Determination of the critical parameters of momentary external pressure for a spherical shell with initial deflection

Abstract

A solution is presented for the problem of the dynamic loss of stability of a spherical shell subjected to momentary external pressure. The shell, reinforced in two directions, is regarded as being structurally orthotropic. Within the primary depression which develops during the loss of stability, the shell is considered to be shallow and have a radius of curvature r~ differing from the nominal radius r and determined with allowance for the presence of an initial deflection which propagates over the entire region of the depression. Here, it is assumed that the presence of the initial deflection does not disturb the convexity of the shell. The critical value of the compressive forces in the radial sections of the shell are determined within the framework of a linear formulation of the problem, with the use of analytical criteria of dynamic instability [2], for linear and parabolic laws of change in the compressive forces over time.