Probabilistic buckling of imperfect hemispherical shells containing a distribution of defects

TL;DR

This study investigates how a distribution of imperfections affects the buckling strength of hemispherical shells, using simulations validated by experiments, and finds that the knockdown factor follows a Weibull distribution, indicating extreme-value behavior.

Contribution

It extends understanding of shell buckling by modeling multiple imperfections and characterizing knockdown factor statistics with a Weibull distribution.

Findings

Knockdown factor statistics fit a Weibull distribution.

Interactions between two defects reveal complex regimes.

Shell buckling behaves as an extreme-value statistics phenomenon.

Abstract

The buckling of spherical shells is plagued by a strong sensitivity to imperfections. Traditionally, imperfect shells tend to be characterized empirically by the knockdown factor, the ratio between the measured buckling strength and the corresponding classic prediction for a perfect shell. Recently, it has been demonstrated that the knockdown factor of a shell containing a single imperfection can be predicted when there is detailed a priori knowledge of the defect geometry. Still, addressing the analogous problem for a shell containing many defects remains an open question. Here, we use finite element simulations, which we validate against precision experiments, to investigate hemispherical shells containing a well-defined distribution of imperfections. Our goal is to characterize the resulting knockdown factor statistics. First, we study the buckling of shells containing only two defects, uncovering nontrivial regimes of interactions that echo existing findings for cylindrical shells. Then, we construct statistical ensembles of imperfect shells, whose defect amplitudes are sampled from a lognormal distribution. We find that a 3-parameter Weibull distribution is an excellent description for the measured statistics of knockdown factors, suggesting that shell buckling can be regarded as an extreme-value statistics phenomenon.