Multi-body dynamical modeling and prediction of flexible origami/kirigami structures by affine transformation

Abstract

A generalized multi-body dynamical modeling method of Origami/Kirigami structures considering the elastic–flexible coupling of surfaces and nonlinear creases is proposed. For different structures with complex spatial configuration and constraints, an Affine Transformation (AT) technique based on Absolute Nodal Coordinate Formulation (ANCF) is proposed to make the modeling more convenient and efficient. The surfaces are discretized by triangle reduced elements, and the constitutive relations of creases are described by nonlinear state-dependent torque constraints. The proof of the topological invariance of configurations is also given. The simulation of the folding capacity and dynamic behaviors on two Origami structures, Origami solar array mechanism, and enclosed Yoshimura Origami, are given, which verifies the effectiveness of the modeling method. Additionally, the quantitative dynamic behaviors contributes to the design principle of a Kirigami structure for multi-stability. Comparisons between theoretical results from modeling and experiments demonstrate the effectiveness of the modeling method and crease design. The AT-ANCF lays a theoretical foundation for dynamic prediction and design for large deformation Origami/ Kirigami structures, which has significant potential applications in dynamic properties design in the fields of aerospace, robotic etc.