Folding pattern design and deformation behavior of origami based conical structures

Abstract

In recent times, origami-inspired deployable structures have received significant interest from the research community as a major area of research in the fields of science and technology. This paper deals with the geometry and the deformation behavior of deployable cones based on the four-fold line origami concept. First, a novel geometric design algorithm is presented to develop axially foldable conical structures based on generalized Miura-ori pattern, which is then utilized to investigate the influence of four design parameters on folding geometry. The foldability of thus obtained origami patterns is verified with the help of physical models. The geometric incompatibilities during the deployment are highlighted using a simple experiment, showing the unfolding sequence of a paper model. The deformations due to incompatibilities are analyzed by adopting the concept of pin-jointed truss modeling of the origami structures. A mathematical model of the deployment problem is formulated to capture the deployment deformations of the structure, on the basis of which an algorithm for deformation analyses is developed. One example is considered to characterize the deformation behavior of the conical origami structures as the design parameters of the folding pattern are varied. The analytical findings demonstrate that the fold line strains of the origami cone are very sensitive to the changes in three design parameters, number of origami units (m), fold angle (α0), and angle θ2; except the length ratio (lr0). The variation in design parameters may induce bi-stability in the deployment path of the conical structure. The findings of the analytical investigation are verified numerically, demonstrating that the strain responses obtained from the numerical analyses are completely consistent with the analytical results.