Folding a ridge-spring

© 2019 A ridge-spring is a thin-walled bent strip with flat side panels. It may be folded elastically along its length, to create a localised hinge region of mostly uniform cylindrical curvature and bending moment, which do not vary with the fold angle of hinge. A simple analysis shows a common grouping in closed-form expressions; α4/3 · (b/t)1/3, where α is the pitch angle of the ridge line, b is the strip width and t its thickness. More accurate calculations of the hinge curvature and moment confirm the robustness of simpler expressions, which are compared to data obtained from finite element simulations. It is shown that, for many initial geometries, theoretical predictions of curvature and moment are typically within 10% of the computational results—which project the same dimensional performance. We also compare a ridge-spring to a more familiar tape-spring of equal cross-sectional proportions. For moderate pitch angles and relatively small thicknesses, it is shown that a ridge-spring has a higher folded hinge curvature and bending moment, comparatively, which may prove attractive for certain applications

Confirming inextensional theory

Thin, initially-flat plates can deform inextensionally and elastically during large out-of-plane deformations. This paper revisits an analytical method for describing the developable shapes of displaced plate, in order to quantify and validate its effectiveness. Results from practical experiments and finite element analysis are compared to theoretical predictions from well-known examples, and excellent correlations are obtained.VRS was supported by a PhD studentship from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom.This is the published manuscript. The final published version was first published by Elsevier here: http://www.sciencedirect.com/science/article/pii/S0020768314002339

De-wrinkling of pre-tensioned membranes

Thin membranes are used in the spacecraft industry as extremely lightweight structural components. They need to be stiffened, usually by applying discrete forces, and this increases their susceptibility to wrinkling in regions where high tensile stresses develop. We consider a regular polygonal membrane uniformly loaded at its corners by equal forces and we prevent wrinkle formation by trimming the edges of the polygon into very gentle curves. We confirm this performance through simple physical experiments using Kapton, a typical membrane material and, using computational analysis, we show how the distribution of compressive stresses, responsible for causing wrinkles, dissipates following trimming. Finally, we accurately predict the required level of trimming for any number of sides of polygon using a simple, linear model, which invokes a plate-bending analogy.This is the published manuscript. It was originally published in the International Journal of Solids and Structures here: http://www.sciencedirect.com/science/article/pii/S0020768314001875

Folding the Carpenter's Tape: Boundary Layer Effects

Abstract The “carpenter’s measuring tape” is a thin spring-steel strip, preformed to a curved cross section of radius R, which is straight when being used for measuring. Under bending moments, it forms a localized hinge, in which the transverse curvature is suppressed, and the longitudinal radius r is approximately equal to R. Rimrott made a simple strain energy analysis of the hinge region for isotropic material, which predicted that r = R. Both experimental observations and finite element computations show that ξ = r/R > 1, where the value of ξ exceeds unity by up to 15%, depending on whether the tape is bent in “equal-sense” or “opposite-sense” curvature; ξ varies linearly with Poisson’s ratio in both cases. We make a minor change to Rimrott’s analysis by introducing a boundary layer, in order better to satisfy the physical conditions at the free edges; this successfully accounts for the observed behavior of the tape.Non

The flexural mechanics of creased thin strips

© 2019 Many structures in Nature and Engineering are dominated by the influence of folds. A very narrow fold is a crease, which may be treated with infinitesimal width for a relatively simple geometry; commensurately, it operates as a singular hinge line with torsional elastic properties. However, real creases have a finite width and thus continuous structural properties. We therefore consider the influence of the crease geometry on the large-displacement flexural behaviour of a thin creased strip. First, we model the crease as a shallow cylindrical segment connected to initially flat side panels. We develop a theoretical model of their coupled flexural behaviour and, by adjusting the relative panel size, we capture responses from a nearly singular crease up to a full tape-spring. Precise experiments show good agreement compared to predictions.Cambridge Home and European Scholarship Schem

Magnetic actuation and transition shapes of a bistable spherical cap

Multistable shells have been proposed for a variety of applications; however, their actuation is almost exclusively addressed through embedded piezoelectric patches. Additional actuation techniques are needed for applications requiring high strains or where remote actuation is desirable. Part of the reason for the lack of research in this area is the absence of appropriate models describing the detailed deformation and energetics of such shells. This work presents a bistable spherical cap made of iron carbonyl-infused polydimethylsiloxane. The magnetizable structure can be actuated remotely through permanent magnets while the transition is recorded with a high-speed camera. Moreover, the experiment is reproduced in a finite element (FE) dynamic model for comparison with the physical observations. High-speed footage of the physical cap inversion together with the FE modeling gives valuable insight on preferable intermediate geometries. Both methods return similar values for the magnetic field strength required for the snap-through. High-strain multistable spherical cap transformation is demonstrated, based on informed material selection. We discover that non-axisymmetric transition shapes are preferred in intermediate geometries by bistable spherical caps. We develop the methods for design and analysis of such actuators, including the feasibility of remote actuation methods for multistable shells.EGL acknowledges financial support by the Alexander S. Onassis Public Benefit Foundation and the Cyprus State Scholarship Foundation. SKS acknowledges funding by the European Research Council (ERC) grant EMATTER [#280078].This is the final published version. It first appeared at http://www.tandfonline.com/action/showCopyRight?doi=10.1080%2F19475411.2014.997322#tabModule

Shape of a bistable composite tape-spring in folding

A composite tape-spring structure is a thin-walled, laminated open slit tube. With fibres oriented at ±45˚, it is stable in both the extended and coiled configurations. In this research, we devise a simple ‘free’ bending system with minimal constraints to evaluate the folding nature of composite tape-springs. The shape of the tape-spring is characterised by considering both the shape during folding and the final folded shape. Experiments are carried out on composite tapes with different geometries: a finite element model is established and calibrated using the experimental results; a parametric study on the folded tape shape is performed based on a theoretical model to evaluate the effects of the initial geometry. Torsional buckling is clearly observed, and complemented with details from the FE model. Here, we show good agreement between experiments, simulation and theoretical analysis.Technology Strategy Boar