The work described in this paper is concerned with providing a rational asymptotic analysis of the wrinkling bifurcation experienced by a thin elastic hemispherical segment subjected to vertical tensile forces on its upper rim. This is achieved by considering the interplay between two boundary layers and matching the corresponding solutions associated with each separate region. Our key result is a four-term asymptotic formula for the critical load in terms of a small parameter proportional to the ratio between the thickness and the radius of the shell. Comparisons of this formula with direct numerical simulations provide further insight into the range of validity of the results derived herein.

本文所描述的工作涉及对薄弹性半球形部分在其上边缘受到垂直拉力时所经历的起皱分叉现象进行合理的渐近分析。这是通过考虑两个边界层之间的相互作用并匹配与每个单独区域关联的相应解决方案来实现的。我们的关键结果是一个临界载荷的四项渐进公式，其中的小参数与壳体的厚度和半径之比成比例。此公式与直接数值模拟的比较可进一步了解此处得出的结果的有效性范围。