KSME International Journal

, Volume 14, Issue 1, pp 39–47 | Cite as

Bifurcation modes in the limit of zero thickness of axially compressed circular cylindrical shell

  • Youngjoo Kwon
Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design


Bifurcation intability modes of axially compressed circular cylindrical shell are investigated in the limit of zero thickness (i.e., h (thickness) → 0) analytically, adopting the general stability theory developed by Triantafyllidis and Kwon(1987) and Kwon(1992). The primary state of the shell is obtained in a closed form using the asymptotic technique, and then the straightforward bifurcation analysis is followed according to the general stability theory to obtain the bifurcation modes in the limit of zero thickness in a full analytical manner. Hence, the closed form bifurcation solution is obtained. Finally, the result is compared with the classical one.

Key Words

Strain Energy Density Function Stören-Rice Hypoelastic Material Characteristic Equation Multiple Scales Asymptotic Technique Bifurcation Modes 


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  1. Almroth, B. O. and Holmes, A. M. C. and Bush, D. O., 1964, “An Experimental Study of the Buckling of Cylinders Under Axial Compression,”Experimental Mechanics, pp. 263–270.Google Scholar
  2. Almroth, B. O., 1966, “Influence of Edge Conditions on the Stability of Axially Compressed Cylindrical Shell,”AIAA Journal Vol. 4 No. 1, pp. 134–140.CrossRefGoogle Scholar
  3. Donnell, L. H., 1934, “A New Theory for the Buckling of Thin Cylinders Under Axial Compression and Bending,”ASME Transactions Vol. 56, pp. 795–806.Google Scholar
  4. Donnell, L. H. and C. C. Wan, 1950, “Effect of Imperfections on Buckling of Thin Cylinders and Columns Under Axial Compression,”J. of Applied Mechanics Vol. 17 No. 1, pp. 73–83.MATHGoogle Scholar
  5. Donoghue, M., Stevenson, R., Kwon, Y. J. and Triantafyllidis, N., 1989, “An Experimental Verification of the Hemispherical Cup Puckering Problem,”J. of Engineering Materials and Technology Vol. 111, pp. 248–254.CrossRefGoogle Scholar
  6. Evensen, D. A., 1964, “High-Speed Photographic Observation of the Buckling of Thin Cylinders,”Experimental Mechanics, pp. 110–117.Google Scholar
  7. Hill, R., 1957, “On Uniqueness and Stability in the Theory of Finite Elastic Strain,”J. of the Mechanics and Physics of Solids Vol. 5, pp. 229–241.MATHCrossRefGoogle Scholar
  8. Hill, R., 1958, “A General Theory of Uniqueness and Stability in Elastic-Plastic Solids,”J. of the Mechanics and Physics of Solids Vol. 6, pp. 236–249.MATHCrossRefGoogle Scholar
  9. Hoff, N. J. and Soong, T. C., 1965, “Buckling of Circular Cylindrical Shells in Axial Compressioin,”International J. of Mechanical Sciences Vol. 7, pp. 489–520.CrossRefGoogle Scholar
  10. Hoff, N. J., 1966, “The Perflexing Behaviour of Thin Circular Cylindrical Shells in Axial Compression,”Israel J. of Technology Vol. 4 No. 1, pp. 1–28.Google Scholar
  11. Horton, W. and Durham, S. C., 1965, “Imperfections, a Main Contributor to the Scatter in Experimental Values of Buckling Load,”International J. of Solid and Structures Vol. 1, pp. 59–72.CrossRefGoogle Scholar
  12. Hutchinson, J. W., 1974, “Plastic Buckling,”Adv. Appl. Mech. Vol. 14 (Edited by C. S. Yih), Academic Press, New York, pp. 67–145.Google Scholar
  13. Kármán, Theodore Von and Tsien, Hsue-Shen, 1941, “The Buckling of Thin Cylindrical Shells Under Axial Compression.”J. of the Aeronautical Sciences Vol. 8 No. 8, pp. 303–312.MATHGoogle Scholar
  14. Kim, Y. S., Son, Y. J. and Park, J. Y., 1999, “Bifurcation Analysis of Wrinkling Formation for Anisotropic Sheet,”KSME International Journal Vol. 13 No. 3, pp. 221–228.Google Scholar
  15. Koiter, W. T., 1945, “On the Stability of Elastic Equilibrium,” (in Dutch), Doc. Thesis, Delft University Amsterdam.Google Scholar
  16. Kwon, Y. J., 1992, “Buckling Theory in Solid Structure with Small Thickness (Part 1) —General Formul-ation of Problem-,”KSME Journal Vol. 6 No. 2, pp. 109–113.Google Scholar
  17. Kwon, Y. J., 1993, “Buckling Theory in Solid Structure with Small Thickness: Part 2 Application to the Externally Pressurized Cylindrical Shell Buckling,”KSME Journal Vol. 7 No. 2, pp. 113–126.Google Scholar
  18. Lorenz, R., 1908, “Aschsensymmetrisxhe Verzerrungen inüd nnwandigen Hohlzylinder,”Zeitschrift des Vereines Deutscher Ingenieure, 52, pp. 1707–1717.Google Scholar
  19. Nachbar, W. and Hoff, N. J., 1962, “The Buckling of a Free Edge of an Axially-Compressed Circular Cylindrical Shell,”Quart. Appl. Math. XX, pp. 267–277.MathSciNetGoogle Scholar
  20. Pak, C. H., 1995, “On the Lateral Instability of a Thin Beam under Periodic Bending Loads,”KSME Journal Vol. 9 No. 4, pp. 438–451.Google Scholar
  21. Timoshenko, S. P. and Gere, J. M., 1961,Theory of Elastic Stability, 2nd ed., McGrawHill Book Co., Inc., New York.Google Scholar
  22. Tennyson, R. C., 1969, “Buckling Modes of Circular Cylindrical Shells Under Axial Compression,”AIAA Journal Vol. 1 No. 8, pp. 1481–1487.CrossRefGoogle Scholar
  23. Triantafyllidis, N. and Kwon, Y. J., 1987, “Thickness Effects on the Stability of Thin Walled Structures,”J. of the Mechanics and Physics of Solids Vol. 35 No. 5, pp. 643–674.MATHCrossRefGoogle Scholar
  24. Yoshimura, Y., 1955, “On the Mechanism of Buckling of a Circular Cylindrical Shell Under Axial Compression,”NACA TM 1390.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2000

Authors and Affiliations

  1. 1.Department of Mechanical Design and Production EngineeringHongik UniversityChungnamKorea

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