Recent experimental and numerical results have illustrated the importance of spatially localised buckling modes in the loss of stability of axially compressed cylinders. Particular interest has focused on a single localised dimple that circumferentially multiplies along a post-critical equilibrium path of oscillating end-shortening—a phenomenon known as snaking. In contrast, multi-dimple buckling modes and their snaking equilibrium paths have not been studied in detail. In this work, two spatially localised modes—namely, a single dimple and two adjacent dimples—are identified as fundamental “building blocks” that can be repeated in intervals around the cylinder circumference to create different multi-dimple patterns and ensuing snaking sequences. Each snaking sequence circumferentially multiplies the starting dimple pattern until one ring of diamond-shaped buckles, ranging from eight to twelve waves, is complete. This set of five re-stabilised post-buckling modes matches the diamond-shaped rings of buckles observed by Yamaki in his seminal experiments, and uncovers their origins for the first time. By changing the applied loading from rigid to dead loading, however, the formation of a single dimple does not lead to a ring of buckles but to kinking of the cylinder. We show that snaking is possible when pre-buckling and periodic post-buckling states co-exist at the same total potential and localised buckles can be inserted between the two competing modes at little energetic cost. Overall, the findings strengthen the contemporary perspective that spatial localisation plays a key role in the buckling and post-buckling behaviour of axially compressed cylinders.

最近的实验和数值结果表明，空间局部屈曲模式在轴向压缩气缸稳定性损失中的重要性。特别引起关注的是一个单一的局部凹痕，该凹痕沿振动的末端缩短的临界后平衡路径在圆周上成倍增加，这种现象被称为“蛇行”。相反，尚未对多凹坑屈曲模式及其曲折的平衡路径进行详细研究。在这项工作中，两个空间局部化的模式（即一个凹痕和两个相邻的凹痕）被确定为基本的“构建块”，可以在圆柱体圆周上以一定间隔重复这些重复，以创建不同的多凹痕图案并随后形成蛇咬序列。每个蛇击序列在周向上使起始的凹坑图案成倍增加，直到完成一圈八至十二波的菱形扣环为止。这五个重新稳定的后屈曲模式集与Yamaki在开创性实验中观察到的菱形扣环相匹配，并首次揭示了它们的起源。然而，通过将施加的载荷从刚性载荷改变为静载荷，单个凹窝的形成不会导致扣环，而是会导致圆柱体扭结。我们表明，当前屈曲状态和周期性后屈曲状态以相同的总电势并存，并且可以在两个竞争模式之间以很少的能量成本插入局部屈曲时，就可以进行曲折。总体，