圆柱壳屈曲中缺陷敏感性的起源
The Origin of Imperfection Sensitivity in the Buckling of Cylindrical Shells
- École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过数值延拓和分岔分析揭示，圆柱壳屈曲的缺陷敏感性源于缺陷几何改变分岔结构，而非仅缺陷大小。
AI中文摘要：
轴向压缩下薄圆柱壳的屈曲是亚临界失稳的经典例子，其对微小缺陷高度敏感，微小的几何变化即可导致屈曲阈值发生巨大改变。为揭示这种敏感性的起源，我们使用数值延拓和分岔分析，同时系统地改变单个局部高斯缺陷的深度和尺寸。我们表明，不完善壳体的失稳源于完善壳体中已存在的局部平衡态。通过打破平移对称性，缺陷钉扎了这些平衡态，并改变了它们与不完善基态的连接方式。因此，缺陷几何的微小变化可以切换触发屈曲的分岔，导致屈曲阈值出现非单调和不连续的变化，以及屈曲模式的突变。因此，缺陷敏感性不仅仅是缺陷幅度的敏感性，而是底层分岔结构对缺陷几何的敏感性。
英文摘要：
Buckling of thin cylindrical shells under axial compression, a classical example of a subcritical instability, is highly sensitive to small imperfections, with minute geometric variations causing large changes in buckling threshold. To uncover the origin of this sensitivity, we use numerical continuation and bifurcation analysis while systematically varying the depth and size of a single localized Gaussian defect. We show that the instabilities of the imperfect shell originate from localized equilibria already present in the perfect shell. By breaking translation symmetry, the defect pins these equilibria and changes how they connect to the imperfect base state. Small changes in defect geometry can thereby switch the bifurcation that triggers buckling, producing non-monotonic and discontinuous changes in buckling threshold and abrupt changes in buckling mode. Imperfection sensitivity is therefore not simply sensitivity to imperfection magnitude, but sensitivity of the underlying bifurcation structure to imperfection geometry.
