Deployment dynamics of tape springs

Tape springs are straight, thin-walled strips with a curved cross-section. Following recent proposals for large deployable structures exploiting the structural simplicity and robustness of such springs as deployment actuators, the paper investigates the dynamic deployment of a tape spring that is either coiled around a circular hub, or folded into a zigzag pattern. It is shown that in both cases the spring deforms by forming an elastically deformed region with zero transverse curvature and uniform longitudinal curvature. The process of formation and growth of a fold belongs to a wide class of propagating instabilities. It is characterized by a high peak moment and a lower propagation moment. A compact characterization of the moment-rotation relationship for an elastic fold is presented. A key feature is that the bending moment on either side of a fold moving along a uniform tape spring, away from any end supports, is constant, whereas this moment increases near a support. Compact and accurate two-dimensional theories are developed to simulate the self-actuated deployment of tape springs. It is shown that conservative energy formulations are appropriate for coiled springs, where the velocity field is smooth, but not for springs With localized folds. To simulate the motion of such localized folds a non-conservative impulse-momentum formulation is proposed, and it is found that this model can accurately predict both the steady motion of the folds along the tape spring and their rebound against the end supports.