Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2012-2pp.205-211

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 47, Issue 2 / 2012 | Next article >>
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
<< Previous article | Volume 47, Issue 2 / 2012 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100