Equilibrium path and stability analysis of rigid origami using energy minimization of frame model

Abstract

This paper presents a method of equilibrium path analysis and stability analysis of an equilibrium state for a rigid origami, which consists of rigid flat faces connected by straight crease lines (folding lines) and can be folded and unfolded without deformation of its faces. This property is well suited to the application to deployable structures and morphing building envelopes consisting of stiff panels. In this study, a frame model which consists of hinges and rigid frame members is used to model the kinematics of a rigid origami. Faces and crease lines of a rigid origami are represented by frame members and hinges, respectively. External loads are applied to the nodes of a frame model, and the displacements of some nodes are fixed. Small rotational stiffness proportional to the length of a crease line is assumed in each hinge to uniquely determine the equilibrium state, which is obtained by solving the optimization problem for minimizing the total potential energy under the conditions so that the displacements of the nodes and the members are compatible. The optimization problem is solved by the augmented Lagrangian method, and the positive definiteness of the Hessian of the augmented Lagrangian is investigated to determine the stability of the equilibrium state. Equilibrium path analyses are carried out and bifurcations of the equilibrium paths are investigated for examples with waterbomb patterns.

Analytical and Numerical Investigation of Second-Order Infinitesimal Mechanism in Rigid Origami

“…To evaluate the results of the infinitesimal mechanism analysis described above, a large deformation analysis is carried out, and the obtained folding path is investigated with respect to the transition of the coefficients of the infinitesimal mechanism modes. In this study, for the large deformation analysis, the frame model [38,39] consisting of frame members and hinges is used in the general-purpose finite element analysis software Abaqus 2022 [45]. Fig.…”

“…In addition, finite deformation paths are generated by large deformation analysis of the frame model shown in Fig. 1(c), which consists of frame members and hinges and is suitable for analysis using general-purpose finite element analysis software [38,39]. By using the frame model, we can easily assign small rotation stiffness to the hinges, and this stiffness stabilizes the convergence process at each step in the large deformation analysis.…”