Hazel Andrew L, Mullin Tom
School of Mathematics, and Manchester Centre for Nonlinear Dynamics, University of Manchester, Oxford Road, Manchester M13 9PL, UK.
Mathematical Institute, University of Oxford, Radcliffe Observatory, Woodstock Road, Oxford OX2 6GG, UK
Philos Trans A Math Phys Eng Sci. 2017 May 13;375(2093). doi: 10.1098/rsta.2016.0227.
We report the results of an experimental and numerical investigation into the buckling of thin elastic rings confined within containers of circular or regular polygonal cross section. The rings float on the surface of water held in the container and controlled removal of the fluid increases the confinement of the ring. The increased compressive forces can cause the ring to buckle into a variety of shapes. For the circular container, finite perturbations are required to induce buckling, whereas in polygonal containers the buckling occurs through a linear instability that is closely related to the canonical Euler column buckling. A model based on Kirchhoff-Love beam theory is developed and solved numerically, showing good agreement with the experiments and revealing that in polygons increasing the number of sides means that buckling occurs at reduced levels of confinement.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'
我们报告了一项关于限制在圆形或正多边形横截面容器内的薄弹性环屈曲的实验和数值研究结果。这些环漂浮在容器中所盛水的表面，通过控制排出液体可增加环的约束。增加的压缩力会使环屈曲成各种形状。对于圆形容器，需要有限扰动来引发屈曲，而在多边形容器中，屈曲通过与经典欧拉柱屈曲密切相关的线性不稳定性发生。基于基尔霍夫-洛夫梁理论开发了一个模型并进行了数值求解，结果与实验显示出良好的一致性，且揭示出在多边形中增加边的数量意味着在约束水平降低时就会发生屈曲。本文是主题为“复杂介质中通过不稳定性进行图案化：理论与应用”这一特刊的一部分。
