Parametric design of developable structure based on yoshimura origami pattern

Abstract

Origami is an ancient art form and can be divided into rigid and non-rigid origami. Rigid origami is suitable for the design of building structures because the panels are not twisted and deformed during the folding process. Currently, rigid origami structures are generally built with steel. However, compared with natural, non-polluting wood, steel has a high energy consumption and a high environmental impact. Based on this situation, this paper designs a developable wooden building structure using the Yoshimura origami model. First, the Jacobian matrix method was used to analyze the degree of freedom of the basic unit of the Yoshimura origami pattern, following which the motion trajectory required by the target structure was obtained. Secondly, by analyzing the relationship between the plane angle α and dihedral angle θ, three interaction rules were obtained, and the formula for determining the structure size was established by using the plane angle α, dihedral angle θ, the number of valley folds n and the unit length l. Subsequently, two enhancement schemes, the quadrangle enhancement scheme and the triangle enhancement scheme, were proposed to increase the height of the structure. After comparing the deformation and failure types of origami structures based on Cross-Laminated Timber, a triangular reinforcement scheme was chosen to increase the height of the structure. Finally, a new connection method was developed that allowed the origami structure to be practically applied. This research demonstrates the possibility of developing a timber structure based on Yoshimura origami.