Concurrent topology and geometry optimization of origami structures via strain energy minimization

Le résumé fourni par la source

Abstract Origami with programmable mechanical responses has emerged as an important topic in mechanics and materials research. Its geometric design space offers substantial tunability in stiffness, stability and deformation modes. However, the design of origami structures, especially non-rigid ones, remains a formidable challenge. Inspired by the self-organization of thin sheets into stable, low-energy origami configurations in nature, this paper proposes a unified optimization framework for rigid and non-rigid origami patterns via concurrent topology and geometry optimization. The framework uses the nonlinear bar-and-hinge model, which represents panel bending and crease folding within a unified hinge constitutive model. Consequently, topology optimization is achieved by switching between bending and folding hinges. Meanwhile, geometry optimization is achieved by adjusting the locations of origami vertices. Sensitivity analysis is carried out to enable the use of efficient gradient-based algorithms. Several numerical examples are provided, including the reproduction of origami bases, the Miura-ori and the Kresling tube, representing both rigid and non-rigid origami patterns. These examples demonstrate the effectiveness and versatility of the proposed method, highlighting its potential for mechanically efficient and innovative origami design.

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