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Localized deformation and randomly shaped imperfections are salient features of buckling-type instabilities in thin-walled load-bearing structures. However, it is generally agreed that their complex interactions in response to mechanical loading are not yet sufficiently understood, as evidenced by buckling-induced catastrophic failures which continue to today. This study investigates how the intimate coupling between localization mechanisms and geometric imperfections combine to determine the statistics of the pressure required to buckle (the illustrative example of) a hemispherical shell. The geometric imperfections, in the form of a surface, are defined by a random field generated over the nominally hemispherical shell geometry, and the probability distribution of the buckling pressure is computed via stochastic finite element analysis. Monte-Carlo simulations are performed for a wide range of the shell's radius to thickness ratio, as well as the correlation length of the spatial distribution of the imperfection. The results show that over this range, the buckling pressure is captured by the Weibull distribution. In addition, the analyses of the deformation patterns observed during the simulations provide insights into the effects of certain characteristic lengths on the local buckling that triggers global instability. In light of the simulation results, a probabilistic model is developed for the statistics of the buckling load that reveals how the dimensionless radius plays a dual role which remained hidden in previous deterministic analyses. The implications of the present model for reliability-based design of shell structures are discussed.
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