability, and Oscillations of Depressed Shells of Curvature of Two Kinds," Izv. Natst. Akad. Nauk Resp. Arm. Ser. Mat. 56 (4), 39-45 (2003).
17.  S. A. Kabrits, E. I. Mikhailovskii, P. E. Tovstik, et al., General Nonlinear Theory of Elastic Shells (Izd-vo St. Petersburg Univ., St. Petersburg, 2002) [in Russian].
18.  P. E. Tovstik, "Stability of Multilayer Cylindrical Shell under Axial Compression," Izv. Vyssh. Uchebn. Zaved., North Caucasus region, Natural Sciences, Special Issue, 107-110 (2004).
19.  P. E. Tovstik and T. P. Tovstik, "On the 2D Models of Plates and Shells Including the Transversal Shear," ZAMM Mech. 87 (2), 160-171 (2007).
20.  V. A. Rodionova, B. F. Titaev, and K. F. Chernykh, Applied Theory of Anisotropic Plates and Shells (Izd. St. Petersburg Inst., St. Petersburg, 1996) [in Russian].
21.  V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multi-Layer Constructions (Mashinostroenie, Moscow, 1980) [in Russian].
22.  A. Yu. Ishlinskii, "On a Limit Transition in the Theory of Stability of Elastic Rectilinear Plates," Dokl. Akad. Nauk SSSR 95 (3), 477-479 (1954) [Soviet Math. Dokl.].
23.  N. V. Banichuk and A. Yu. Ishlinskii, "Some Special Features of Problems of the Stability and Vibrations of Rectangular Plates," Prikl. Mat. Mekh. 59 (4), 620-625 (1995) [J. Appl. Math. Mech. (Engl. Transl.) 59 (4), 599-606 (1995)].
24.  N. F. Morozov, M. V. Paukshto, and P. E. Tovstik, "Stability of a Surface Layer under a Thermal Loading," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 130-139 (1998) [Mech. Solids (Engl. Transl.) 33 (1), 106-113 (1998)].
25.  N. V. Valishvili, Computer Calculation Methods for Shells of Rotations (Mashinostroenie, Moscow, 1976) [in Russian].
26.  N. A. Alfutov, Foundations of Computations of Elastic Systems for Stability (Mashinostroenie, Moscow, 1978) [in Russian].
Received 04 October 2007
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