Shallowness effect on buckling of spherical shells

We study the buckling of clamped spherical caps under uniform pressure. Since the 1960s, several theoretical and computational studies have addressed the non-monotonic relationship between the shallowness of the shells and its critical buckling pressure. However, there is a lack of precise experiments to corroborate these predictions. Using a recently developed technique, we fabricate polymeric spherical shells containing a precise geometric defect. We vary the shallowness of our shells by precisely changing the location of the clamped boundary conditions and measure the critical buckling pressure. Finite element simulations are conducted to analyze the buckling behavior of our shallow shells, in excellent agreement with the experiments. We find that the critical buckling pressure and the shallowness parameter have a decaying sinusoidal relationship, hence, the buckling strength of shallow shells can be larger or smaller than that of complete spherical shells. Moreover, this sinusoidal form is systematically characterized which is affected by a geometric defect.