Morphing of symmetric cross-ply cylindrical shells by minimising the Brazier moment: Optimised hinge folding

Aerospace and industries where both localised compliance and weight savings play a central role in design can benefit from using flexible hinges. These morphing structures use no mechanical hinges for folding. They fold by exploiting the limit point, i.e. the Brazier moment, of a geometrically nonlinear structural response characteristic of thin-walled beams under bending. Therefore, a smaller Brazier moment induces smaller non-classical stresses in the hinge during folding. Two aspects make cross-ply laminates attractive for designing flexible hinges. Firstly, the difference between the Brazier moment of an optimal symmetric generic laminate and that of an optimal symmetric cross-ply is relatively small. Secondly, cross-ply laminates do not exhibit extension-shear or bend-twist couplings which can induce complex deformations which can present challenges during design, especially considering that available analytical solutions of the Brazier moment neglect their effects. Driven by these premises, this work contributes to the preliminary design of flexible hinges by offering an analytical solution of the optimum symmetric cross-ply laminate for minimising the Brazier moment, which is subsequently validated through geometrically nonlinear finite element analysis. Moreover, this work provides insights into the prediction of the folding load considering the effects of local buckling instabilities.