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. (C) 2014 Elsevier Ltd. All rights reserved.