 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| D.V. Boiko, L.P. Zheleznov, and V.V. Kabanov, "Studies of Nonlinear Deformation and Stability of Noncircular Cylindrical Shells in Transverse Bending," Mech. Solids. 47 (2), 205-211 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
2 |
Pages |
205-211 |
| DOI |
10.3103/S0025654412020070 |
| Title |
Studies of Nonlinear Deformation and Stability of Noncircular Cylindrical Shells in Transverse Bending |
| Author(s) |
D.V. Boiko (Chaplygin Siberian Research Aviation Institute, Polzunova 21, Novosibirsk, 630021 Russia, dvboiko@ngs.ru)
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 variational finite element method in displacements is used to solve the problem of geometrically nonlinear deformation and stability of cylindrical shells with a noncircular contour of the cross-section. Quadrangle finite elements of shells of natural curvature are used. In the approximations of element displacements, the displacements of elements as solids are explicitly separated. The variational Lagrange principle is used to obtain a nonlinear system of algebraic equations for the unknown nodal finite elements. The system is solved by the method of successive loadings and by the Newton-Kantorovich linearization method. The linear system is solved by the Crout method. The critical loads are determined in the process of solving the nonlinear problem by using the Sylvester stability criterion. An algorithm and a computer program are developed to study the problem numerically. The nonlinear deformation and stability of shells with oval and elliptic cross-sections are investigated in a broad range of variation of the elongation and ellipticity parameters. The shell critical loads and buckling modes are determined. The influence of the deformation nonlinearity, elongation, and ellipticity of the shell on the critical loads is examined. |
| Keywords |
noncircular cylindrical shell, transverse bending, nonlinear deformation, stability, finite element method, numerical study, critical load, buckling mode |
| References |
| 1. | E. I. Grigolyuk and V. V. Kabanov,
Stability of Shells
(Nauka, Moscow, 1978)
[in Russian]. |
| 2. | L. P. Zheleznov and V. V. Kabanov, "Nonlinear Deformation and
Stability of Noncircular Cylindrical Shells under Internal Pressure
and Axial Compression," Zh. Prikl. Mekh. Tekhn. Fiz. 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, "Nonlinear Deformation and
Stability of Reinforced Cylindrical Shells in Bending," in
Spatial Structures in Krasnoyarsk Region (KISI,
Krasnoyarsk, 1985), pp. 75-83 [in Russian]. |
| 4. | V. A. Postnov and I. Ya. Kharkhurim,
Finite Element Method
in Design of Ship Structures
(Sudostroenie, Leningrad, 1974) [in
Russian]. |
| 5. | B. P. Demidovich and I. A. Maron,
Foundations of Computational Mathematics
(Nauka, Moscow, 1966)
[in Russian]. |
| 6. | L. V. Kantorovich and G. P. Akilov,
Functional Analysis in Normed Spaces
(Fizmatgiz, Moscow, 1959; Pergamon Press, Oxford, 1964). |
| 7. | S. V. Astrakharchik, L. P. Zheleznov, and V. V. Kabanov, "Study of Nonlinear Deformation and Stability of Shells and Panels of Nonzero Gaussian Curvature," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2,
102-108 (1994) [Mech. Solids (Engl. Transl.)]. |
| 8. | J. H. Wilkinson and K. Reinsch,
Handbook of ALGOL Algorithms. Linear Algebra
(Mashinostroenie, Moscow, 1976)
[in Russian]. |
| 9. | D. V. Boiko, L. P. Zheleznov, and V. V. Kabanov, "The Non-Linear
Deformation and Stability of Elliptical Cylindrical Shells under
Transverse Bending," Prikl. Mat. Mekh. 67 (6), 933-939
(2003) [J. Appl. Math. Mech. (Engl. Transl.) 67 (6),
819-824 (2003)]. |
| 10. | Yu. G. Konoplev and A. A. Sachenkov,
"Theoretical and Experimental Method in Problems of Stability of Cylindrical Shells of Elliptic Cross-Section,"
in Studies in Theory of Plates and Shells, Vol. 17, No. 1,
Ed. by K. Z. Galimov and A. V. Sachenkov
(KGU, Kazan, 1984),
pp. 135-152
[in Russian]. |
|
| Received |
07 June 2010 |
| Link to Fulltext |
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