Some types of rigid origami possess specific geometric properties. They have a single degree of freedom, and can experience large configuration changes without cut or being stretched. This study presents a numerical analysis and finite element simulation on the folding behavior of deployable origami structures. Equivalent pin-jointed structures were established, and a Jacobian matrix was formed to constrain the internal mechanisms in each rigid plane. A nonlinear iterative algorithm was formulated for predicting the folding behavior. The augmented compatibility matrix was updated at each step for correcting the incompatible strains. Subsequently, finite element simulations on the deployable origami structures were carried out. Specifically, two types of generalized deployable origami structures combined by basic parts were studied, with some key parameters considered. It is concluded that, compared with the theoretical values, both the solutions obtained by the nonlinear algorithm and finite element analysis are in good agreement, the proposed method can well predict the folding behavior of the origami structures, and the error of the numerical results increases with the increase of the primary angle.
Extended framework of Hamilton’s principle for single-degree-of-freedom nonlinear damping systems
