International Applied Mechanics

, Volume 46, Issue 8, pp 919–928 | Cite as

Stability of circumferentially corrugated cylindrical shells under external pressure

  • I. Yu. Babich
  • N. B. Zhukova
  • N. P. Semenyuk
  • V. M. Trach

Corrugated shells of revolution that may be considered cylindrical when the corrugation amplitude is small are analyzed for stability. The corrugations are transverse to the axis of revolution. Isotropic and orthotropic shells with sine-shaped meridian under uniform external compression are analyzed for stability. It is shown that the stability of corrugated shells can be significantly improved, compared with cylindrical shells, by selecting appropriate number and amplitude of half-waves. A relationship between the buckling modes and the change in the critical loads is established


stability corrugated shell of revolution sine-shaped meridian uniform external compression buckling modes 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. A. Ambartsumyan, General Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1974).Google Scholar
  2. 2.
    L. E. Andreeva, “Design of corrugated membranes as anisotropic plates,” Inzh. Sb., 31, 128–141 (1955).Google Scholar
  3. 3.
    G. L. Vanin, N. P. Semenyuk, and R. F. Emel’yanov, Stability of Shells Made of Reinforced Materials [in Russian], Naukova Dumka, Kyiv (1978).Google Scholar
  4. 4.
    S. K. Godunov, “Numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk, 16, No. 3, 171–174 (1961).zbMATHMathSciNetGoogle Scholar
  5. 5.
    E. I. Grigolyuk and V. I. Shalashilin, Problems of Nonlinear Deformation: Parameter Continuation Method in Nonlinear Problems of Solid Mechanics [in Russian], Nauka, Moscow (1988).Google Scholar
  6. 6.
    Ya. M. Grigorenko and N. N. Kryukov, Numerical Solution of Static Problems for Flexible Layered Shells with Variable Parameters [in Russian], Naukova Dumka, Kyiv (1988).Google Scholar
  7. 7.
    V. M. Gulyaev, V. A. Bazhenov, and P. P. Lizunov, Nonclassical Theory of Shells and Its Application to Engineering Problems [in Russian], Vyshcha Shkola, Lviv (1978).Google Scholar
  8. 8.
    B. Ya. Kantor, Contact Problems in the Nonlinear Theory of Shells of Revolution [in Russian], Naukova Dumka, Kyiv (1990).zbMATHGoogle Scholar
  9. 9.
    A. V. Karmishin, V. A. Lyaskovets, V. I. Myachenkov, and A. N. Frolov, Statics and Dynamics of Thin-Walled Shell Structures [in Russian], Mashinostroenie, Moscow (1975).Google Scholar
  10. 10.
    V. M. Muratov and A. T. Tubaivskii, “Experimental stability analysis of corrugated shells,” Khim. Neft. Mashinostr., No. 3, 18–20 (1992).Google Scholar
  11. 11.
    K. E. Tsiolkovsky, “Dirigible, stratoplane, and spaceship,” Grazhd. Aviats., No. 9, 7–8 (1933).Google Scholar
  12. 12.
    V. I. Feodos’ev, Elastic Elements in Precision Instrument Making [in Russian], Oborongiz, Moscow (1949).Google Scholar
  13. 13.
    A. V. Boriseiko, N. P. Semenyuk, and V. M. Trach, “Canonical equations in the geometrically nonlinear theory of thin anisotropic shells,” Int. Appl. Mech., 46, No. 2, 165–174 (2010).CrossRefADSGoogle Scholar
  14. 14.
    D. Buchnell, “Crippling and buckling of corrugated ring-stiffened cylinders,” AIAA J., 9, No. 5, 357–421 (1972).Google Scholar
  15. 15.
    N. Daxner, T. Fletscher, and F. G. Rammerstorfer, “Optimum design of corrugated board under buckling constraints,” in: 7th World Congr. on Structural and Multidisciplinary Optimization, Seoul (2007), pp. 349–358.Google Scholar
  16. 16.
    S. Luo, J. C. Suhling, J. M. Considine, and T. L. Laufenberg, “The bending stiffnesses of corrugated board,” Mech. Cellul. Mater., 36, 15–26 (1992).Google Scholar
  17. 17.
    C. T. F. Ross, “A redesign of the corrugated tin can,” Thin-Wall. Struct., 26, No. 3, 179–193 (1996).CrossRefGoogle Scholar
  18. 18.
    N. P. Semenyuk and I. Yu. Babich, “Stability of longitudinally corrugated cylindrical shells under uniform surface pressure,” Int. Appl. Mech., 43, No. 11, 1236–1247 (2007).CrossRefADSGoogle Scholar
  19. 19.
    N. P. Semenyuk, V. M. Trach, and N. B. Zhukova, “Incremental analysis of the nonlinear behavior of thin shells,” Int. Appl. Mech., 44, No. 9, 1025–1031 (2008).CrossRefADSGoogle Scholar
  20. 20.
    N. P. Semenyuk, V. M. Trach, and V. V. Ostapchuk, “Nonlinear axisymmetric deformation of anisotropic spherical shells,” Int. Appl. Mech., 45, No. 10, 1101–1111 (2009).CrossRefADSGoogle Scholar
  21. 21.
    N. P. Semenyuk, N. B. Zhukova, and V. V. Ostapchuk, “Stability of corrugated composite noncircular shells under external pressure,” Int. Appl. Mech., 43, No. 12, 1380–1389 (2007).CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • I. Yu. Babich
    • 1
  • N. B. Zhukova
    • 1
  • N. P. Semenyuk
    • 1
  • V. M. Trach
    • 2
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.National University of Water Management and Natural Resource UseRivneUkraine

Personalised recommendations