Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T16:44:04.898Z Has data issue: false hasContentIssue false

A Comparison of the Characteristic Equations in the Theory of Circular Cylindrical Shells

Published online by Cambridge University Press:  07 June 2016

D. S. Houghton
Affiliation:
The College of Aeronautics, Cranfield
D. J. Johns
Affiliation:
The College of Aeronautics, Cranfield
Get access

Summary

Characteristic equations are derived for thin circular shells, based on various approximations to the linear elastic theory of small deformations. By representing the deformation in a Fourier series in the circumferential direction, the roots of these equations are computed for a range of the significant parameters and compared.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1961

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.)

References

1. Jaeger, L. A. and Chilver, A. H. Characteristics Equations in the Theory of Circular Cylindrical Shells. Nuclear Reactor Containment Building and Pressure Vessels. Proceedings of Symposium. Butterworths, London, 1960.Google Scholar
2. Biezeno, C. B. and Grammel, R. Engineering Dynamics, Vol. II. Blackie, London, 1956.Google Scholar
3. Novozhilov, V. V. The Theory of Thin Shells. Noordhoff, Groningen, 1959.Google Scholar
4. Timoshenko, S. Theory of Plates and Shells. McGraw-Hill, 1940.Google Scholar
5. Love, A. E. H. A Treatise on the Mathematical Theory of Elasticity. 4th Edition, Cambridge University Press, 1927.Google Scholar
6. Houghton, D. S. and Johns, D. J. Deformation Equations for Non-Circular Cylinders. Journal of the Royal Aeronautical Society, December 1960.Google Scholar
7. Bijlaard, P. P. Stresses from Local Loadings in Cylindrical Pressure Vessels. Transactions of the American Society of Mechanical Engineers, August 1955.Google Scholar
8. Vlasov, V. S. Basic Differential Equations in the General Theory of Elastic Shells. N.A.C.A. T.M. 1241, 1951.Google Scholar
9. Donnell, L. H. Stability of Thin Walled Tubes under Torsion. N.A.C.A. Report 479, 1933.Google Scholar
10. Flügge, W. Statik und Dynamik der Schalen. Springer, Berlin, 1934.Google Scholar
11. Naghdi, P. M. and Berry, J. G. On the Equations of Motion of Cylindrical Shells. Journal of Applied Mechanics, June 1954.CrossRefGoogle Scholar
12. Morley, L. S. D. An Improvement on Donnell's Approximation for Thin Walled Circular Cylinders. Quarterly Journal of Mechanics, Vol. 12, 1959.Google Scholar
13. Kennard, E. H. The New Approach to Shell Theory. Journal of Applied Mechanics, Vol. 20, 1953.Google Scholar
14. Hoff, N. J. The Accuracy of Donnell's Equations. Journal of Applied Mechanics, Vol. 22, p. 329,1955.Google Scholar
15. Yuan, S. W. Thin Cylindrical Shells Subjected to Concentrated Loads. Quarterly of Applied Mathematics, Vol. 4, p. 13, 1946.Google Scholar
16. Ting, L. and Yuan, S. W. On Radial Deflection of a Cylinder of Finite Length with Various End Conditions. Journal of the Aeronautical Sciences. Vol. 25, p. 230, April 1958.Google Scholar