Abstract
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.'
Highlights
It is well known that thin-walled elastic rings, beams and tubes are prone to buckling instabilities when under compressive loads [1,2]
The trivial branch is shown as a dotted line and, because the ring adopts the same shape as the funnel boundary, the branch is given by equality between both areas
We have demonstrated that there is a qualitative difference between constrained buckling of an elastic ring when the confining geometry changes from circular to polygonal
Summary
It is well known that thin-walled elastic rings, beams and tubes are prone to buckling instabilities when under compressive loads [1,2]. The comparison on the main branch (solid line and markers), which has the full symmetries of the square, is good except at large cross-sections, which may be due to meniscus effects forcing the ring to lie out of the plane and giving a smaller projected area.
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