Mathematical Model of Tomoe-Type Kirigami Structure

Abstract

Starshade, which is one of the deployable membrane space structures, has sensors and actuators on the membrane to maintain its shape. Therefore, flexible printed wiring is attached to the entire membrane. However, since the membrane is folded and stored during launch, there is a risk that the flexible printed wiring will break at the crease with a small radius of curvature. The authors adopt Tomoe-type kirigami structure for the solution. Tomoe-type kirigami is a structure in which characteristic cuts are made on a plane. When the membrane is flat-planed, the Tomoe-type kirigami is also flat-planed and has no distortion. When the membrane is folded, Tomoe-type kirigami transforms into a triangular shape with three large bent beams. Since the radius of curvature of bending of Tomoe-type kirigami structure is very large, the wiring will not break. However, when Tomoe-type kirigami is deformed from its planar shape, a restoring force acts against the deflection and applies an out-of-plane load to the base film. Since the starshade requires high accuracy of shape determination, and since multiple Tomoe-type kirigami are arranged on the entire membrane, it is necessary to estimate the external force applied to the base membrane by Tomoe-type kirigami. Therefore, in this presentation, we proposed a mechanical model of Tomoe-shaped kirigami structure, and made it possible to estimate the external force by calculation. The validity of the proposed mechanical model was verified by shape measurement experiments, and it was confirmed that the mechanical model and the experimental results were in good agreement.