Simon D. Guest

Geometry of Miura-folded metamaterials

This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson’s ratio for in-plane deformations and a positive Poisson’s ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.

Analytical models for bistable cylindrical shells

Thin cylindrical shell structures can show interesting bistable behaviour. If made unstressed from isotropic materials they are only stable in the initial configuration, but if made from fibre-reinforced composites they may also have a second, stable configuration. If the layup of the composite is antisymmetric, this alternative stable configuration forms a tight coil; if the layup is symmetric the alternative stable configuration is helical. A simple two-parameter model for these structure is presented that is able to distinguish between these different behaviours.

On the determinacy of repetitive structures

This paper shows that repetitive, infinite structures cannot be simultaneously statically, and kinematically, determinate.

A symmetry extension of Maxwell's rule for rigidity of frames

A symmetry extension of Maxwells rule for rigidity of frames is found. This rule subsumes and strengthens Maxwells 1864 rule by requiring that the internal and external degrees of freedom of a pin-jointed structure are not only numerically equal, but are also equisymmetric. A number of special cases of Maxwells original rule are studied to show the improved insight that the symmetry-adapted version can give.

An introduction to the analysis of symmetric structures

Abstract This paper aims to review and explain the techniques used to analyse symmetric structures subject to a general loading. After an extensive review of previous work in this field, the paper introduces the most general way of describing the full symmetry properties of a structure, based on group representation theory, and shows how this approach can be used to systematically simplify a structural analysis. A technique which is better known to structural engineers, known as the Fourier method, is also presented, but it is shown that this method is a special case of the group representation theory method. For both methods the techniques that are used to block-diagonalize the full stiffness matrix of a structure are presented, and it is also shown that substructuring techniques can be used so that the full stiffness matrix never needs to be generated.

Symmetry-adapted equilibrium matrices

A number of authors have previously used group representation theory to block-diagonalise the stiffness matrix of a symmetric structure. This paper describes how similar techniques can be used to block-diagonalise the equilibrium matrix of a symmetric structure. This is shown to provide useful insight into the static and kinematic response of such systems. In particular, it simplifies finding and classifying states of self-stress and mechanisms, as well as reducing the computational effort required for a Force Method analysis.

A NEW CONCEPT FOR SOLID SURFACE DEPLOYABLE ANTENNAS

Abstract This paper presents a new class of rigid-panel deployable antennas. The antenna surface is divided into a series of panels, which fold by wrapping around a central hub. All connections between the panels are made by revolute joints. This new folding technique has significant advantages over previous concepts, both in terms of packaged size, and mechanical simplicity. Furthermore, the size and shape of the packaged reflector can be readily adapted to any particular set of mission requirements. A small hardware demonstrator, which has been designed, manufactured and successfully tested, is discussed in the paper.

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.

Detection of finite mechanisms in symmetric structures

Abstract Using group representation theory, it is possible to block-diagonalise the equilibrium matrix of a symmetric structure. This analysis can identify the symmetry properties of any states of self-stress or mechanisms present in the structure. This paper will show that in some cases, this linear analysis, combined with symmetry arguments, can show that particular mechanisms of a symmetric structure must be finite.

Multistable corrugated shells

We have been constructing and investigating multistable corrugated shell structures. The multistability arises from the interaction between internal prestresses created during forming and nonlinear geometrical changes during deformation. Using a simplified analytical elastic model, we homogenize the properties of the shells through simultaneously considering the material on two scales: the ‘local’ scale of the isotropic material; and the ‘global’ scale of the corrugated sheet, which is then modelled as an equivalent flat sheet with anisotropic properties. This model is applied to simulate two modes of bistability observed in prototypes: first, prestressed corrugated shells that, when buckled, can coil up into a tube repeatably and reversibly; and second, corrugated sheets with a symmetry-breaking ‘twisting’ curvature. The model gives an intuitive understanding of the behaviour, and has enabled us to understand forming processes that give the behaviour we wish, including tristable shells that combine both bistable modes.