150 research outputs found
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Folding a ridge-spring
Ā© 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; Ī±4/3 Ā· (b/t)1/3, where Ī± 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 resultsāwhich 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
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Multistable grid and honeycomb shells
The manufacturing of multistable shells has been dominated by the use of pre-stressed and composite
materials. Here we advocate the use of common materials through a simple design that requires no
pre-stressing and has an initially developable geometry. A rudimentary demonstrator is constructed
and serves as the starting point for further study. An existing homogenisation model for a lattice structure
is combined with an analytical strain energy model from the literature to show the mechanical properties
needed to construct an initially developable, bistable grid shell. The concept is also tested in a
commercial finite element package, where a number of parametric studies are performed. Both the demonstrator
and the FE model confirm the validity of the design while a series of parametric studies helps
establish the limits of this behaviour with respect to local and global geometry of grid shell and honeycomb
structures.EGL was supported by scholarships from the Alexander S. Onassis
Public Benefit Foundation and the Cyprus State Scholarship
Foundation.This is the accepted manuscript of a paper published in the International Journal of Solids and Structures, Volume 59, 1 May 2015, Pages 46ā57, DOI: 10.1016/j.ijsolstr.2015.01.002
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
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Effects of Boundary Conditions on Bistable Behaviour in Axisymmetrical Shallow Shells
Multistable shells are thin-walled structures that have more than one stable state of self-stress. We consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a Foppl-von KĆ”rmĆ”n analytical model. By employing a Rayleigh-Ritz approach, we identify stable shapes from local minima in the strain energy formulation, and we formally characterise the level of influence of the boundary conditions on the critical geometry for achieving bistable inversionāan effect not directly answered in the literature. Systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs. For typical caplike shells, it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases i.e. when boundary movements in-plane are resisted but when their rotations are not; however, for certain other shapes and large in-plane stiffness values, bistability can be enhanced by resisting but not entirely preventing edge rotations. Our predictions are furnished as detailed regime maps of the critical geometry, which are accurately correlated against finite element analysis. Furthermore, the suitability of single degree-of-freedom models, for which solutions are achieved in closed form, are evaluated and compared to our more accurate predictions
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Folding the Carpenter's Tape: Boundary Layer Effects
Abstract
The ācarpenterās measuring tapeā 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 Ī¾ = r/R > 1, where the value of Ī¾ exceeds unity by up to 15%, depending on whether the tape is bent in āequal-senseā or āopposite-senseā curvature; Ī¾ varies linearly with Poissonās ratio in both cases. We make a minor change to Rimrottās 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
Ā© 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
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Inverted cones and their elastic creases
We study the elastic inversion of a right circular cone, in particular, the uniform shape of the narrow crease that divides its upright and inverted parts. Our methodology considers a cylindrical shell analogy for simplicity where the crease is the boundary layer deformation. Solution of its governing equation of deformation requires careful crafting of the underlying assumptions and boundary conditions in order to reveal an expression for the crease shape in closed form. We can then define the characteristic width of crease exactly, which is compared to a geometrically nonlinear, large displacement finite element analysis. This width is shown to be accurately predicted for shallow and steep cones, which imparts confidence to our original assumptions. Using the shape of crease, we compute the strain energy stored in the inverted cone, in order to derive an expression for the applied force of inversion by a simple energy method. Again, our predictions match finite element data very well. This study may complement other studies of creases traditionally formed in a less controlled manner, for example, during crumpling of lightweight sheets
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
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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 Ā±45Ė, it is stable in both the extended and coiled configurations. In this research, we devise a simple āfreeā 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
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