基于旋转对称单元的六折痕折纸结构折痕创新研究

【作者】 陈耀； 严嘉怡； 李佳强； 冯健；

【机构】 东南大学土木工程学院国家预应力工程研究中心；

【摘要】 目前,折纸应用研究主要聚焦于Miura、Waterbomb及Kresling折纸,Waterbomb折纸因其双稳态、拓扑规整简洁等特性被成功应用于耗能构件、可折叠帆板等。为了探求更具一般性六折痕折纸的平面可折叠性,本文降低了Waterbomb折纸基本单元的对称性,基于该类折纸的几何拓扑方式,提出了一种新型旋转对称（C₂对称）基本单元。根据折纸单元的平面可折叠条件,建立折纸顶点的几何约束方程组,通过图解法及MATLAB优化工具箱算法,求解折纸单元内部可平折点坐标,得到了基本单元为C₂对称型单元的Waterbomb衍生折纸的折痕模式。这种折痕创新设计方法适用于任意已知的C₂对称型矩形单元和六边形单元。更多还原

【Abstract】 Waterbomb origami technology is widely used in deployable structures such as folding roofs and large solar panels due to its bistability and simple topology. Its basic elements are mainly axisymmetric rectangular elements or axisymmetric hexagonal elements derived from rectangular elements. This axisymmetric basic unit makes waterbomb origami meet the requirements of symmetrical folding, and it folds with a single degree of freedom, which limits the diversity of origami structure. At present, the research on the application of Waterbomb origami technology mainly focuses on the traditional Waterbomb origami whose basic unit is the axisymmetric figure. In order to explore the foldability of Waterbomb origami with more general basic unit, this paper reduces the symmetry of the traditional Waterbomb origami basic unit. Based on the topology of Waterbomb origami, a C₂ symmetrical basic unit is proposed according to the folding condition of origami unit. Based on MATLAB platform, using graphic method and PSO algorithm, we get the crease pattern derived from Waterbomb origami whose basic unit is C₂ symmetrical basic unit. This innovative design method is suitable for any known C₂ symmetric rectangular unit and C₂ symmetric hexagonal unit.更多还原