Confined wrinkling of thin elastic rods, sheets and cones
Thin-walled structures, such as plates and shells, become more vulnerable to in-plane compressive effects as their thickness is reduced, where they may buckle out-of-plane at lower than operational loads. Here, a novel approach allows the thin structures to buckle, but within a prescribed confinement to ensure higher-mode buckling and hence a reasonable post-buckling capacity. The main aim is to understand and predict this confined buckling behaviour of some simple thin-walled structural forms: a rod, rectangular sheet, trapezium, rectangle with a central hole, cone and conical frustum. Rods and planar sheets are initially buckled into their first mode by applying a small axial displacement. Confinement is achieved by placing the buckled sheet between two parallel rigid plates, which are gradually moved towards each other until the sheet buckles further. Cones and frusta are confined immediately without initial buckling. Physical experiments and finite element analyses are used to investigate and observe the confined buckling response, as well as to verify the analytical models derived to predict the behaviour. Here it is shown that, as they are confined, the sheets progressively buckle into higher modes, forming more and more sinusoidal waves or wrinkles. Rods and rectangular sheets form straight wrinkles with constant wavelengths. Less regular shapes, such as trapezia and rectangles with a hole, form curved wrinkles with a variable wavelength, which is inversely proportional to the square root of the geometric strain. For all initially planar sheets, wrinkle directions align approximately perpendicularly to free edges. On the other hand, cones form hoop wrinkles with an almost constant wavelength, while frusta form a combination of inner radial and outer hoop wrinkles, with the transition between the two moving closer to the outer edge for larger inner holes. Radial wrinkles at the inner edge have a constant wavelength, which is proportional to the confinement gap between the rigid plates. All structures considered exhibit a variable stiffness, with the load capacity on average increasing exponentially with confinement. The results extend the limited literature on confined buckling and wrinkling, and are part of the first known study to include irregularly shaped confined wrinkled sheets. Direct applications could utilise the variable stiffness of the confined rods and sheets, by setting the confinement gap to achieve a certain stiffness or load carrying capacity.