Buckling of general spherical shells under external pressure (Q1819998)

Theoretical studies of critical pressures for spherical shells are primarily limited to shallow ones. The present work is devoted to the investigation of stability of general spherical shells under external pressure with various end-conditions. The governing nonlinear differential equations for the axisymmetric deformations of spherical shells, which defines the unique states of lowest potential energy under given pressures, are solved exactly by using the method of multisegment integration, developed by \textit{A. Kalnins} and \textit{J. F. Lestingi} [J. Appl. Mech. 34, 59-64 (1967; Zbl 0149.227)]. The critical pressure for a particular shell is interpreted from the fact that any further increase in pressure, no matter how small, will cause enormous shell deformation indicating that the state of lowest potential energy for any increase in pressure is far from that at the critical pressure. Numerical results for a few shells, ranging from shallow to hemispherical, are presented here as examples and compared with others, where available.