Influence of transverse curvature on the stability of pre-stressed helical structures

This study is concerned with the stability characteristics of helix shaped structures made of anisotropic, pre-stressed, thin flanges arranged in such a way as to enable and develop multi-stability. Previous research on similar structures assumed the structural response of the flanges to be one-dimensional due to the narrow width of the pre-stressed members in comparison to their length. In this work, a refined two-dimensional model of the flanges is employed to model the influence of transverse curvature as well as the membrane strain energy associated with the non-zero Gaussian curvature deformations. While longitudinal curvature changes and twist are inherent to the geometry of the helices; the transverse curvature results from a consideration of boundary effects and the minimisation of the (expensive) membrane elastic energy. A qualitative study of the changes in transverse curvature reveals ways of simplifying the two-dimensional model into a simpler, closed form, one-dimensional version applicable to helices with relatively narrow flanges. Correlation is found between experimental results, finite element modelling and analytical predictions for the two models.