Finite difference method

Abstract: The behavior of axisymmetric dynamic snap-through of elastic, clamped shallow spherical shells under a uniform pressure has been investigated by.several authors. In most of the previous work, approximate methods were used, and as yet no positive conclusion has been made on the critical load for snap-through. In this paper, a numerical method is developed for solving the governing nonlinear differential equations of this problem. Two types of loading conditions are included-—an impulsive load and an instantaneous ly applied step load with infinite duration. In the case of impulsive loading, it is found from the quasi-static problem under zero load that the only equilibrium, position of the shell is its undeformed configuration. Hence, if we define the dynamic snap-through based on the finite jump behavior of deflection then there is no possibility for dynamic snap-through under impulsive loading. In the case of step loading, the snap-through loads are evaluated for a wide range of the geometrical parameter of the shell. Comparison of the present calculated critical loads with the previous results from approximate methods is made. It is found that the present critical load checks closely with an experimental value of the critical load for one value of the geometrical parameter of the shell.