Statistical scaling of safety factors for buckling of spherical shells with non-interacting defects

Abstract

The resistance to buckling of a thin-walled structure subjected to a deterministic load exhibits significant variability due to the random nature of inevitable imperfections in its nominal geometry. The risk of buckling is increased if the loading is also random. To account for these uncertainties, the design of such structures requires the use of appropriate safety factors. This study presents a mechanistic model for the safety factors of pressurized spherical shells containing non-interacting Gaussian-shaped localized defects with a fixed normalized width but random amplitudes, and subjected to uniform pressure of random magnitude. The probability distribution of the buckling pressure is modeled using a finite weakest-link approach. The results show that for a given load distribution the failure probability increases with increasing number of defects (the maximum number of non-interacting defects being proportional to the shell’s dimensionless radius) and approaches a constant value. The model is used to determine the central safety factor, defined as the ratio of the mean buckling pressure to the mean applied load, for a specified target failure probability. The safety factor is shown to strongly depend on the dimensionless radius, a result which is understood as a form of statistical scaling. This finding suggests that the current practice of using a constant and size-independent safety factor cannot ensure a uniform target failure probability across all shell sizes.