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The Elements of the Buckling of Curved Plates

Published online by Cambridge University Press:  28 July 2016

H. L. Cox  and
E. Pribram
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Extract

The buckling of a round tube or curved A plate under axial compression is an example of that class of instability in which the initial buckled form becomes itself at once unstable. As a result the buckle immediately develops to a large amplitude, often with loud noise. This class of instability has been aptly termed “oil canning” from a familiar example.

Thorough investigation of oil canning problems must always be tedious. As for any buckling problem it is essential to use large deflection theory and, since the amplitude of buckle rapidly becomes large, it is necessary also to consider in detail the distribution of the membrane (or mid-plane) stresses due to the buckle. This necessity, in combination with peculiar buckled forms, renders the complete solution even for a tube extremely difficult and tedious. Moreover, since the buckled form for a complete tube does not accord at all well with the edge conditions for a curved plate, the full analysis for the latter is almost prohibitively difficult.

Type
Research Article
Information
The Aeronautical Journal , Volume 52 , Issue 453 , September 1948 , pp. 551 - 565
Copyright
Copyright © Royal Aeronautical Society 1954

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References

References

1. Von Kármán, TH. and Hsue-Shen, Tsien. The Buckling of Thin Cylindrical Shells under Axial Compression. Journal of the Aeronautical Sciences, June 1941.CrossRefGoogle Scholar
2. Leggett, D. M. A. and Jones, R. P. N.. The Behaviour of a Cylindrical Shell under Axial Compression when the Buckling Load has been Exceeded. R.A.E., S.M.E. Report No. 3204 (ARC number 6135), 1942.Google Scholar
3. Koiter, W. T. Over de stabiliteit van het elastisch evenwicht (Dissertation), Amsterdam, 1945.Google Scholar
4. Marguerre, K.. On the Strength of Shells of Small Curvature. Proceedings 5th International Congress of Applied Mechanics.Google Scholar
5. Cox, H. L. The Buckling of a Flat Rectangular Plate under Axial Compression and its Behaviour after Buckling. Aero. Res. Council, Report and Memorandum No. 2041, 1945.Google Scholar
6. Jackson, K. B. and Hall, A. H. Curved Plates in Compression. National Research Council of Canada, Report No. MM-180, 1945.Google Scholar
7. Leggett, D. M. A. The Buckling of a Long Curved Panel under Axial Compression. Aeronautical Research Council Rep. & Mem. No. 1899, 1942.Google Scholar
8. Welter, G.. Curved Aluminium Alloy Sheets in Compression for Monocoque Constructions. Journal of the Aeronautical Sciences, July 1945.Google Scholar

Bibliography

9. Southwell. General Theory of Elastic Stability. Phil. Trans. A. Vol. 213 (1913).Google Scholar
10. Chwalla, E. Collapse of Tubes under End Thrust. Z.A.M.M. 10, p. 72 (1930).Google Scholar
11. Redshaw, S. C. Elastic stability of a thin curved panel. A.R.C. R. & M. 1565. May, 1933.Google Scholar
12. Lundquist, E. E. Strength tests of thin-walled duralumin cylinders in compression. N.A.C.A. Report No. 473. 1933.Google Scholar
13. Donnell, L. H. A new theory for the buckling of thin cylinders under axial compression and bending. A.S.M.E. Trans. Vol. 56. No. 11. November, 1934.Google Scholar
14. Heck and Ebner. Formeln und Berechungsverfahren fuer die Festigkeit von Platten und Schalenkonstruktionen. Luftfahrtforschung Vol. XI, p. 221 (1935).Google Scholar
15. Gerard and Dickens. Stressed-skin structures. Compression tests of panels with tubular stiffeners. A.R.C. R. &M. 1830, Dec, 1936.Google Scholar
16. Ballerstedt and Wagner. Versuche über die Festigkeit dünner unversteifter Zylinder unter Schub-und Längskräften. Luftfahrtforschung Vol. 13, No. 9, p. 309. September, 1936.Google Scholar
17. Ebner. Theorie und Versuche zur Festigkeit1 von Schalenruempfen. Luftfahrtforschung Vol. XIV, p. 93 (1937).Google Scholar
18. Redshaw. Elastic stability of a curved plate under axial thrusts. J. R.Ae.S., Vol. 42, 1938.Google Scholar
19. Wenzek, W. A.. The effective width of curved sheet after buckling. N.A.C.A. T.M. 880.Google Scholar
20. Kanemitsu and Nojima. Axial compression test of thin circular cylinders. Calif. Inst. Tech. Thesis. 1939.Google Scholar
21. Kármán, Dunn and Tsien. Influence of curvature on the buckling characteristics of structures. Jnl. Aero. Sci, p.276. 1940.CrossRefGoogle Scholar
22. Cox and Clenshaw. Compression tests on curved plates of thin sheet Duralumin. A.R.C. R. & M. 1894. November, 1941.Google Scholar
23. Lundquist, E. E.. Preliminary data on buckling strength of curved sheet panels in compression. N.A.C.A. A.R.R. 24. Nov., 1941.Google Scholar
24. Fischel, J. R.. The compressive strength of thin aluminium-alloy sheet in the plastic region. Jnl. Aero. Sci., p. 373. Aug., 1941.CrossRefGoogle Scholar
25. Roark. Stresses and deflections in thin shells and curved plates due to concentrated and variously distributed loading. N.A.C.A. T.N. 806. 1940.Google Scholar
26. Levy, Mcpherson and Ramberg. Effect of rivet and spot-weld spacing on the strength of axially loaded sheet-stringer panels of 24 S-T aluminium alloy. N.A.C.A. T.N. 856. Aug., 1942.Google Scholar
27. Stowell, E.. Critical compressive stress for curved sheet supported along all edges and elastically restrained against rotation along the unloaded edges. N.A.C.A. R.B. 3107. September, 1943.Google Scholar
28. Lundquist and Schuette. Critical stresses for plates. N.A.C.A. A.R.R. 3L27. October 1943.Google Scholar
29. Levy, S.. Large deflection theory of curved sheet. N.A.C.A. T.N. 895. May 1943.Google Scholar
30. Crate and Levin. Data on buckling strength of curved sheet in compression. N.A.C.A. A.R.R. 3L04. October 1943.Google Scholar
31. Holt, M.. Tests of aluminium-alloy stiffenedsheet specimens cut from an airplane wing. N.A.C.A. T.N. 883. January, 1943.Google Scholar
32. Some investigations of the general instability of stiffened metal cylinders. Part 4. N.A.C.A. T.N. 908. August, 1943.Google Scholar
33. Mcpherson, Fienup and Zibritosky. Effect of developed width on strength of axially loaded curved sheet stringer panels. N.A.C.A. A.R.R. 4H08. November, 1944.Google Scholar
34. Ramberg, Levy and Fienup. Effect of curvature on strength of axially loaded sheetstringer panels. N.A.C.A. T.N. 944. August, 1944.Google Scholar
35. Cox, H. L.. Note on the buckling of curved plates under axial compression. A.R.C. Report-No. 8406. February, 1945.Google Scholar
36. Dei Poli, Sandro. Il comportamento elastico delle pareti di forma cilindrica non perfetta, soggette a compressione. Politecnico di Milano. October, 1945.Google Scholar
37. Welter, G.. Influence of different factors on buckling loads of curved thin aluminium-alloy sheets for monocoque constructions. J. Aero. Sci., p. 204. April, 1946.Google Scholar
38. Welter, G.. The effect of radius of curvature and preliminary artificial eccentricities on buckling loads of curved thin aluminiumalloy sheets for monocoque constructions. J. Aero. Sci., p. 593. November, 1946.Google Scholar
39. Stowell. Critical compression stress for curved sheet supported along all edges. N.A.C.A. R.B. 3107. 1946.Google Scholar
40. Batdorf, Schildcrout and Stein. Critical stress of thin-walled cylinders in axial compression. N.A.C.A. T.N. 1343. June, 1947.Google Scholar
41. Batdorf. A simplified method of elasticstability analysis for thin cylindrical shells. 1 : Donnell's Equation and 2 : Modified equilibrium Equation. N.A.C.A. T.N. 1341 and 1342. June, 1947.Google Scholar
42. Dei Poli, Sandro. Sul calcolo delle pareti cilindriche compresse secondo le generatrici. Politecnico di Milano. June, 1946.Google Scholar
43. Dei Poli, Sandro. Ricerche sperimentali sulle pareti cilindriche compresse secondo le generatrici. Politecnico di Milano. February, 1947.Google Scholar
44. Dei Poli, Sandro. Sulla stabilita elastica della striscia cilindrica compressa secondo le generatrici. Accademia delle Scienze di Torino. Voi. 81. 1946-47.Google Scholar