SOME RECENT RESULTS ON THE BUCKLING MECHANISM OF SPHERICAL CAPS

The curve of pressure versus deformation for a spherical cap subjected to external pressure is frequently assumed to be similar to that of Fig. 1. Here P is a loading parameter and D(P) is a measure of the deformation (e.g. maximum displacement). This curve implies that for P > P(U) and for P < P(L) there is only one equilibrium state. For each P in P(L) < P < P(U) there are three equilibrium states and the cap must buckle at some P in this interval. We call P(L) and P(U), respectively, the upper and lower buckling loads. Points on the branch 0U correspond to unbuckled equilibrium states, those on the branch LN to buckled states and those on UL to
unstable states.