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S.A. Lukankin and V.N. Paimushin, "Static and Dynamic Buckling Modes of a Cylindrical Shell under External Pressure," Mech. Solids. 49 (1), 83-98 (2014)
Year 2014 Volume 49 Number 1 Pages 83-98
DOI 10.3103/S0025654414010105
Title Static and Dynamic Buckling Modes of a Cylindrical Shell under External Pressure
Author(s) S.A. Lukankin (Scientific and Technical Center for Problems in Dynamics and Strength, Tupolev Kazan State Technical University, K. Marksa 10, Kazan, 420111 Russia, lukankin@dsm.kstu-kai.ru)
V.N. Paimushin (Scientific and Technical Center for Problems in Dynamics and Strength, Tupolev Kazan State Technical University, K. Marksa 10, Kazan, 420111 Russia, dsm@dsm.kstu-kai.ru)
Abstract We consider the problem of static and dynamic buckling modes of thin shells under external hydrostatic pressure. If the statement of the problem uses the linearized equations of motion obtained in the moderately large bending theory of shells according to the classical or refined model, then part of terms related to the external load in these equations are assumed to be conservative, and the other terms are assumed to be nonconservative. In this connection, we study four statements of the elastic stability problem for a cylindrical shell with hinged faces. The first of them is the statement of the static boundary value problem in the sense of Euler, where the action of external pressure is assumed to be conservative. The second statement is used to study small vibrations near the static equilibrium by a dynamic method for the same conservative load. The third and fourth statements of the problem correspond to the action of a nonconservative load and are similar to the first and second statements, respectively. They use the linearized equations of equilibrium and motion constructed earlier in a consistent version on the basis of a Timoshenko type model and allowing one to reveal all classical and nonclassical shell buckling modes.
Keywords external hydrostatic pressure, follower load, cylindrical shell, linearized equations of motion, hinging, Euler criterion, dynamic criterion
References
1.  E. I. Grigolyuk and V. V. Kabanov, Stability of Shells (Nauka, Moscow, 1978) [in Russian].
2.  V. N. Paimushin and V. I. Shalashilin, "Geometrically Non-Linear Equations in the Theory of Momentless Shells with Applications to Problems on the Non-Classical Forms of Loss of Stability of a Cylinder," Prikl. Mat. Mekh. 70 (1), 100-110 (2006) [J. Appl. Math. Mech. (Engl. Transl.) 70 (1), 91-101 (2006)].
3.  V. N. Paimushin, "Torsional, Flexural, and Torsional-Flexural Buckling Modes of a Cylindrical Shell under Combined Loading," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 125-136 (2007) [Mech. Solids (Engl. Transl.) 42 (3), 437-446 (2007)].
4.  V. N. Paimushin, "Problems of Geometric Non-Linearity and Stability in the Mechanics of Thin Shells and Rectilinear Columns," Prikl. Mat. Mekh. 71 (5), 855-893 (2007) [J. Appl. Math. Mech. (Engl. Transl.) 71 (5), 772-805 (2007)].
5.  V. N. Paimushin, "Static and Dynamic Beam Forms of the Loss of Stability of a Long Orthotropic Cylindrical Shell under External Pressure," Prikl. Mat. Mekh. 72 (6), 1014-1027 (2008) [J. Appl. Math. Mech. (Engl. Transl.) 72 (6), 738-747 (2008)].
6.  G. I. Kolosov, "Stability of the Equilibrium State of an Axially Compressed Closed Circular Cylindrical Shell with Respect to Small Perturbations," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 77-83 (2006) [Mech. Solids (Engl. Transl.) 41 (2), 60-64 (2006)].
7.  V. V. Bolotin, Nonconservative Problems of the Theory of Elastic Stability (Fizmatgiz, Moscow, 1961; Pergamon Press, New York, 1963).
8.  K. Z. Galimov, Foundations of Nonlinear Theory of Thin Shells (Kazan Univ., Kazan, 1975) [in Russian].
9.  R. B. Rikards and G. A. Teters, Stability of Shells of Composite Materials (Zinatne, Riga, 1974) [in Russian].
10.  K. Z. Galimov (Editor), Theory of Shells with Transverse Shear Taken into Account (Kazan Univ., Kazan, 1977) [in Russian].
11.  V. N. Paimushin, "A Version of Nonlinear Theory of Thin Shells of Timoshenko Type," Prikl. Mekh. 22 (6), 40-47 (1986).
12.  K. Z. Galimov, V. N. Paimushin, and I. G. Tregulov, Foundations of Nonlinear Theory of Shells (Fen, Kazan, 1996) [in Russian].
13.  E. I. Grigolyuk and F. N. Shklyarchuk, "Equations of Perturbed Motion of a Body with a Thin-Walled Elastic Shell Partially Pilled with a Liquid," Prikl. Mat. Mekh. 34 (3), 401-411 (1970) [J. Appl. Math. Mech. (Engl. Transl.) 34 (3), 379-389 (1970)].
14.  V. N. Paimushin, "On Static and Dynamic Buckling Modes of a Rod-Strip Loaded by Follower Forces," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 95-106 (2008) [Mech. Solids (Engl. Transl.) 43 (4), 600-609 (2008)].
15.  V. N. Paimushin and N. V. Polyakova, "The Consistent Equations of the Theory of Plane Curvilinear Rods for Finite Displacements and Linearized Problems of Stability," Prikl. Mat. Mekh. 73 (2), 303-324 (2009) [J. Appl. Math. Mech. (Engl. Transl.) 73 (2), 1014-1027 (2009)].
Received 31 March 2011
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