Stiffness and Stability of Spiral-Wrapped Doubly Curved Shells

Through finite element simulations, this work shows that intermediate stable equilibria about a crease line can be predicted by a single non-dimensional parameter encompassing material and geometric properties of a spiral-wrapped reflector design. Intermediate stable equilibria can be avoided by increasing thickness, decreasing opening angle, or increasing degrees of rotational symmetry. The addition of supporting ribs greatly increases both the stability and stiffness of these reflectors. Preliminary deployment simulations suggest that even reflectors with intermediate stable equilibria can dynamically self-deploy using only stored elastic strain energy from folding.