Geodesic
Solving the stability problem for a thin shell under impulsive loading
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 1, pp. 5-11 Cet article a éte moissonné depuis la source Math-Net.Ru

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The stability problem for a thin shell under an axial impulsive load is considered. A new approach to building a mathematical model is presented, 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 that determines the dependence between the load intensity and the problem's initial conditions is derived. In the above formulation, 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.
Keywords: shell, stability, impulse. 
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L. U. Bakhtieva; F. Kh. Tazyukov. Solving the stability problem for a thin shell under impulsive loading. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 1, pp. 5-11. http://geodesic.mathdoc.fr/item/UZKU_2014_156_1_a0/

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