Nonlinear dynamics analysis of origami structures based on the bar hinge model

Existing origami folding and deployment approaches focus on static and kinematic analysis, while nonlinear dynamic folding and deployment remain unexplored. In this study, we present a nonlinear dynamics approach that uses the Lagrangian method in order to analyze the origami structures, treating a nodal coordinate vector as a variable. The proposed approach investigates the nonlinear folding and deployment mechanisms of origami structures using the zero-thickness bar hinge model with the finite element method. The method is applicable to general rigid and non-rigid origami structures, regardless of whether they have a single degree of freedom or multiple degrees of freedom. The proposed method is employed to compute the large displacements and deformations of the origami structures, conduct energy analysis, and compute the inner forces generated during the analysis of structures under varying loads and boundary constraints. Examples of rigid and non-rigid origami structures include a simple fold origami structure, a large-scale Miura origami structure, and a Kreslin structure. The results demonstrate the successful acquisition of dynamic characteristics during analysis, and the numerical accuracy of the proposed method is validated by simulating the virtual truss prototype of the structure using the multi-body dynamic software ADAMS. The comparison of the outcomes demonstrates the accuracy and efficiency of the proposed method. Furthermore, the parametric analyses of the structures are carried out to explore the impact of the geometric parameters on deployment behaviors. The nonlinear dynamic folding analysis reveals the origami structure's dynamic response under varying geometric and dynamic parameters.