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The Elastic Instability of a Complete Spherical Shell

Published online by Cambridge University Press:  07 June 2016

J.M.T. Thompson
J.M.T. Thompson*
Affiliation:
Department of Engineering, University of Cambridge
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Summary

The elastic instability of a complete spherical shell under uniform external pressure is studied experimentally and theoretically. The premature snapping of a thin elastic shell, made of polyvinyl chloride, is seen to be classical in nature. The experimental maximum pressure and pre-snapping bending deformation are correlated with the theoretical behaviour of an initially imperfect shell. The large deflection behaviour of a perfect shell is assessed experimentally, and the stable post-buckling states are observed to be rotationally symmetric. A fairly precise theoretical analysis of these states is performed, the use of a high-speed digital computer allowing a considerable advance over previous treatments. The experimental and theoretical post-buckling curves are in good agreement, yielding the first detailed correlation of post-snapping equilibrium states in the field of shell instability.

Type
Research Article
Information
Aeronautical Quarterly , Volume 13 , Issue 2 , May 1962 , pp. 189 - 201
Copyright
Copyright © Royal Aeronautical Society. 1962

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References

1. Fung, Y.C. and Sechler, E.E. Instability of Thin Elastic Shells. Proceedings of the First Symposium on Naval Structural Mechanics, Pergamon Press, 1960.Google Scholar
2. Von Kármán, T. and Tsein, H.S. TheBucklingofSphericalShellsbyExternal Pressure. Journal of the Aeronautical Sciences, Vol. 7, p. 43, December 1939.Google Scholar
3. Kempner, J. Postbuckling Behaviour of Axially Compressed Circular Cylindrical Shells. Journal of the Aeronautical Sciences, Vol. 21, p. 329, May 1954.Google Scholar
4. Donnell, L.H. and Wan, C.C. Effect of Imperfections on Buckling of Thin Cylinders and Columns under Axial Compression. Journal of Applied Mechanics, Vol. 17, p. 73. March 1950.CrossRefGoogle Scholar
5. Budiansky, B. Buckling of Clamped Shallow Spherical Shells. The Theory of Thin Elastic Shells, North Holland Publishing Company, Amsterdam, 1960.Google Scholar
6. Thompson, J.M.T. Elastic Buckling of ThinSpherical Shells. Proceedings of the Symposium on Nuclear Reactor Containment Buildings and Pressure Vessels, Butterworths, 1960.Google Scholar
7. Thompson, J.M.T. The Elastic Instability of Spherical Shells. Ph.D.Dissertation, Cambridge University, September 1961.Google Scholar
8. Flügge, W. Stresses in Shells. Springer, Berlin, 1960.Google Scholar
9. Hildebrand, F.B. Introduction to Numerical Analysis. McGraw-Hill, 1956.Google Scholar
10. Thompson, J.M.T. Stability of Elastic Structures and their Loading Devices. Journal of Mechanical Enginering Science, Vol. 3, p. 153, June 1961.Google Scholar
11. Tsien, H.S. A Theory for the Buckling of Thin Shells. Journal of the Aeronautical Sciences, Vol. 9, p. 373, August 1942.Google Scholar
12. Yoshimura, Y. and Uemura, M. The Buckling of Spherical Shells due to External Pressure. Reports, Institute of Science and Technology, University of Tokyo, Vol. 3, p. 316, 1949.Google Scholar
13. Mushtari, H.M. and Surkin, R.G. On the Non-linear Stability Theory of Elastic Equilibrium of a Thin Spherical Shell under the Influence of Uniformly Distributed Normal External Pressure. Prikladnaya Matematika i Mekhanika, Vol. 6, No. 14, p. 573, 1950.Google Scholar
14. Mushtari, H.M. On the Theory of Stability of a Spherical Shell Subjected to External Pressure. Prikladnaya Matematika i Mekhanika, Vol. 19, No. 2, p. 251, 1955.Google Scholar
15. Surkin, R.G. Problem of Loss of Stability of a Spherical Shell Subjected to an External Evenly Distributed Pressure. Izvestiya Kazanskogo Filiala Akademii Nauk SSSR, Seriya Fiziko-Matematicheskh i Teknicheskh Nauk, No. 10, p. 51, 1956.Google Scholar