A probabilistic buckling model for hemispherical shells with non-interacting localized defects

This paper presents a combined computational and analytical investigation on the probability distribution of the knockdown factor of hemispherical shells containing multiple non-interacting localized geometrical defects. In the analytical model, the statistics of the knockdown factor for shells with a single defect are explicitly linked to the statistics of the defect amplitude. The model is then extended to shells with multiple non-interacting defects of random amplitudes through a finite weakest-link formulation, which predicts how the mean and coefficient of variation of the knockdown factor depend on the number of defects on the shell surface. The results of extreme value statistics are further used to derive the limiting form of the knockdown-factor distribution. The analytical investigation is accompanied by a series of stochastic finite element (SFE) simulations of hemispherical shells of different dimensions and with different sizes of the zone containing the defects. The analytical model is shown to be in excellent agreement with the simulation results. The main outcome of the analytical model is a statistical size effect on the knockdown factor, governed by the dimensionless radius, for shells containing the maximum possible number of non-interacting defects. A similar size effect has recently been reported for hemispherical shells with continuous random imperfect surfaces. Together, these results offer a new perspective on the universal statistical role of the dimensionless radius in governing the buckling behavior of geometrically imperfect hemispherical shells.