The buckling of clamped shallow spherical shells under uniform pressure

Abstract

In view of the wide discrepancy between previous theoretical and experimental results the problem of the buckling of clamped spherical shells under uniform external pressure is reexamined. A theoretical study is carried out to determine if asymmetrical modes participate in the snap-through process. It is shown that asymmetrical buckling does occur in a certain range of a geometric parameter, at loads which are significantly less than those predicted from symmetrical theory. Additional effects can be expected if the shell has symmetrical or asymmetrical imperfections, however, the present study considers only the perfect shell. Experiments were carried out with copper shells fabricated by an electroforming process. The initial imperfections in the test specimens were of the order of 1/10 of the thickness. The buckling loads of these shells exceeded the loads which have previously been reported by as much as a factor of two at higher values of the geometrical parameter [lamda]. Good agreement is found between theory and experiment, and with the recently published asymmetrical theory of Huang.