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On the Bifurcational Buckling of Elastic Beams, Plates and Shallow Shells

Published online by Cambridge University Press:  07 June 2016

G. G. Pope*
Affiliation:
Royal Aircraft Establishment, Farnborough
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Summary

The buckling behaviour of elastic beams, plates and shallow shells must often be investigated by calculating the slope at the instant of buckling of a curve relating the applied loading and the deformation parallel to the undeformed middle surface. This paper demonstrates the circumstances under which this slope can be calculated exactly without taking into account changes in the mode shape as the buckle amplitude increases.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1968

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References

1. Koiter, W. T. On the stability of elastic equilibrium. Thesis, Delft, 1945. (English translation NASA-TT-F-10833, 1967.)Google Scholar
2. Thompson, J. M. T. Basic principles in the general theory of elastic stability. Journal of the Mechanics and Physics of Solids. Vol. 11, p. 13, 1963.CrossRefGoogle Scholar
3. Thompson, J. M. T. Eigenvalue branching configurations and the Rayleigh-Ritz procedure. Quarterly of Applied Mathematics, Vol. 22, p. 244, 1964.CrossRefGoogle Scholar
4. Sewell, M. J. On the connexion between stability and the shape of the equilibrium surface. Journal of the Mechanics and Physics of Solids, Vol. 14, p. 203, 1966.CrossRefGoogle Scholar
5. Mushtam, K. M. and Galimov, K. Z. Non-linear theory of thin elastic shells. Translated by the Israel program for scientific translations, for NASA, 1961.Google Scholar
6. Timoshenko, S. P. and Gere, J. M. Theory of elastic stability, Chapter 7. 2nd Edition, McGraw-Hill, New York, 1961.Google Scholar
7. Chilver, A. H. Coupled modes of elastic stability. Journal of the Mechanics and Physics of Solids, Vol. 15, p. 15, 1967.CrossRefGoogle Scholar
8. Mansheld, E. H. Some identities on structural flexibility after buckling. Aeronautical Quarterly, Vol. IX, p. 300, 1958.CrossRefGoogle Scholar
9. Mansfield, E. H. On the analysis of elastic plates of variable thickness. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 15, p. 167, 1962.CrossRefGoogle Scholar
10. Pope, G. G. The buckling behaviour in axial compression of slightly-curved panels, including the effect of shear deformability. To be published in the International Journal of Solids and Structures.Google Scholar