Mechanics of Composite Materials

, Volume 55, Issue 1, pp 41–52 | Cite as

Numerical Simulation of the Process of Loss of Stability of Composite Cylindrical Shells Under Combined Quasi-Static and Dynamic Actions

  • N. A. AbrosimovEmail author
  • A. V. Elesin
  • L. A. Igumnov

Based on the applied theory of shells, an energy-consistent resolving system of equations is constructed, and a complex numerical method is developed which, within in the framework of an explicit variational-difference scheme, makes it possible to solve both quasi-static and dynamic problems of nonlinear nonaxisymmetric deformation and buckling of composite cylindrical shells. The quasi-static loading mode is simulated by setting an internal pressure in the form of a linearly increasing function reaching a steady-state value during three periods of vibration of a composite cylindrical shell at the lower form. The critical buckling load is determined by the characteristic kink on the maximum deflection–loading amplitude curve. The reliability of the method developed is substantiated by comparing calculation results with experimental data. The characteristic forms and critical buckling loads of GRP cylindrical shells as functions of the level of preloading by a quasi-static internal pressure and of the subsequent dynamic loading by an external pressure are analyzed for various reinforcement patterns in a wide range of loading rate.


composite materials cylindrical shells nonlinear deformation stability numerical methods quasi-static and dynamic loads 



This work was performed at a financial support of the Federal program “Investigations and elaborations in the priority development directions of the scientific tehnological complex of Russia on years 2014-2020,” according to agreement NO. 14.578.21.0246 (unique identifier RFMEFI 57817X0246) and RFFI (grants Nos. 16-08-01124 and 18-08-01234).


  1. 1.
    L. I. Manevich, G. V. Mikhailov, I. D. Pavlenko, and E. F. Prokopalo, “Research on the stability of shells at a joint action of static and dynamic loads,” Prikl. Mekh., XIII, No. 1, 27-32 (1977).Google Scholar
  2. 2.
    V. N. Baskakov A. I. Kostoglotov, and L. A. Shvetsova, “Investigation of the dynamic stability of smooth cylindrical shells,” Probl. Prochn. No. 5, 31-33 (1982).Google Scholar
  3. 3.
    V. V. Bendyukov and V.V. Deryushev, “Dynamic short-wave instability of thin-walled cylindrical shells at the local action of an external pressure pulse,” Probl. Prochn., No. 4, 36-43 (1995).Google Scholar
  4. 4.
    E. D. Skurlatov, “An experimental study on the behaviour of cylindrical shells at dynamic loadings,” Probl. Prochn., No. 9, 79-83 (1972).Google Scholar
  5. 5.
    A. I. Kostoglotov, V. V. Bendyukov, V. V. Deryushev, and L. A. Shevtsov, “ Investigation of the process of loss of stability of smooth thin-walled cylindrical shells at the local action of a radiation pulse,” Probl. Prochn., No. 5, 56-62 (2004).Google Scholar
  6. 6.
    V. M. Dubrovin and T. A. Butina, “Modeling the dynamic stability of a cylindrical shell at the action of an axial compressing load,” Matemat. Model. Chisl. Metodi, No. 6, 46-57 (2015).Google Scholar
  7. 7.
    A. A. Kolomoets and A. S. Modin, “Nonlinear dynamics of a preliminary loaded imperfect cylindrical shell at the action of a nonuniform external pressure,” Vest. Saratov. Gos. Tekhn. Univ., No. 80, 7-12 (2015).Google Scholar
  8. 8.
    A. E. Bogdanovich and E. G. Feldmane, “Calculation of the supporting capacity of cylindrical shells under dynamic loading,” Mech. Compos. Mater., No. 3, 334-340 (1980).Google Scholar
  9. 9.
    A. E. Bogdanovich and E. G. Feldmane, “Strength and axisymmetric deformation of laminate cylindrical shells under axial impact,” Mech. Compos. Mater., No. 4, 449-456 (1982).Google Scholar
  10. 10.
    A. E. Bogdanovich, Nonlinear Problems of the Dynamics of Cylindrical Composite Shells [in Russian], Riga, Zinatne (1987).Google Scholar
  11. 11.
    I. V. Victorova and P. E. Tovstik, “Some problems of the stability of anisotropic cylindrical shells,” Tr. XIII Mezhdunar. Konf. “Sovr. Probl. Mekh. Sploshn. Sredy”, Rostov-on-Don, 57-62 (2009).Google Scholar
  12. 12.
    E. L. Jansen, “Dynamic stability problems of anisotropic cylindrical shells via a simplified analysis,” Nonlinear Dynamics, 39, 349-367 (2005).CrossRefGoogle Scholar
  13. 13.
    C. Bisagni, “Dynamic buckling of fiber composite shells under impulsive axial compression,” Thin-Walled Struct., 43, 499-514 (2005).CrossRefGoogle Scholar
  14. 14.
    T. Rahman, E. L. Jansen, and Z. Gürdal, “Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method,” Nonlinear Dynamics, 66, No. 3, 389-401 (2011).CrossRefGoogle Scholar
  15. 15.
    L. A. Shapovalov, “Consideration of transverse compression in equations of the nonlinear dynamics of shells,” Izv. RAN, Mekh. Tverd. Tela, No. 3. 156-168 (1997).Google Scholar
  16. 16.
    A. K. Malmeister, V. P. Tamuzh, and G. A. Teters, Strength of Polymer and Composite Materials [in Russian], Riga, Zinatne (1980).Google Scholar
  17. 17.
    N. A., Abrosimov and V. G. Bazhenov, “Nonlinear Problems of Dynamics of Composite Structures [in Russian], Nizhni Novgorod, Izd NNGU (2002).Google Scholar
  18. 18.
    V. V. Vasil’yev, Mechanics of Structures from Composite Materials [in Russian], M, Mashinostroenie (1988).Google Scholar
  19. 19.
    N. A. Abrosimov, A. V. Elesin, and S. A. Pirogov, “A numerical analysis of nonaxisymmetric strains and progressive destruction of layered composite cylindrical shells in pulsed loading,” Probl. Prochn. Plastich., 77, No. 1, 23-32 (2015).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • N. A. Abrosimov
    • 1
    Email author
  • A. V. Elesin
    • 1
  • L. A. Igumnov
    • 1
  1. 1.N. I. Lobachevsky Scientific Research Institute of Mechanics of the National Research Nizhni Novgorod State UniversityNizhni NovgorodRussia

Personalised recommendations