Instability-Induced Origami Design by Topology Optimization

Instability-induced wrinkle patterns of thin sheets are ubiquitous in nature, which often result in origami-like patterns that provide inspiration for the engineering of origami designs. Inspired by instability-induced origami patterns, we propose a computational origami design method based on the nonlinear analysis of loaded thin sheets and topology optimization. The bar-and-hinge model is employed for the nonlinear structural analysis, added with a displacement perturbation strategy to initiate out-of-plane buckling. Borrowing ideas from topology optimization, a continuous crease indicator is introduced as the design variable to indicate the state of a crease, which is penalized by power functions to establish the mapping relationships between the crease indicator and hinge properties. Minimizing the structural strain energy with a crease length constraint, we are able to evolve a thin sheet into an origami structure with an optimized crease pattern. Two examples with different initial setups are illustrated, demonstrating the effectiveness and feasibility of the method.