Abstract
The results of buckling tests on circular cylinders heated uniformly along axial strips are presented and discussed. Calculations of critical temperature based upon the small-deflection theory for thin circular cylindrical shells are included and a comparison is made between theoretical and experimental results. Cylinders heated along axial strips of given widths have a theoretically predicted behaivor which corresponds reasonably well to the behavior obtained by experiment. Curves are included showing the variation of critical temperature with respect to heated axial-strip width.
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Abbreviations
- D :
-
flexural rigidity\(D = \frac{{Et^3 }}{{12(1 - \nu ^2 )}}\), lb in
- E :
-
Young's modulus of elasticity, lb/in.2
- L :
-
length of cylindrical shell, in
- R :
-
mean radius of cylindrical shell, in
- T :
-
temperature rise above ambient, °F
- T 0 :
-
temperature rise above ambient along median axial generator of cylindrical shell (y=0), °F
- T cr :
-
temperature rise above ambient at instant of buckling, °F
- T 0cr :
-
temperature rise above ambient which existed at center of cylindrical shell (x=0,y=0) at instant of buckling, °F
- T xcr :
-
temperature rise above ambient which existed at location of deformation pattern (x=x cr ,y=0) at instant of buckling, °F
- b :
-
width of axial-heated strip, in
- k 1 :
-
attenuation coefficient in expression for assumed temperature distribution
- k 2 :
-
attenuation coefficient in expression for assumed deformation pattern
- m :
-
number of axial half waves in deformation pattern
- n :
-
number of circumferential half waves in deformation pattern
- t :
-
wall thickness of cylindrical shell, in
- t cr :
-
elapsed time between initiation of heating and instant ofbuckling, sec
- w :
-
radial displacement inz-direction, in
- w 0 :
-
radial displacement inz-direction along median axial generator of cylindrical shell (y=0), in
- x,y,z :
-
axial, circumferential and radial coordinates of a point on median surface of cylindrical shell
- x cr :
-
distance along median axial generator to location of deformation pattern, in
- Φ:
-
thermal energy radiated to axial-heated strip, watts/in2
- α:
-
coefficient of linear thermal expansion, in./in./°F
- \(\lambda _x\) :
-
axial half wavelength of buckles in deformation pattern, in
- \(\lambda _y\) :
-
circumferential half wavelength of buckles in deformation pattern, in
- ν:
-
Poisson's ratio
- \(\sigma _x\) :
-
median surface stress in axial direction, lb/in2
- \(\sigma _{xcl}\) :
-
classical buckling stress of a uniformly compressed thin cylindrical shell, lb/in2.\(\sigma _{xcl} = 0.6\frac{{Et}}{R}\)
- ϕ:
-
circumferential angular coordinate on median surface of cylindrical shell (ϕ=y/R)
- \(\nabla ^4\) :
-
Linear operator\(\nabla ^4 = \frac{{\partial ^4 }}{{\partial x^4 }} + 2\frac{{\partial ^4 }}{{\partial x^2 \partial y^2 }} + \frac{{\partial ^4 }}{{\partial y^4 }}\)
- \(\nabla ^8\) :
-
Linear operator\(\begin{gathered} \nabla ^8 = \frac{{\partial ^8 }}{{\partial x^8 }} + 4\frac{{\partial ^8 }}{{\partial x^6 \partial y^2 }} + 6\frac{{\partial ^8 }}{{\partial x^4 \partial y^4 }} \hfill \\ + 4\frac{{\partial ^8 }}{{\partial x^2 \partial y^6 }} + \frac{{\partial ^8 }}{{\partial y^8 }} \hfill \\ \end{gathered}\)
- cl :
-
classical
- cr :
-
critical or buckling
- 0:
-
along axial generator aty=0
Bibliography
Brazier, L.G., “On the Flexure of Thin Cylindrical Shells and Other Thin Sections”,Proc. Royal Soc. London, Series A,116,104–111 (Nov.1927).
Flügge, W., “Die Stabilität der Kreiszylinderschale”,Ingenieur-Archiv,3 (5)463–506 (1932).
Donnell, L. H., “A New Theory for the Buckling of Thin Cylinders under Axial Compression and Bending,”Trans. ASME,56, (11),795–806 (1934).
Lundquist, E. E., “Strength Tests of Thin-Walled Duralumin Cylinders in Pure Bending”, NACA TN 479 (1933).
Mossman, R. W., and Robinson, R. G., “Bending Tests of Metal Monocoque Fuselage Construction”, NACA TN 357 (1930).
Peterson, J. P., “Bending Tests of Ring Stiffened Circular Cylinders,” NACA TN 3735 (1956).
Hoff, N. J., “Buckling of Thin Cylindrical Shells under Hoop Stresses Varying in Axial Direction,”Jnl. Appl. Mech.,24 (3),405 (1957).
Anderson, M. S., “Combinations of Temperature and Axial Compression Required for Buckling of a Ring Stiffened Cylinder”, NACA TN D-1224 (1962).
Anderson, M. S., Pride, R. A., and Hall, J. B., “Effects of Rapid Heating on Strength of Aircraft Components”, NACA TN 4051 (1957).
Hoff, N. J., “Thermal Buckling of Thin Walled Circular Cylindrical Shells”, Stanford Univ., SUDAER No. 137 (Oct. 1962).
Abir, D., andNardo, S.V., “Thermal Buckling of Circular Cylindrical Shells under Circumferential Temperature Gradients,”Jnl Aerospace Sciences,26 (12),803 (1959).
Hill, D. W., “Buckling of a Thin Circular Cylindrical Shell Heated Along an Axial Strip”, Stanford Univ., SUDAER No. 88 (Dec. 1959).
Hoff, N. J., Chao, C. C., and Madsen, W. A., “Buckling of a Thin Walled Circular Cylindrical Shell Heated Along an Axial Strip”, Stanford Univ., SUDAER No. 142 (Sept. 1962).
Hoff, N. J., “The Analysis of Structures”,John Wiley and Sons, Inc., New York, 1st ed., 206–218 (1956).
Bierens de Haan, D., “Nouvelles Tables d'Intégrales Définies”,Hafner Publishing Co., New York, 386 (1957).
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A. Jaworski, was Postdoctoral Fellow at Department of Aeronautics and Astronautics, Stanford University
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Ross, B., Mayers, J. & Jaworski, A. Buckling of thin cylindrical shells heated along an axial strip. Experimental Mechanics 5, 247–256 (1965). https://doi.org/10.1007/BF02327148
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DOI: https://doi.org/10.1007/BF02327148