The Butterfly Defect Effect in Cylindrical Shell Buckling: Non-localized Interactions of Localized Imperfections
We investigate the buckling of axially compressed cylindrical shells containing localized defects, focusing on interactions among multiple defects and between them and the shell edges. Using high-fidelity finite-element simulations, we first characterize the parameter space of single-dimple sensitivity, defect-edge coupling, and pairwise defect-defect interactions. Building on this deterministic baseline, we run stochastic simulations of shells with randomly distributed imperfections whose amplitudes are sampled from a log-normal distribution. Post-buckling deformations form non-axisymmetric, butterfly-shaped patterns whose `wings' reach far across the shell surface. This spatial extent induces unavoidable interactions with neighboring defects and the clamped edges, so that buckling is not necessarily initiated by the deepest defect. A larger defect population raises the likelihood of an extreme defect, producing a statistical size effect: as the mean number of defects grows, the mean knockdown factor decreases asymptotically and its variability decays exponentially. The butterfly defect effect qualitatively explains the scatter in historical experimental data by correlating the knockdown factor with the cylinder length-to-thickness ratio ($H/t$) rather than the radius-to-thickness ratio ($R/t$) alone, thereby establishing $H$ as a key parameter for stability alongside $R$ and $t$. Nonetheless, the knockdown factors obtained here remain well above those reported in historical experiments, indicating that the localized Gaussian dimple, though nearly the worst-case imperfection for spherical shells, is not so for cylinders.