From Shallow to Deep: Buckling Behavior of Clamped Spherical Caps

We revisit the buckling of clamped spherical caps under uniform pressure, focusing on the effect of the shallowness and geometric imperfection. For decades, studies on the relationship between shallowness and buckling pressure have flourished. However, a large discrepancy between the analytic solution and experiments has been reported, mainly on the shallow spherical caps. We first experimentally investigate the buckling of clamped spherical caps over the broad shallowness range. We also conduct finite element simulations by varying shallowness and the defect geometry. The buckling pressure of the shells shows the decaying sinusoidal form with increasing shallowness, in excellent agreement between experimental and FEM results. Moreover, we find the shell with a small defect and specific shallowness non-axisymmetrically buckles at multiple snap-through regions on the side of the shell (between the pole and the clamped boundary). On the other hand, the shell with a larger defect axisymmetrically buckles at the pole regardless of its shallowness. With the parametric studies, we provide the buckling strength and behavior criteria varying the defect geometry.