Tape-rings are a novel variation on standard tape-spring geometry, manufactured as a toroidal cap. We investigate the flattening behaviour of a tape-ring between two plates: which is shown to exhibit novel bending-stretching coupling. In particular, the change in Gaussian curvature causes tension along the outer edge and compression on the inside, which leads to circumferential buckling of the inner edge, or transverse buckling of the cross-section if axisymmetry is enforced. The flattened strains and flattening force are predicted via analytical solutions, which are shown to agree well with FEA results and physical experiments.
Clarkson et al. (Sun,) studied this question.