 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| D.V. Boiko, L.P. Zheleznov, and V.V. Kabanov, "Studies of Nonlinear Deformation and Stability of Oval and Elliptic Cylindrical Shells under Axial Compression," Mech. Solids. 44 (5), 762-768 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
5 |
Pages |
762-768 |
| DOI |
10.3103/S0025654409050136 |
| Title |
Studies of Nonlinear Deformation and Stability of Oval and Elliptic Cylindrical Shells under Axial Compression |
| Author(s) |
D.V. Boiko (Chaplygin Siberian Research Aviation Institute, Polzunova 21, Novosibirsk, 630021 Russia)
L.P. Zheleznov (Chaplygin Siberian Research Aviation Institute, Polzunova 21, Novosibirsk, 630021 Russia, lev@wsr.ru)
V.V. Kabanov (Chaplygin Siberian Research Aviation Institute, Polzunova 21, Novosibirsk, 630021 Russia, ni010@yandex.ru) |
| Abstract |
The stability of noncircular shells, in contrast to that of circular ones, has not been studied sufficiently well yet. The publications about circular shells are counted by thousands, but there are only several dozens of papers dealing with noncircular shells. This can be explained on the one hand by the fact that such shells are less used in practice and on the other hand by the difficulties encountered when solving problems involving a nonconstant curvature radius, which results in the appearance of variable coefficients in the stability equations. The well-known solutions of stability problems were obtained by analytic methods and, as a rule, in the linear approximation without taking into account the moments and nonlinearity of the shell precritical state, i.e., in the classical approximation. Here we use the finite element method in displacements to solve the problem of geometrically nonlinear deformation and stability of cylindrical shells with noncircular contour of the transverse cross-section. We use quadrilateral finite elements of shells of natural curvature. In the approximations to the element displacements, we explicitly distinguish the displacements of elements as rigid bodies. We use the Lagrange variational principle to obtain a nonlinear system of algebraic equations for determining the unknown nodal finite elements. We solve the system by a step method with respect to the load using the Newton-Kantorovich linearization at each step. The linear systems are solved by the Kraut method. The critical loads are determined with the use of the Silvester stability criterion when solving the nonlinear problem. We develop an algorithm for solving the problem numerically on personal computers. We also study the nonlinear deformation and stability of shells with oval and elliptic transverse cross-section in a wide range of variations in the ovalization and ellipticity parameters. We find the critical loads and the shell buckling modes. We also examine how the critical loads are affected by the strain nonlinearity and the ovalization and ellipticity of shells. |
| Keywords |
shell, nonlinear strain, elasticity |
| References |
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Stability of Shells
(Nauka, Moscow, 1978)
[in Russian]. |
| 2. | L. P. Zheleznov and V. V. Kabanov,
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43 (4), 155-160 (2002)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
43 (4), 617-621 (2002)]. |
| 3. | V. V. Kabanov and S. V. Astrakharchik,
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in Three-Dimensional Structures in the Krasnoyarsk Region,
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[in Russian]. |
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| 7. | S. V. Astrakharchik, L. P. Zheleznov, and V. V. Kabanov,
"Study of Nonlinear Strain and Stability of Shells and Panels of Nonzero Gaussian Curvature,"
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No. 2, 102-108 (1994)
[Mech. Solids (Engl. Transl.)]. |
| 8. | J. H. Wilkinson and C. Reinsch,
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| 9. | L. P. Zheleznov and V. V. Kabanov,
"Study of Nonlinear Strain and Stability of Noncircular Cylindrical Shells under Axial Compression,"
in Numerical Methods for Solving Elasticity and Plasticity Problems.
Proc. 17th Interrepublic Cong. 2001,
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[in Russian]. |
| 10. | B. Kh. Inozemtsev,
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in Proc. 6th All-Union Conf. in the Theory of Shells and Plates
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pp. 444-450
[in Russian]. |
| 11. | S. N. Kan and Yu. I. Kaplan,
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in Strength of Materials and Structural Theory, No. 21
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[in Russian]. |
| 12. | Kh. M. Mushtari,
"On an Approach to Solving Problems of Stability for Thin Cylindrical Shells with Arbitrary Cross-Section,"
Sb. Nauch. Trudov Kazan. Aviats. Inst.,
No. 4, 19-31 (1935). |
|
| Received |
29 January 2007 |
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