Simulation of Dynamics During Deployment of Foldable Origami Structures

Abstract

Foldable origami-based structures are a type of deployable structures that are increasingly applied in the space and building industries. When folded, the small size of such structures facilitates transportation and storage. Meanwhile, the properties of their larger deployed state may be of interest to different applications. A stable working condition is established by locking the structure in its deployed state, as in the process of deployment, the driving forces may generate a dynamic effect, thus leading to instability of the system. Hence, the study of dynamic characteristics of such structures, including trajectory, duration, velocity, and acceleration is of paramount importance. In this paper, based on the general dynamic equation and Lagrange’s equations of the first kind, the finite element method is adopted to investigate the dynamic deployment of foldable plate structures in terms of the generalized nodal coordinates. The proposed geometric description of a quadrilateral plate element is based on a folding plate composed of refined triangular elements, which are used to approximate the real shells in the structure. Subsequently, a MATLAB framework is developed on the basis of the element using the Newmark integration and the Newton–Raphson iteration method to simulate the deployment process of the structure. Comparisons between MATLAB results and ADAMS results verify the reliability of the framework in analyzing the dynamic deployment of the foldable origami-based structures with sufficient accuracy.