Submitted by Paula Block on Wed, 18/09/2024 - 15:59
Well done to Jamie Clarkson whose paper “Torsional buckling of a tape-spring: Review and Renew” was published in the International Journal of Solids and Structures and available to view online on: https://www.sciencedirect.com/science/article/pii/S0020768324003512 Jamie is from Cohort 3 and in his second PhD year.
Jamie’s research area is on the structural mechanics of novel tape-spring geometries. Tape-springs are long, thin, strips with transverse curvature, widely used as deployable structures. A carpenter’s tape measure is a familiar example. Jamie explains: If you take a tape measure in your hands and bend it in the “opposite sense” direction, so the deformed surface is saddle-like, it will bend uniformly until reaching a peak load, whereupon the curvature localises into a hinge-like “fold” with a loud snap. If, instead, you bend it in the “equal-sense” direction, so the deformed surface is like a bicycle mudguard, the tape will buckle torsionally at a fairly low load.
Mansfield’s 1973 paper on tape-springs solved the twisting curvature kxy as a function of the longitudinal curvature kx; however, the resulting expressions contained hyperbolic functions of kx, and thus cannot be solved in closed form to find, for example, the longitudinal curvature at which torsional buckling initiates and recedes. In his paper, “Torsional buckling of a tape-spring: Review and renew”, Jamie presents a new approximate solution which leads to closed form expressions for the curvature at which torsional buckling initiates, and the critical condition for whether torsional buckling will occur at all. This will aid the early-stage “back of the envelope” design of deployable structures, as the previous solution was not in closed form and required numerical evaluation.
Jamie has also written a second paper on this. He explains: Tape-spring fold formation is an example of elastic localisation, which occurs in any elastic system with an “up-down-up” stress-strain relationship. By splitting into two regions, or phases, of differing strain, one low strain and the other high strain, the total strain energy can be minimised. The strain in each phase is governed by the Maxwell Equal Areas construction. In tape-springs, the fold radius is approximately equal to the initial transverse radius r, but differs slightly depending on the thickness of the spring. In his second paper, “Elastic localisation with particular reference to tape-springs”, Jamie developed a new proof of the Maxwell Equal Areas construction, and by its application obtained more accurate predictions of tape-spring fold radius. This paper has been published in the Journal of Applied Mechanics: https://doi.org/10.1115/1.4066324; an open-access version is available on Apollo: https://doi.org/10.17863/CAM.111981.
“I am very pleased to have published two papers and am hoping to publish a couple more in the coming months.” - Jamie Clarkson