标题： 近似完美球壳的屈曲数值研究 显示英文标题

标题： A numerical study on the buckling of near-perfect spherical shells

摘要： 我们展示了使用有限元方法进行数值研究的结果，以研究包含单个局部高斯凹陷缺陷的接近完美的球形壳体的屈曲强度，其轮廓系统地变化至幅度消失的极限。 在这一极限下，我们的模拟揭示了半球、完整球体和部分球冠的不同屈曲行为。 半球壳表现出边界主导的屈曲模式，导致降额因子为0.8。 相比之下，完整球壳在其极点表现出局部屈曲，降额因子接近于1。 此外，对于部分球壳，我们观察到随着帽角的变化，屈曲模式从边界模式过渡到这些局部屈曲模式。 我们通过系统地检查离散化水平、求解器参数和半径与厚度比对降额因子的影响来描述这些行为。 具体而言，我们确定了在哪些条件下降额因子在不同壳体配置中收敛。 我们的研究结果强调了在接近完美极限的壳体屈曲模拟中，精确控制数值参数的重要性，证明了在离散化和求解器参数上的精确选择对于准确预测不同壳体几何结构下的不同屈曲模式至关重要。 显示英文摘要

摘要： We present the results from a numerical investigation using the finite element method to study the buckling strength of near-perfect spherical shells containing a single, localized, Gaussian-dimple defect whose profile is systematically varied toward the limit of vanishing amplitude. In this limit, our simulations reveal distinct buckling behaviors for hemispheres, full spheres, and partial spherical caps. Hemispherical shells exhibit boundary-dominated buckling modes, resulting in a knockdown factor of 0.8. By contrast, full spherical shells display localized buckling at their pole with knockdown factors near unity. Furthermore, for partial spherical shells, we observed a transition from boundary modes to these localized buckling modes as a function of the cap angle. We characterize these behaviors by systematically examining the effects of the discretization level, solver parameters, and radius-to-thickness ratio on knockdown factors. Specifically, we identify the conditions under which knockdown factors converge across shell configurations. Our findings highlight the critical importance of carefully controlled numerical parameters in shell-buckling simulations in the near-perfect limit, demonstrating how precise choices in discretization and solver parameters are essential for accurately predicting the distinct buckling modes across different shell geometries.