Geometric design and deployment behavior of origami inspired conical structures
H C Sharma, Sanjay Upadhyay
Abstract
This study investigates the folding pattern design and deployment behavior of origami-based foldable conical structures. The geometric analysis is performed to design the six fold line pattern to obtain foldable conical structures. A single-story origami cone, modeled with pin-jointed framework, is selected for the analytical investigation. The axial strains, nodal forces, relative rotation of the fold polygons, and the strain energy during the deployment are obtained analytically. Moreover, the influence of design parameters (m and α1) on the deployment behavior of a single story cone is investigated. The results indicate that several fold configurations exhibit a bistable behavior during the motion, and these bistable configurations undergo lesser deformations than other singly stable fold configurations. Then, the folding and deployment process is simulated numerically using FE software to verify the accuracy of the analytical approach. The numerical results are completely consistent with the analytical results. The existence of bistability is verified using the variation of elastic strain energy during the motion. An analytical approach to obtain the bistability points for any conical folding pattern is presented and verified using numerical simulations. The influence of design parameters, materials, and scaling on the bistability point is also investigated. The results show that the bistability is solely a geometrical phenomenon, and scaling does not change the deformation behavior of the cone. Finally, the deployment dynamics of both singly stable and bistable multistory conical structures are discussed, with their potential applications.