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Solution of the stability problem for a thin shell under impulsive loading

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Abstract

The stability problem for a thin shell under an axial impulsive load is considered. A new approach to building a mathematical model is presented, which is based on the Ostrogradskii-Hamilton principle of stationary action. It is shown that the problem reduces to a system of nonlinear differential equations that can be solved numerically and by using an approximate calculation algorithm developed by the authors. A formula determining the dependence between the load intensity and the initial conditions of the problem is derived. In the above setting, the stability problem for a circular cylindrical shell is solved. To determine the critical value of the load impulse, the Lyapunov theory of dynamic stability is used.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, Kremlevskaya ul. 18, Kazan, 420008, Tatarstan, Russia

    L. U. Bakhtieva & F. Kh. Tazyukov

Authors
  1. L. U. Bakhtieva
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  2. F. Kh. Tazyukov
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Correspondence to L. U. Bakhtieva.

Additional information

Original Russian Text © L.U. Bakhtieva, F.Kh. Tazyukov, 2014, published in Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2014, Vol. 156, No. 1, pp. 5–11.

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Bakhtieva, L.U., Tazyukov, F.K. Solution of the stability problem for a thin shell under impulsive loading. Lobachevskii J Math 35, 384–389 (2014). https://doi.org/10.1134/S1995080214040027

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  • DOI: https://doi.org/10.1134/S1995080214040027

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