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Tape springs are straight, thin-walled strips with a curved cross-section. Following recent proposals for large deployable structures exploiting the structural simplicity and robustness of such springs as deployment actuators, the paper investigates the dynamic deployment of a tape spring that is either coiled around a circular hub, or folded into a zigzag pattern. It is shown that in both cases the spring deforms by forming an elastically deformed region with zero transverse curvature and uniform longitudinal curvature. The process of formation and growth of a fold belongs to a wide class of propagating instabilities. It is characterized by a high peak moment and a lower propagation moment. A compact characterization of the moment-rotation relationship for an elastic fold is presented. A key feature is that the bending moment on either side of a fold moving along a uniform tape spring, away from any end supports, is constant, whereas this moment increases near a support. Compact and accurate two-dimensional theories are developed to simulate the self-actuated deployment of tape springs. It is shown that conservative energy formulations are appropriate for coiled springs, where the velocity field is smooth, but not for springs with localized folds. To simulate the motion of such localized folds a non-conservative impulsemomentum formulation is proposed, and it is found that this model can accurately predict both the steady motion of the folds along the tape spring and their rebound against the end supports.

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.

Seven form-finding methods for tensegrity structures are reviewed and classified. The three kinematical methods include an analytical approach, a non-linear optimisation, and a pseudo-dynamic iteration. The four statical methods include an analytical method, the formulation of linear equations of equilibrium in terms of force densities, an energy minimisation, and a search for the equilibrium configurations of the struts of the structure connected by cables whose lengths are to be determined, using a reduced set of equilibrium equations. It is concluded that the kinematical methods are best suited to obtaining only configuration details of structures that are already essentially known. The force density method is best suited to searching for new configurations, but affords no control over the lengths of the elements of the structure. The reduced coordinates method offers a greater control on elements lengths, but requires more extensive symbolic manipulations.

This paper presents a detailed experimental study of the evolution and shape of reversible corrugations, or wrinkles, in initially flat, linear-elastic and isotropic thin foils subject to in-plane loads. Two sets of experiments were carried out, on a rectangular membrane under simple shear and on a square membrane subjected to two pairs of equal and opposite diagonal forces at the corners. Salient findings are that: the wrinkle profile is generally well approximated by a half sine wave in the longitudinal direction, with constant or linearly-varying transverse wavelength; sudden changes in the shape of the membrane, accompanied by changes in the number of wrinkles, occur in both cases; in the sheared membrane the wrinkle pattern remains essentially unchanged for increasing shear displacement, whereas in the square membrane a large diagonal wrinkle appears when the corner load ratio is around 3.

This is the third and final part of a study of wrinkles in thin membrane structures. High-fidelity, geometrically nonlinear finite element models of membrane structures, based on thin-shell elements, are used to simulate the onset and growth of wrinkles. The simulations are carried out with the ABAQUS finite element package. The accuracy of the results is demonstrated by computing the characteristics of the wrinkles in two specific membrane structures that were investigated experimentally and analytically in the first two papers in this series.

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