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The buckling behavior of uniformly heated thin circular cylindrical shells

An experimental investigation is undertaken to provide design-stability data for uniformly heated, clamped, thin circular cylindrical shells

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Abstract

The results of buckling tests on uniformly heated, clamped, thin circular cylindrical shells are presented and discussed. Particular attention is paid to both the actual buckling process and the ensuing post-buckling behavior. Load vs. end-shortening curves are included. The possibility of “snap-through” buckling which occurs at a value of end shortening greater than that corresponding to the maximum supported load is experimentally verified. A comparison of the present experimental results with available theory is made. It is observed that the experimental values of the buckling temperature can be substantially greater than the temperatures calculated by linear theory from the experimental buckling loads; however, the buckling stresses are the same whether the loading is thermal or mechanical.

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Abbreviations

E :

Young’s modulus of elasticity, lb/in.2

L :

length of cylindrical shell, in.

P :

axial compressive load, lb

R :

mean radius of cylindrical shell, in.

T :

temperature rise above ambient, °F

T i :

temperature of cylindrical shell prior to test (equivalent to ambient temperature), °F

Z :

cylinder curvature parameter\(Z = L^2 /Rt\sqrt {1 - v^2 }\)

n :

number of circumferential half-waves in deformation pattern

k x :

axial-stress coefficient\(k_x = \frac{{12\sigma _x (1 - v^2 )}}{{\pi ^2 E}}\left( {\frac{L}{t}} \right)^2\)

t :

wall thickness of cylindrical shell, in.

t bu :

elapsed time between initiation of heating and instant of bucking, sec

u, v, w :

axial, circumferential and radial displacements of a point on median surface of cylindrical shell, in.

x, y, z :

axial, circumferential and radial coordinates of a point on median surface of cylindrical shell

α:

coefficient of linear thermal expansion, in./in. °F

\(\bar \varepsilon\) :

end-shortening ratio\(\bar \varepsilon = (\alpha {\rm T}L)_{cr} /(\alpha TL)_{cl}\)

ν:

Poisson’s ratio

\(\sigma _x\) :

axial-compressive stress, lb/in.2

(1):

refers to axial-stress coefficient which is determined from axial load

(2):

refers to axial-stress coefficient which is determined from temperature rise

bu :

refers to quantity at the instant of buckling (equivalent tocr)

cl :

classical

cr :

critical, refers to quantity at the instant of buckling

eq :

equivalent

References

  1. Hoff, N.J., “Thermal Buckling of Thin-Walled Circular Cylindrical Shells,”SUDAER No. 137, Dept. Aeronautics and Astronautics, Stanford Univ., Stanford, Calif., October 1962 (see also, Flambement Thermique des Coques Cylindriques Circulair à Parois Minces, High Temperatures in Aeronautics, Proc. 50th Anniv. Symp. Laboratorio di Aeronautica of the Politecnico di Torino, Torino, Italy, September 1962, ed. Carlo Ferrari, Pergamon Press, Oxford, England, 1963).

    Google Scholar 

  2. Libove, C., and Tong, K. N., “The Influence of Thickness-Wise Temperature Gradients on the Large Deflections and Stability of Thin Elastic Shells,” Syracuse Univ. Rsch. Inst., SURI Rpt. No. NE 790-612T, Syracuse, N. Y., February 1961.

  3. Hoff, N. J., “Buckling of Thin Cylindrical Shells Under Hoop Stresses Varying in Axial Direction,”Jnl. Appl. Mech.,24 (3)405–412 (September 1957).

    MATH  MathSciNet  Google Scholar 

  4. Zuk, W., “Thermal Buckling of Clamped Cylindrical Shells,”Jnl. Aeronautical Sci.,24 (5),359 (1957).

    Google Scholar 

  5. Johns, D. J., Houghton, D. S., and Webber, J. P. H., “Buckling Due to Thermal Stress of Cylindrical Shells Subjected to Axial Temperature Distributions”, Rpt. No. 147, Coll. Aeronautics, Cranfield, England (May 1961).

  6. Anderson, M. S., “Combinations of Temperature and Axial Compression Required for Buckling of a Ring-Stiffened Cylinder”, NASA TN D-1224 (April 1962).

  7. Anderson, M. S., “Thermal Buckling of Cylinders, Collected Papers on Instability of Shell Structures”, NASA TN D-1510, 255–266 (December 1962).

  8. Abir, D., andNardo, S. V., “Thermal Buckling of Circular Cylindrical Shells Under Circumferential Temperature Gradients”,Jnl. Aerospace Sci.,26 (12),803 (1959).

    MathSciNet  Google Scholar 

  9. Hill, D. W., “Buckling of a Thin Circular Cylindrical Shell Heated Along an Axial Strip”,SUDAER No. 88, Dept. Aeronautics and Astronautics, Stanford Univ., Stanford, Calif. (December 1959).

    Google Scholar 

  10. Hoff, N. J., Chao, C. C., andMadsen, W. A., “Buckling of a Thin Walled Circular Cylindrical Shell Heated Along an Axial Strip”,SUDAER No. 142, Ibid. (September 1962) [see also, Jnl. Appl. Mech.,31 (2) (June 1964)].

    Google Scholar 

  11. Ross, B., Mayers, J., andJaworski, A., “Buckling of Thin Circular Cylindrical Shells Heated Along an Axial Strip”,Experimental Mechanics,5 (9),247–256 (1965).

    Google Scholar 

  12. Gerard, G., and Becker, H., Handbook of Structural Stability, Pt. III, “Buckling of Curved Plates and Shells”, NACA TN 3783 (Aug. 1957).

  13. Batdorf, S. B., “A Simplified Method of Elastic Stability Analysis for Thin Cylindrical Shells”, NACA Rept. No. 874 (June 1947).

  14. Harris, L. A., Suer, H. S., Skene, W. T., andBenjamin, R. J., “The Stability of Thin-Walled Unstiffened Circular Cylinders under Axial Compression Including the Effects of Internal Pressure”,Jnl. Aeronautical Sci. 24 (8),587 (1957).

    Google Scholar 

  15. Sunakawa, M., “Deformation and Buckling of Cylindrical Shells Subjected to Heating”,Rpt. No. 370, Aero. Rsch. Inst., Univ. of Tokyo, Tokyo, Japan (July 1962).

    Google Scholar 

  16. Hoff, N. J., “A Non-Linear Model Study of the Thermal Buckling of Thin Elastic Shells”,SUDAER No. 173, Dept. Aeronautics and Astronautics, Stanford Univ., Stanford, Calif., November 1963 [see also, Jnl. Appl. Mech., Ser. E,32 (1), 71–75 (March 1965)].

    Google Scholar 

  17. Thielemann, W. F., “New Developments in the Non-Linear Theories of the Buckling of Thin Cylindrical Shells”,Aeronautics and Astronautics, ed. N. J. Hoff andW. G. Vincenti, 76, Pergamon Press, London (1960).

    Google Scholar 

  18. Thielemann, W. F., “On the Postbuckling Behavior of Thin Cylindrical Shells, Collected Papers on Instability of Shell Structures”, NASA TN D-1510, 203–216 (December 1962).

  19. Ross, B., Hoff, N. J. andHorton, W. H., “The Buckling Behavior of Uniformly Heated Thin Circular Cylindrical Shells”,SUDAER No. 225, Dept. Aeronautics and Astronautics, Stanford University, Stanford, Calif. (April 1965).

    Google Scholar 

  20. Heise, O., “Die Experimentelle Ermittlung der Beullasten von Längsgedrückten dünnwandigen Kreiszylinderschalen”, DFL-Bericht No. 214, Deutsche Forschungsanstalt für Luft und Raumfahrt E. V., Braunschweig, Germany (1963).

  21. von Kármán, T. andTsien, H. S., “The Buckling of Thin Cylindrical Shells under Axial Compression”,Jnl. Aeronautical Sci.,8, (8),303–312 (June 1941).

    Google Scholar 

  22. Hoff, N. J., andMadsen, W. A., “Recent Results Obtained on the Snap-Through and Postbuckling Load of Axially Compressed Circular Cylindrical Shells”,SUDAER, No. 227, Dept. of Aeronautics and Astronautics, Stanford Univ., Stanford, Calif. (April 1965).

    Google Scholar 

  23. Batdorf, S. B., Schildcrout, M., and Stein, M., “Critical Stress of Thin-Walled Cylinders in Axial Compression”, NACA TR 887 (1947).

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Author information

Authors and Affiliations

  1. Stanford Research Institute, Menlo Park, Calif.

    B. Ross (Engineering Physicist)

  2. Department of Aeronautics and Astronautics, Stanford University, USA

    N. J. Hoff (Head) & W. H. Horton (Associate)

Authors
  1. B. Ross
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  2. N. J. Hoff
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  3. W. H. Horton
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Additional information

was formerly Research Associate, Department of Aeronautics and Astronautics, Stanford University, Stanford, Calif.

This paper is based on part of a dissertation submitted to Stanford University in partial fulfillment of the requirements for the PhD degree.

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Ross, B., Hoff, N.J. & Horton, W.H. The buckling behavior of uniformly heated thin circular cylindrical shells. Experimental Mechanics 6, 529–537 (1966). https://doi.org/10.1007/BF02327232

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