Song Keyao, Zhou Xiang, Zang Shixi, Wang Hai, You Zhong
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, No. 800 Dongchuan Road, Shanghai 200240, People's Republic of China.
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX3 0PL, UK.
Proc Math Phys Eng Sci. 2017 Apr;473(2200):20170016. doi: 10.1098/rspa.2017.0016. Epub 2017 Apr 12.
This paper presents a mathematical framework for the design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns that can simultaneously fit two target surfaces with rotational symmetry about a common axis. The geometric parameters of the crease pattern and the folding angles of the target folded state are determined through a set of combined geometric and constraint equations. An algorithm to simulate the folding motion of the designed crease pattern is provided. Furthermore, the conditions and procedures to design folded ring structures that are both developable and flat-foldable and stacked folded structures consisting of two layers that can fold independently or compatibly are discussed. The proposed framework has potential applications in designing engineering doubly curved structures such as deployable domes and folded cores for doubly curved sandwich structures on the aircraft.
本文提出了一种基于梯形折痕图案设计刚性可折叠双曲折纸镶嵌的数学框架，该框架能够同时贴合两个关于公共轴具有旋转对称性的目标曲面。通过一组组合的几何方程和约束方程确定折痕图案的几何参数以及目标折叠状态的折叠角度。提供了一种模拟所设计折痕图案折叠运动的算法。此外，还讨论了设计既可展又可平折的折叠环结构以及由两层组成的可独立或兼容折叠的堆叠折叠结构的条件和步骤。所提出的框架在设计工程双曲结构方面具有潜在应用，例如飞机上双曲夹层结构的可展开穹顶和折叠芯。
