Solving the stability problem for a thin shell under impulsive loading

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.