期刊
JOURNAL OF MECHANICAL DESIGN
卷 143, 期 1, 页码 -出版社
ASME
DOI: 10.1115/1.4047437
关键词
origami; flat-foldability; particle swarm optimization; graph theory; periodicity; folding; computational geometry; computational kinematics; computer-aided design; design automation; design optimization; kinematics; smart materials and structures
资金
- National Natural Science Foundation of China [51978150, 51850410513]
- Southeast University Zhongying Young Scholars Project
- Fundamental Research Funds for the Central Universities
- Alexander von Humboldt-Foundation
This study uses geometric-graph-theoretic representation of flat-foldable origami tessellations and proposes an optimization framework for developing flat-foldable origami patterns with four-fold vertices. The effectiveness and feasibility of this method have been verified with several origami patterns, showcasing that it is more efficient and cost-saving compared to traditional analytical approaches and genetic algorithms.
Flat-foldable origami tessellations are periodic geometric designs that can be transformed from an initial configuration into a flat-folded state. There is growing interest in such tessellations, as they have inspired many innovations in various fields of science and engineering, including deployable structures, biomedical devices, robotics, and mechanical metamaterials. Although a range of origami design methods have been developed to generate such fold patterns, some non-trivial periodic variations involve geometric design challenges, the analytical solutions to which are too difficult. To enhance the design methods of such cases, this study first adopts a geometric-graph-theoretic representation of origami tessellations, where the flat-foldability constraints for the boundary vertices are considered. Subsequently, an optimization framework is proposed for developing flat-foldable origami patterns with four-fold (i.e., degree-4) vertices, where the boundaries of the unit fragment are given in advance. A metaheuristic using particle swarm optimization (PSO) is adopted for finding optimal solutions. Several origami patterns are studied to verify the feasibility and effectiveness of the proposed design method. It will be shown that in comparison with the analytical approach and genetic algorithms (GAs), the presented method can find both trivial and non-trivial flat-foldable solutions with considerably less effort and computational cost. Non-trivial flat-foldable patterns show different and interesting folding behaviors and enrich origami design.
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