Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

Abstract

We study the buckling of hemispherical elastic shells subjected to the combined effect of pressure loading and a probing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systematically varying the indentation displacement and the geometry 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 predictions from the literature. Inspired by a nondestructive technique 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.

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

“…While the experimental studies by Marthelot et al [2017] and Virot et al [2017] applied probing with a one-sided force (the poker in figure 10 pushes but cannot pull), the numerical results in figures 1, 3 and 5 extend the equilibrium surface for the probed shell to negative probe forces, achievable, for example, by gluing the poker to the shell (as proposed in the introduction). Gluing corresponds to a two-sided clamp, prescribing the displacement of the shell at the probed point.…”

“…For the pressurized hemi-sphere subject to the displacement-controlled probing, a dimple buckle forms under the probe confined to the vicinity of the pole prior to collapse. Curves of experimentally measured probe force versus probe displacement for 11 values of prescribed pressure from Marthelot et al [2017] are shown in Fig. 7 for a shell with R/t = 119 which buckled under pressure alone at p/p C = 0.74.…”

“…The solid lines are results computed using the numerical method presented by Hutchinson and Thompson [2017]. Marthelot et al [2017] also evaluated the work, W, done by the probe to reach the unstable equilibrium state, which for a prescribed pressured is proportional to the area under the curve between the origin and intersection of the probing force with the horizontal axis in the figure. This work is the energy barrier against buckling for a shell loaded to that pressure.…”

“…Recent related work on energy barriers of spherical shells is presented by Evkin & Lykhachova [2017]. by Marthelot et al [2017] at various values of the prescribed pressure. The theoretical predictions for a perfect shell from Hutchinson & Thompson [2017& 2018 are shown as solid curves.…”

“…An experimental study probing hemispherical shells has been conducted by Marthelot et al [2017]. Historically it is well established that the cylindrical shell under axial compression and the spherical shell under external pressure have comparably catastrophic and imperfection-sensitive buckling behaviour.…”