Geometric design of arbitrarily curved bi-stable deployable arches with discrete joint size

Abstract

The deployable structures presented in this work are bi-stable in the sense of being self-standing and stress-free when fully closed or fully deployed, but exhibit incompatibilities between the member lengths at intermediate geometric configurations during the deployment process, which lead to the occurrence of second-order strains and stresses resulting in a snap-through phenomenon that “locks” the structures in their deployed configuration. Until now the geometric shapes that were possible in the deployed configuration were only flat or curved with constant curvature. This limitation is addressed in the present paper by proposing a geometric design methodology for deployable arches of arbitrary curvature, accounting also for the discrete joint size, and applying it successfully for the geometric design of a semi-elliptical arch. The arch is then modeled with finite elements, and a geometrically non-linear analysis is performed in order to verify the deployability feature. Further verification is provided by the construction of a small-scale physical model. A preliminary structural design indicates the overall feasibility of the arch for short to medium spans and light loads.