Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T23:38:24.525Z Has data issue: false hasContentIssue false
  • English
  • Français

Orthotropic behaviour of shells and stability of uniaxially compressed cylinders

Published online by Cambridge University Press:  04 July 2016

M. S. Hanna  and
A. W. Beshara
M. S. Hanna
Affiliation:
Ain Shams University Cairo, Egypt
A. W. Beshara
Affiliation:
Ain Shams University Cairo, Egypt
Get access Rights & Permissions [Opens in a new window]

Abstract

Shells, stability under various types of loadings and their combinations have not yet been completely investigated. This is due to incomplete knowledge of shell philosophy. The aim of this study is to provide a complete and integrated method for treating shell problems on a pure statical basis. This study introduces shell orthotropic behaviour, discusses hoop stress resultant actions, and applies the shell equilibrium equations to a uniaxially compressed cylindrical shell with finite length and fixed ends. Theoretical results are also compared with previously published experimental work. The behaviour of shells in elastic and plasto-elastic range is discussed for a wide range of shell geometries (dimensions), material properties, methods of manufacture, material imperfections, and methods of load application. From this study we conclude mainly that shells behave orthotropically. Their flexural rigidities are related to their radii of curvature and the resultant buckling mode. The buckling strength of a shell depends on shell geometry, material properties, buckling mode and shell coefficient H. This shell coefficient is affected by the method of manufacture, existing imperfections, degree of plasticity, and the method of load application. H can be evaluated by experiment.

Type
Research Article
Information
The Aeronautical Journal , Volume 97 , Issue 963 , March 1993 , pp. 111 - 117
Copyright
Copyright © Royal Aeronautical Society 1993 

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. Lorenz, R. Achsen symmetrische verzerrungen in dunnwandigen hohlzlinder, Zeit shrift des vereines Deutscher Ingenieure, October 1908, 52, pp 1706-13.Google Scholar
2. Southwell, R. V. The Strength of Tubular Struts, Phil Trans Ser A, 213, p 187, 1913.Google Scholar
3. Timoshenko, S. P. Theory of elastic stability McGraw Hill Books, New York, 1936, p 439.Google Scholar
4. Robertson, A. The strength of Tubular struts, British Aeronautical Research Committee, R&M 1185, 1929.Google Scholar
5. Flugge, W., Die stabilitaet der kreiszylinderschale, Ing Arch, 1932, 3, p 463.Google Scholar
6. Eung, Y. C. and Sechler, E. E. Instability of thin elastic shells, In: Structural mechanics, Proceedings of First symposium on Naval Structural Mechanics, Pergamon Press, 1960.Google Scholar
7. Donnell, L. H. and Wan, C. C. Effect of imperfections on buckling of thin cylinders and columns under axial compression, J Appl Mech, 1950, 17, (1), p 73.Google Scholar
8. Von Karman, T. and Tsien, H. S. The buckling of thin cylindrical shells under axial compression, J Aeronaut Set, 1941, 8, (8), p 302.Google Scholar
9. Tsien, H. S. A theory for the buckling of thin shells, J Aeronaut Sci, 1942, 9, (10), p 373.Google Scholar
10. Hanna, M. S. New approach for the elastic instability of cylindrical-shells, Engrs Mag, May 1985, 41, (362), pp 85–90.Google Scholar
11. Huber, M. T. Teorya Plyt, Lvov, 1922.Google Scholar
12. Wilson, W. M. and Newmark, N. M. The strength of thin cylindrical shells as columns, Bull No 255, Eng Exp Sta, Univ III, 28 February, 1933.Google Scholar
13. Donnell, L. H. A new theory for the buckling of thin cylinders un der axial compression and bending, Trans Amer Soc Mech Engrs, 1934, 56 p 795.Google Scholar
14. Kappus, R. Druck, Beige-und Torsionsversuche mit Holmrohren aus stahl Aero 70, Jahrvuch 1939 der Deutschen Luftfahrtforschung, pp 1426–1438.Google Scholar
15. Lundquist, E. E. Strength Tests of Thin-Walled Duralumin Cylinders in Compression, NACA Report No 473, 1933.Google Scholar
16. Babcock, C. D. and Sechler, E. E. The effect of initial imperfections on the buckling stress of cylindrical shells, NASA TN-D-2005, 1963.Google Scholar
17. Almroth, B. O., Holmes, A. M. C. and Brush, D. O. An experimental study of the buckling of cylinders under axial compression, Exp Mech, 1964, 4, pp 263–270.Google Scholar
18. Tennyson, R. C. Buckling modes of circular cylindrical shells under axial compression, AIAA J, August 1969, 7, (8), pp 1481–1487.Google Scholar
19. Yamaki, N., Otomo, K. and Matsuda, K. Experiments on the post-buckling behaviour of circular cylindrical shells under compression, Exp Mech, January 1975, pp 23–28.Google Scholar
20. Weingarten, V. I., Morgan, E. J. and Seide, P. The final report on development design criteria for elastic stability of thin shells structures, STL/TR-60-0000-19425, September 1960, pp 39.Google Scholar