AI 中文总结
研究含局部缺陷的轴向压缩圆柱壳屈曲，通过有限元模拟确定参数空间，进行随机模拟发现屈曲后呈蝴蝶形图案，有统计尺寸效应，蝴蝶缺陷效应解释实验数据分散性并确定$H$为稳定性关键参数，所得屈服系数高于历史实验值。
AI 中文摘要
我们研究了含有局部缺陷的轴向压缩圆柱壳的屈曲问题，重点关注多个缺陷之间以及它们与壳边缘之间的相互作用。通过高保真有限元模拟，首先确定了单凹痕敏感性、缺陷 - 边缘耦合和成对缺陷 - 缺陷相互作用的参数空间。在此基础上，对具有随机分布缺陷的壳进行随机模拟，其幅度从对数正态分布中采样。屈曲后变形形成非轴对称的蝴蝶形图案，其‘翅膀’跨越壳表面很远。这种空间范围导致与相邻缺陷和夹紧边缘不可避免的相互作用，因此屈曲不一定由最深的缺陷引发。更多的缺陷会增加出现极端缺陷的可能性，产生统计尺寸效应。蝴蝶缺陷效应通过将屈服系数与圆柱长径比（$H/t$）而非仅与半径厚度比（$R/t$）相关联，定性地解释了历史实验数据中的分散性，从而确定$H$与$R$和$t$一样是稳定性的关键参数。然而，这里得到的屈服系数仍远高于历史实验报告的值，表明局部高斯凹痕虽然对球壳几乎是最坏情况的缺陷，但对圆柱壳并非如此。
英文摘要
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.
