Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T04:09:42.705Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear oscillations and buckling of anisotropic cylindrical shells under large initial stresses

Published online by Cambridge University Press:  17 February 2009

Rasajit Kumar Bera
Rasajit Kumar Bera
Affiliation:
Department of Mathematics, Presidency College, Calcutta, 700073, West Bengal, India.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The large-amplitude oscillations and buckling of an anisotropic cylindrical shell subjected to the initial inplane biaxial normal stresses have been analysed. The concept of anisotropy used by Lekhnitsky has been introduced into the field equations for cylindrical shells of isotropic material deduced by Donnell. The method of Galerkin and the method of successive approximation have been used to obtain the desired approximate solution. The expression for the critical loads for the buckling of anisotropic cylindrical shells has been obtained during intermediate stages of analysis. Some relevant frequency response graphs of the obtained solution are also presented. The minimum critical loads for various classes of anisotropy have also been given at the end of the discussion, to exhibit the effects of large deflections and imperfections on elastic buckling.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 3 , January 1990 , pp. 330 - 346
Copyright
Copyright © Australian Mathematical Society 1990

References

[1] Ambartsumian, A. and Khachaturian, A. A., “On the stability of vibrations of anisotropic plates”, Izv. Akad. Nauk SSSR, Old. Tekhn., Nauk (1960) 113–122.Google Scholar
[2] Bolotin, V. V., The dynamic stability of elastic systems (English translation), (Holden Day, San Francisco, 1964).Google Scholar
[3] Donnell, L. H., “A new theory for the buckling of thin cylinders under axial compression and bending”, Trans. Amer. Soc. Mech. Eng. 56 (1934) 795–815.CrossRefGoogle Scholar
[4] Evan-Iwanowski, R. M., “On the parametric response of structures”, Appl. Mech. Rev., 18 (1965) 699–702.Google Scholar
[5] Harris, G. Z. and Mansfield, E. H., “On the large deflection vibrations of elastic plates”, Philos. Trans. Roy. Soc. London Ser. A 261 (1967) 289–300.Google Scholar
[6] Lekhnitsky, S. G., Anisotropic plates (English translation), (Gordon and Breach Science Publishers, New York, 1956).Google Scholar
[7] Nowacki, W., “Problems of the stability and free vibrations of a cylindrical shell”, App. Mech. 3 (1955) 17–23.Google Scholar
[8] Nowinski, J. L., “Nonlinear oscillations and stability of plates under large initial stress”, Tech. Rep. 51 (Mechn. Eng. Dept., University of Delaware, Newark, Delaware, 1965), 1–20.Google Scholar
[9] Sunakawa, M., “Influences of temperature change and large amplitude on free flexural vibration of rectangular elastic plates”, Tokyo University ISAS Rep. 402, 31 (1966) 3–15.Google Scholar
[10] Timoshenko, S. P., Vibration problems in engineering (D. Van Nostrand Company Inc., 1961) 270–278.Google Scholar
[11] Timoshenko, S. P. and Gere, J. M., Theory of elastic stability (McGraw-Hill Book Company Inc., Second ed. 1961) 465–470.Google Scholar