Snaking and laddering in axially compressed cylinders
Snaking and laddering in axially compressed cylinders
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DOI：
10.1016/j.ijmecsci.2021.106297
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发表时间：
2021-01-29
影响因子：
7.3
通讯作者：
Pirrera, A.
中科院分区：
文献类型：
--
作者：
Groh, R. M. J.;Hunt, G. W.;Pirrera, A.
最近的实验和数值结果表明，空间局部屈曲模式的轴向压缩圆筒的稳定性损失的重要性。特别感兴趣的是一个单一的局部凹坑，圆周上增加沿着振荡端部缩短的临界后平衡路径-一种称为蛇形的现象。与此相反，Mull-Dimple屈曲模式及其蛇形平衡路径尚未得到详细研究。在这项工作中，两个空间局部化的模式，即一个单一的酒窝和两个相邻的酒窝，被确定为基本的“积木”，可以重复的间隔周围的圆柱体圆周，以创建不同的多酒窝模式和随后的蛇形序列。每一个蜿蜒的序列周向地增加起始凹坑图案，直到一个菱形的环，从8到12波，是完整的。这组五个重新稳定的后屈曲模式与Yamaki在他的开创性实验中观察到的菱形环相匹配，并首次揭示了它们的起源。然而，通过将所施加的载荷从刚性载荷改变为静载荷，单个凹坑的形成不会导致圆柱体的弯曲环，而是导致圆柱体的扭结。我们表明，当屈曲前状态和周期性屈曲后状态在相同的总势下共存时，蛇形是可能的，并且局部屈曲可以以很小的能量代价插入到两个竞争模式之间。总的来说，研究结果加强了当代的观点，即空间局部化在轴向压缩圆柱体的屈曲和后屈曲行为中起着关键作用。
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, mull-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.