Nonlinear Bending Stability of a Long Flexible Cylindrical Shell with Geometrical Imperfections

The authors put forward a numerical approach to determination of nonlinear bending stability of a long flexible cylindrical shell with geometrical imperfections. The shell wall imperfection in the form of bulging in long half-wave is modeled using a software package for finite-element analysis. Prebuckling and postbuckling behavior of an imperfect shell in bending is studied. The critical normal stress in the shell compression zone is plotted vs. the imperfection amplitude. The bending stability region is determined for a shell with geometrical imperfections.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. 1.

    S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York (1959).

    Google Scholar 

  2. 2.

    A. S. Vol’mir, Stability of Elastic Systems [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  3. 3.

    A. S. Vol’mir, Stability of Deformable Systems [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  4. 4.

    É. L. Aksel’rad, Flexible Shells [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  5. 5.

    V. A. Bazhenov, V. I. Gulyaev, and E. O. Gotsulyak, Stability of Nonlinear Mechanical Systems [in Russian], Vyshcha Shkola, Lvov (1982).

    Google Scholar 

  6. 6.

    V. A. Bazhenov, O. P. Krivenko, and M. O. Solovei, Nonlinear Deformation and Stability of Heterogeneous-Structured Elastic Shells [in Ukrainian], Vipol, Kyiv (2010).

    Google Scholar 

  7. 7.

    G. D. Gavrilenko, “Numerical and analytical approaches to investigation of load-bearing capacity of imperfect shells,” Prikl. Mekh., No. 9, 44–63 (2003).

  8. 8.

    G. D. Gavrilenko, Load-Bearing Capacity of Imperfect Shells [in Ukrainian], Barviks, Dnipropetrovsk (2007).

    Google Scholar 

  9. 9.

    E. A. Gotsulyak, O. A. Luk’yanchenko, and V. V. Shakh, “On stability of cylindrical shells of variable wall thickness with initial imperfections,” Prikl. Mekh., No. 4, 103–108 (2009).

  10. 10.

    E. O. Gotsulyak, I. I. Luk’yanchenko, I. V. Kostina, and I. G. Garan, “Stability of supported cylindrical shell with geometric imperfections under combined loading,” Strength Mater., 44, No. 5, 556–561 (2012).

    Article  Google Scholar 

  11. 11.

    D. G. Shimkovich, Structural Design Using MSC/NASTRAN for Windows [in Russian], DMK Press, Moscow (2001).

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to O. V. Kostina.

Additional information

Translated from Problemy Prochnosti, No. 2, pp. 140 – 147, March – April, 2016.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bazhenov, V.A., Luk’yanchenko, O.O., Kostina, O.V. et al. Nonlinear Bending Stability of a Long Flexible Cylindrical Shell with Geometrical Imperfections. Strength Mater 48, 308–314 (2016).

Download citation


  • nonlinear stability
  • flexible cylindrical shell
  • geometrical imperfection
  • finite-element method
  • bending