Viscoplastic dynamics of isotropic plates of variable thickness under explosive loading

  • Yu. V. Nemirovskii
  • A. P. Yankovskii


A problem of viscoplastic dynamic bending of isotropic plates of variable thickness is formulated. A method for integrating the initial-boundary problem is developed. Numerical results are compared with a known analytical solution obtained within a rigid-plastic model; good agreement is demonstrated. The efficiency of the method developed is verified by numerical computations. It is shown that the final flexure of plates can be reduced severalfold by applying rational design.

Key words

plates explosive loading inelastic dynamics viscoplastic deformation rational design 


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  1. 1.
    H. G. Hopkins and W. Prager, “On the dynamics of plastic circular plates,” Z. Angew. Math. Phys., 5, No. 4, 317–330 (1954).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    K. L. Komarov and Yu. V. Nemirovskii, Dynamics of Rigid-Plastic Structural Elements [in Russian], Nauka, Novosibirsk (1984).Google Scholar
  3. 3.
    M. I. Erkhov, Theory of Ideal Plastic Solids and Structures [in Russian], Nauka, Moscow (1978).Google Scholar
  4. 4.
    F. V. Warnock and J. A. Pope, “The change in mechanical properties of mild steel under repeated impact,” in: Appl. Mechanics Proceedings, Vol. 157, Inst. of Mech. Eng. (1947).Google Scholar
  5. 5.
    P. M. Ogibalov, Issues of Dynamics and Stability of Shells [in Russian], Izd. Mosk. Univ., Moscow (1963).Google Scholar
  6. 6.
    L. M. Kachanov, Foundations of the Theory of Plasticity, North-Holland, Amsterdam-London (1971).MATHGoogle Scholar
  7. 7.
    L. M. Kachanov, Theory of Creep [in Russian], Fizmatgiz, Moscow (1960).Google Scholar
  8. 8.
    Yu. V. Nemirovskii and A. P. Yankovskii, “Elastoplastic bending of rectangular plates reinforced by fibers with a constant cross section,” Mekh. Kompoz. Mater. Konstr., 41, No. 1, 17–36 (2005).Google Scholar
  9. 9.
    V. V. Sokolovskii, Plasticity Theory [in Russian], Vysshaya Shkola, Moscow (1969).Google Scholar
  10. 10.
    Yu. V. Nemirovskii and A. P. Yankovskii, “Generalization of the Runge-Kutta methods and their application to integration of initial-boundary problems of mathematical physics,” Sib. Zh. Vychisl. Mat., 8, No. 1, 51–76 (2005).Google Scholar
  11. 11.
    N. N. Malinin, Applied Theory of Plasticity and Creep [in Russian], Mashinostroenie, Moscow (1968).Google Scholar
  12. 12.
    V. Z. Vlasov and N. N. Leont’ev, Beams, Plates, and Shells on an Elastic Base [in Russian], Fizmatgiz, Moscow (1960).Google Scholar
  13. 13.
    N. N. Kalitkin, Numerical Methods [in Russian], Nauka, Moscow (1978).Google Scholar
  14. 14.
    A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1989).Google Scholar
  15. 15.
    Composite Materials: Handbook [in Russian], Naukova Dumka, Kiev (1985).Google Scholar
  16. 16.
    H. G. Hopkins and W. Prager, “The load-carrying capacities of circular plates,” J. Mech. Phys. Solids, 2, No. 1, 1–13 (1953).CrossRefMathSciNetGoogle Scholar
  17. 17.
    C. J. Maiden and S. J. Green, “Compressive strain rate tests on six selected materials at strain rate from 10−3 to 104 in/in/sec,” J. Appl. Mech., 33, 496–504 (1966).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Yu. V. Nemirovskii
    • 1
  • A. P. Yankovskii
    • 1
  1. 1.Khristianovich Institute of Theoretical and Applied Mechanics, Siberian DivisionRussian Academy of SciencesNovosibirsk

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