Person:

Hutchinson, John

We study the buckling of hemispherical elastic shells sub- jected to the combined effect of pressure loading and a prob- ing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systemat- ically varying the indentation displacement and the geome- try of the probe, we study the effect that the probe induced deflections have on the buckling strength of our spherical shells. The experimental results are then compared to finite element simulations, as well as to recent theoretical predic- tions from the literature. Inspired by a nondestructive tech- nique that was recently proposed to evaluate the stability of elastic shells, we characterize the nonlinear load-deflection mechanical response of the probe for different values of the pressure loading. We demonstrate that this nondestructive method is a successful local way to assess the stability of spherical shells.

We explore the effect of precisely defined geometric imper- fections on the buckling load of spherical shells under exter- nal pressure loading, using finite element analysis that was previously validated through precision experiments. Our nu- merical simulations focus on the limit of large amplitude de- fects and reveal a lower bound that depends solely on the shell radius to thickness ratio and the angular width of the defect. It is shown that, in the large amplitude limit, the buck- ling load depends on an single geometric parameter, even for shells of moderate radius to thickness ratio. Moreover, nu- merical results on the knockdown factor are fitted to an em- pirical, albeit general, functional form that may be used as robust design guideline for the critical buckling conditions of pressurized spherical shells.

Elastic spherical shells loaded under uniform pressure are subject to equal and opposite compressive probing forces at their poles to trigger and explore buckling. When the shells support external pressure, buckling is usually axisymmetric; the maximum probing force and the energy barrier the probe must overcome are determined. Applications of the probing forces under two different loading conditions, constant pressure or constant volume, are qualitatively different from one another and fully characterized. The effects of probe forces on both perfect shells and shells with axisymmetric dimple imperfections are studied. When the shells are subject to internal pressure, buckling occurs as a non-axisymmetric bifurcation from the axisymmetric state in the shape of a mode with multiple circumferential waves concentrated in the vicinity of the probe. Exciting new experiments by others are briefly described.