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General Instability of Stiffened Circular Conical Shells under Hydrostatic Pressure*

Published online by Cambridge University Press:  07 June 2016

M. Baruch  and
J. Singer
M. Baruch
Affiliation:
Israel Institute of Technology
J. Singer
Affiliation:
Israel Institute of Technology
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Summary

Donnell type equilibrium and stability equations are derived for stiffened thin conical shells. The stiffeners are considered closely spaced and are therefore assumed to be “distributed” over the whole surface of the shell. In the proposed theory the stiffeners and their spacing may vary in any prescribed manner, but here only equal and equally spaced stiffeners are dealt with. The force- and moment-strain relations of the combined stiffener-sheet cross section are determined by the assumption of identical normal strains at the contact surface of stiffener and sheet.

The stability equations are solved for general instability under hydrostatic pressure by the method of virtual displacements. The solution used earlier for unstiffened conical shells, which satisfies some of the boundary conditions of simple supports only approximately, is again applied here. The effect of this incomplete compliance with boundary conditions is shown to be negligible by consideration of “boundary work”. The solution proposed for stiffened conical shells involves the concepts of “correcting coefficients” and minimisation of corresponding “error loads”.

Typical examples are analysed and the effect of eccentricity of stiffeners is investigated. Simplified approximate formulae for the critical pressure of frame-stiffened conical shells are also proposed.

Type
Research Article
Information
Aeronautical Quarterly , Volume 16 , Issue 2 , May 1965 , pp. 187 - 204
Copyright
Copyright © Royal Aeronautical Society. 1965

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References

1. Flügge, W. Die Stabilitat der Kreiszylinderschale. Ingenieur Archiv, Vol. 3 p. 463, 1932.CrossRefGoogle Scholar
2. Kendrick, S. The Buckling Under External Pressure of Circular Cylindrical Shells with Evenly Spaced, Equal Strength Circular Ring Frames. Parts I, II and III. Naval Construction Research Establishment, Dunfermline, Reports N.C.R.E. R. 211, 243 and 244, 1953.Google Scholar
3. Bodner, S. R. General Instability of a Ring-Stiffened Circular Cylindrical Shell Under Hydrostatic Pressure. Journal of Applied Mechanics, Vol. 24, No. 4 p. 547, December 1957.Google Scholar
4. Galletly, G. D., Slankard, R. C. and Wenk, E. General Instability of Ring-Stiffened Cylindrical Shells Subject to External Hydrostatic Pressure–Comparison of Theory and Experiment. Journal of Applied Mechanics, Vol. 25, No. 2 p. 259, June 1958.Google Scholar
5. Becker, H. and Gerard, G. Elastic Stability of Orthotropic Shells. Journal of the Aerospace Sciences, Vol. 29, No. 5 p. 505, May 1962.Google Scholar
6. von Sanden, K. and Tolke, F. On Stability Problems in Thin Cylindrical Shells. U.S. Navy DTMB Translation 33, December 1949. (Appeared originally in Ingenieur Archiv, Vol. 3 p. 24, 1932.)Google Scholar
7. Reynolds, T. E. Elastic Lobar Buckling of Ring-Supported Cylindrical Shells Under Hydrostatic Pressure. U.S. Navy DTMB Report 1614, September 1962.Google Scholar
8. Czerwenka, G. Untersuchungen von dünnen kurzen Zylindern, die durch Ringkleinstprofile enger und mittlerer Teilung verstarkt sind und unter Manteldruck stehen. Zeitschrift fiir Flugwissenschaften, Vol. 10, No. 6, pp. 163–202, June 1961.Google Scholar
9. Bijlaard, P. P. Buckling Under External Pressure of Cylindrical Shells Evenly Stiffened by Rings Only. Journal of the Aeronautical Sciences, Vol. 24, No. 6 p. 437, June 1957.Google Scholar
10. Singer, J. and Fersht-Scher, R. Buckling of Orthotropic Conical Shells Under External Pressure. Aeronautical Quarterly, Vol. XV p. 151, May 1964.Google Scholar
11. Serpico, J. C. Elastic Stability of Orthotropic Conical and Cylindrical Shells Subjected to Axisymmetric Loading Condition. Journal of the American Institute of Aeronautics and Astronautics, Vol. 1, No. 1 p. 128, January 1963.CrossRefGoogle Scholar
12. Baruch, M. and Singer, J. Effect of Eccentricity of Stiffeners on the General Instability of Stiffened Cylindrical Shells under Hydrostatic Pressure. Journal of Mechanical Engineering Science, Vol. 5, No. 1 p. 23, March 1963.CrossRefGoogle Scholar
13. Van Der Neut, A. General Instability of Orthogonally Stiffened Cylindrical Shells. Collected Papers on Instability of Shell Structures, 1962. N.A.S.A. T.N. D-1510 p. 309, December 1962.Google Scholar
14. Singer, Josef. Buckling of Conical Shells Under Axlsymmetrical External Pressure. Journal of Mechanical Engineering Science, Vol. 3, No. 4 p. 330, December 1961.Google Scholar
15. Seide, Paul. On the Buckling of Truncated Conical Shells under Uniform Hydrostatic Pressure. Proceedings of the IUTAM Symposium on the Theory of Thin Elastic Shells, p. 363, Delft, Holland, August 1959. North-Holland Publishing Company, Amsterdam.Google Scholar
16. Singer, J., Eckstein, A., Fersht-Scher, R. and Berkovits, A. Buckling of Isotropic, Orthotropic and Ring-Stiffened Conical Shells. Technion Research and Development Foundation, Haifa, Israel T.A.E. Report 30, Section 1, September 1963.Google Scholar
17. Baruch, M. Equilibrium and Stability Equations for Stiffened Shells. Proceedings of the Sixth Israel Annual Conference on Aviation and Astronautics, Israel Journal of Technology, Vol. 2, No. 1 p. 117, February 1964. The Weizmann Scientific Press of Israel and Jerusalem Academic Press Ltd.Google Scholar
18. Hoff, Nicholas J. and Singer, Josef. Buckling of Circular Conical Shells Under External Pressure. Proceedings of the IUTAM Symposium on the Theory of Thin Elastic Shells, p. 339. Delft, Holland, August 1959. North-Holland Publishing Company. Amsterdam.Google Scholar
19. Baruch, M. and Singer, J. General Instability of Stiffened Circular Conical Shells under Hydrostatic Pressure. Technion Research and Development Foundation, Haifa, Israel T.A.E. Report 28, June 1963.Google Scholar
20. Singer, Josef. The Effect of Axial Constraint on the Instability of Thin Conical Shells Under External Pressure. Journal of Applied Mechanics, Vol. 29, No. 1 p. 212, March 1962.Google Scholar
21. Baruch, M. General Instability of Stiffened Circular Conical Shells under Hydrostatic Pressure, Unpublished Doctoral Thesis submitted to the Technion–Israel Institute of Technology, Haifa, January 1963. {In Hebrew.)CrossRefGoogle Scholar
22. Singer, Josef. On the Correlation of the Critical Pressure of Conical Shells with that of Equivalent Cylindrical Shells. Journal of the American Institute of Aeronautics and Astronautics, Vol. 1, No. 11 p. 2675, November 1963.Google Scholar
23. Niordson, F. I. N. Buckling of Conical Shells Subjected to Uniform External Lateral Pressure. Transactions of the Royal Institute of Technology, Sweden, No. 10. 1947.Google Scholar