On zero stiffness

Zero-stiffness structures have the remarkable ability to undergo large elastic deformations without requiring external work. Several equivalent descriptions exist, such as (i) continuous equilibrium, (ii) constant potential energy, (iii) neutral stability and (iv) zero stiffness. Each perspective on zero stiffness provides different methods of analysis and design. This paper reviews the concept of zero stiffness and categorises examples from the literature by the interpretation that best describes their working principle. Lastly, a basic spring-to-spring balancer is analysed to demonstrate the equivalence of the four different interpretations, and illustrate the different insights that each approach brings. This is the accepted version of an article first published in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. The final version is available online at http://pic.sagepub.com/content/early/2013/11/14/0954406213511903.abstract

On rigid origami II: Quadrilateral creased papers

Miura-ori is well-known for its capability of flatly folding a sheet of paper through a tessellated crease pattern made of repeating parallelograms. Many potential applications have been based on the Miura-ori and its primary variations. Here we are considering how to generalize the Miura-ori: what is the collection of rigid-foldable creased papers with a similar quadrilateral crease pattern as the Miura-ori? This paper reports some progress. We find some new variations of Miura-ori with less symmetry than the known rigid-foldable quadrilateral meshes. They are not necessarily developable or flat-foldable, and still only have single degree of freedom in their rigid folding motion. This article presents a classification of the new variations we discovered and explains the methods in detail.George and Lilian Schiff Foundation

On rigid origami I: Piecewise-planar paper with straight-line creases

We develop a theoretical framework for rigid origami, and show how this framework can be used to connect rigid origami and results from cognate areas, such as the rigidity theory, graph theory, linkage folding and computer science. First, we give definitions on important concepts in rigid origami, then focus on how to describe the configuration space of a creased paper. The shape and 0-connectedness of the configuration space are analyzed using algebraic, geometric and numeric methods, where the key results from each method are gathered and reviewed

Mobility of a class of perforated polyhedra

A class of over-braced but typically flexible body-hinge frameworks is described. They are based on polyhedra with rigid faces where an independent subset of faces has been replaced by a set of holes. The contact polyhedron C describing the bodies (vertices of C) and their connecting joints (edges of C) is derived by subdivision of the edges of an underlying cubic polyhedron. Symmetry calculations detect flexibility not revealed by counting alone. A generic symmetry-extended version of the Grübler-Kutzbach mobility counting rule accounts for the net mobilities of infinite families of this type (based on subdivisions of prisms, wedges, barrels, and some general inflations of a parent polyhedron). The prisms with all faces even and all barrels are found to generate flexible perforated polyhedra under the subdivision construction. The investigation was inspired by a question raised by Walter Whiteley about a perforated polyhedron with a unique mechanism reducing octahedral to tetrahedral symmetry. It turns out that the perforated polyhedron with highest (OhOh) point-group symmetry based on subdivision of the cube is mechanically equivalent to the Hoberman Switch-Pitch toy. Both objects exhibit an exactly similar mechanism that preserves TdTd subgroup symmetry over a finite range; this mechanism survives in two variants suggested by Bob Connelly and Barbara Heys that have the same contact graph, but lower initial maximum symmetry.Supported by EPSRC First Grant EP/M013642/1.This is the final version of the article. It first appeared from Elsevier via https://doi.org/10.1016/j.ijsolstr.2016.02.00

Novel stacked folded cores for blast-resistant sandwich beams

Recent research has established the effectiveness of sandwich structures with metallic cellular cores for blast mitigation. The choice of core architecture can enhance sandwich performance, dissipating energy through plastic core compression and exploiting fluid-structure interaction effects to reduce the momentum imparted to the structure by the blast. In this paper we describe the first analysis of a novel sandwich core concept for blast mitigation: the Stacked Folded Core. The core consists of an alternating stacked sequence of folded sheets in the Miura (double-corrugated) pattern, with the stack oriented such that the folding kinematics define the out-of plane compressive strength of the core. It offers a number of distinct characteristics compared to existing cellular cores. (i) The kinematics of collapse of the core by a distinctive folding mechanism give it unique mechanical properties, including strong anisotropy. (ii) The fold pattern and stacking arrangement is extremely versatile, offering exceptional freedom to tailor the mechanical properties of the core. This includes freedom to grade the core properties through progressive changes in the fold pattern. (iii) Continuous manufacturing processes have been established for the Miura folded sheets which make up the core. The design is therefore potentially more straightforward and economical to manufacture than other metallic cellular materials. In this first investigation of the Stacked Folded Core, finite element analysis is used to investigate its characteristics under both quasi-static and dynamic loading. A dynamic analysis of an impulsively loaded sandwich beam with a stacked folded core reveals the versatility of the concept for blast mitigation. By altering the fold pattern alone, the durations of key phases of the dynamic sandwich response (core compression, beam bending) can be controlled. By altering both fold pattern and sheet thickness in the core, the same is achieved without altering the density of the core or the mass distribution of the sandwich beam.This is the author's accepted manuscript. The final version is available from Elsevier at: http://www.sciencedirect.com/science/article/pii/S0020768314003035

Symmetry perspectives on some auxetic body-bar frameworks

Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied to two long known but apparently little studied hinged-hexagon frameworks, and is shown to detect auxetic behaviour in both. In contrast, for double-link frameworks based on triangular and square tessellations, other affine deformations can mix with the isotropic expansion mode.P.W. Fowler acknowledges support from the Royal Society/Leverhulme Trust in the form of a Senior Research Fellowship for 2013. T. Tarnai is grateful for financial support under OKTA grant K81146.This is the final published version distributed under a Creative Commons Attribution License, which can also be found on the publisher's website at: http://www.mdpi.com/2073-8994/6/2/36

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

Folded orthotropic tape-springs

We consider the large-displacement, elastic folding of orthotropic tape-springs—thin-walled curved strips made from metal and from a woven laminated composite. Bending of the strips leads to a tight localised fold with a characteristic radius, connected on both sides to straight parts by doubly-curved transition, or ploy, regions. We calculate the shapes of these consistent features for a range of orthotropic parameters using geometrically non-linear, compact models. This study is our initial foray into the performance of tape-springs as safety latching mechanisms for aircraft landing gear

Review of inflatable booms for deployable space structures: Packing and rigidization

Inflatable structures offer the potential of compactly stowing lightweight structures, which assume a fully deployed state in space. An important category of space inflatables are cylindrical booms, which may form the structural members of trusses or the support structure for solar sails. Two critical and interdependent aspects of designing inflatable cylindrical booms for space applications are i) packaging methods that enable compact stowage and ensure reliable deployment, and ii) rigidization techniques that provide long-term structural ridigity after deployment. The vast literature in these two fields is summarized to establish the state of the art.The work described in this paper forms part of the DeployTech project; the authors gratefully acknowledge the funding from the European Commission Seventh Framework Programme (FP7).This is the accepted, peer-reviewed manuscript of an article originally published in the Journal of Spacecraft and Rockets. The final published version is available at http://arc.aiaa.org/doi/abs/10.2514/1.A32598