Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T19:07:15.268Z Has data issue: false hasContentIssue false
  • English
  • Français

The Post-Buckling Behaviour of Simply-Supported Square Plates

Published online by Cambridge University Press:  07 June 2016

A. C. Walker
A. C. Walker*
Affiliation:
Department of Civil Engineering, University College, London
Get access

Summary

The post-buckling behaviour of flat square plates loaded along two opposite straight edges is analysed using the von Kármán equations, trigonometric series and Galerkin’s method. The unloaded edges are considered to be either free to distort in the plane of the plate or maintained straight but allowed to move bodily; all edges are simply-supported in the out-of-plane direction. The non-linear algebraic equations are solved approximately using a McLaurin’s series expansion technique which facilitates the development of explicit expressions for ultimate load, end shortening and stiffness. The effects of initial geometric imperfections are also studied and it is shown that the results for ultimate load prediction and end shortening are in good agreement with test results.

Information

Type
Research Article
Information
Aeronautical Quarterly , Volume 20 , Issue 3 , August 1969 , pp. 203 - 222
Copyright
Copyright © Royal Aeronautical Society. 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Levy, S. Bending of rectangular plates with large deflections. NACA TR 737, 1942.Google Scholar
2. Coan, J. M. Large deflection theory for plates with small initial curvature loaded in edge compression. Journal of Applied Mechanics, Vol. 18, Transactions, American Society of Mechanical Engineers, Vol. 73, pp. 143–151, 1951.CrossRefGoogle Scholar
3. Yamaki, N. Post-buckling behaviour of rectangular plates with small initial curvatures loaded in edge compression. Journal of Applied Mechanics, Vol. 26, Transactions, American Society of Mechanical Engineers, Vol. 81, Series E, pp. 407–414, 1959.Google Scholar
4. Stein, M. Loads and deformations of buckled rectangular plates. NASA TR R-40, 1959.Google Scholar
5. Walker, A. C. Flat rectangular plates subjected to a linearly-varying edge compressive loading, pp. 208–247 of Thin-walled structures, edited by Chilver, A. H., Chatto & Windus, London, 1967.Google Scholar
6. Schmidt, L. A. et al. Finite deflection structural analysis using plate and shell discrete elements. AIAA Journal, Vol. 6, pp. 781–791, 1968.Google Scholar
7. Thompson, J. M. T. and Walker, A. C. The non-linear perturbation analysis of discrete structural systems. International Journal of Solids and Structures, Vol. 4, pp. 757–768, 1968.Google Scholar
8. Walker, A. C. An analytical study of the rotationally symmetric non-linear buckling of a complete spherical shell under external pressure. To appear in the International Journal of Mechanical Sciences, Vol. 10, pp. 695–710, 1968.Google Scholar
9. Timoshenko, S. P. Theory of elastic stability. McGraw-Hill, New York, 1936.Google Scholar
10. Hu, Pai C. et al. Effect of small deviations from flatness on effective width and buckling of plates in compression. NACA TN 1124, Sept. 1946.Google Scholar
11. Needham, R. A. The ultimate strength of aluminum alloy formed structural shapes in compression. Journal of the Aeronautical Sciences, Vol. 21, No. 4, p. 217, 1954.Google Scholar
12. Heimerl, G. J. and PRIDE, R. A. Plastic buckling of simply-supported plates. NACA TN 1817, 1949.Google Scholar
13. Bijlaard, P. P. and Fisher, G. P. Column strength of H-sections and square tubes in the post-buckling range of component plates. NACA TN 2640, 1952.Google Scholar
14. Gerard, G. The crippling strength of compression elements. Journal of the Aeronautical Sciences, Vol. 25, No. 1, p. 37, 1958.Google Scholar
15. Nishino, F. Buckling strength of columns and their components plates. Doctoral Dissertation, Lehigh University, 1964.Google Scholar
16. Stussi, F. et al. Ausbeulen rechtickiger Platten unter Druck, Biegung und Druck, mit Biegung. Mitteilungen aus dem Institut für Baustatik, ETH Zurich, No. 26, Verlag Leeman, Zurich, 1953.Google Scholar
17. Schumann, L. and Back, G. Strength of rectangular flat plates under edge compression. NACA Report 356, 1931.Google Scholar
18. Perry, S. H. Statistical variation of buckling strength. Doctoral Dissertation, University of London, 1966.Google Scholar
19. Cox, H. L. The buckling of plates and shells. Pergamon Press, London, 1963.Google Scholar
20. Hemp, W. S. The theory of flat panels buckled in compression. ARC R & M 2178, June 1945.Google Scholar