Biomimetic Research for Folding Unfolding Manners

本项目对角木、山毛榉、普通桤木和银等有规则波纹的单叶从芽到完全展开的叶片展开模式进行了观察。在此基础上，本文建立了一系列不同叶脉角度的数值模型，研究了叶脉角度对波纹状叶片展开方式的影响。利用矢量分析和坐标变换，对波纹状叶片展开过程进行了数值模拟。在展开过程中的运动能量也估计检查静脉角，α和折痕间隔比，α * 的影响（= α_2/α_1，α_1为谷折痕到峰折痕的距离，α_2为峰折痕到谷折痕的距离），从模拟结果来看，大α值（如75 °或85 °）的叶片比小α值（如30 °或45 °）的叶片折叠得更紧凑。 ...更多信息 A建议。然而，可以认为具有小α的叶比具有大α的叶更有利。因为，α小的叶片在展开初期可以保持相对较大的叶面积。此外，叶片完全展开所需的总能量随着α的增加而增加。这意味着小的α可能比大的α更有利于波纹叶。常见的山毛榉、角木和常见的桤木具有波纹状的叶子，其最大的α为30厘米至50厘米。从展开方式的考虑，如完全折叠的叶片的几何特性、展开过程中的叶面积和完全展开所消耗的能量，这似乎是一个相当合适的选择。角木的叶片具有α * = 1.0，并且展开时保持平坦的形状。而α * = 1.4的普通桤木叶片呈V型展开。虽然总动能在α * * 1.0和α * = 1.4的叶片中不改变，但α * 1.0的折叠模式具有很大的优势，即相对厚的脉不会彼此重叠。少

In this project, the unfolding pattern of regularly corrugated simple leaves such as hornbeam, beech, common alder and silver birch leaves were observed from buds to fully unfolded leaves. Based on these observations, a number of numerical models with various vein angles were considered to investigate the effect of vein angles on the unfolding manner of a corrugated leaf. By using vector analysis and transformation of coordinates, the unfolding of a corrugated leaf was simulated. The kinematic energy during unfolding of leaves was also estimated to examine the effects of vein angle, alpha, and crease interval ratio, alpha*(= alpha_2/alpha_1, alpha_1 the distance from a valley crease to a crest crease, alpha_2 the distance from a crest crease to a valley crease), on the unfolding manners.From the simulation, the leaf with large alpha such as 75ﾟ or 85ﾟ can be folded more compactly than that with small alpha like 30ﾟ or 45ﾟ, From the geometry of leaves fully folded, therefore, large alph … More a are recommended. From the leaf are a during unfolding, however, it can be considered that the leaf with small alpha is more favorable than that with large alpha. Because, the leaf with small alpha can keep relatively large leaf area in the early stage of unfolding. In addition, the whole energy required for the fully unfolding leaves increases with the increase of alpha. This means that small alpha may be more advantageous for corrugated leaves than large alpha. Common beech, hornbeam and common alder have corrugated leaves whose most alpha are 30ﾟ- 50ﾟ. This appears to be a quite adequate choice from thinking about unfolding manner such as the geometrical properties of fully folded leaf, the leaf area during unfolding and energy consumed by full open of leaves.The leaf of hornbeam has alpha* = 1.0 and unfolds keeping a flat shape. On the other hand, the leaves of common alder with alpha* = 1.4 unfold with V-shape. Although total kinetic energy does not change in leaves with alpha* * 1.0 and alpha* = 1.4, the folding pattern with alpha* 1.0 has a big advantage, i.e. the relatively thick veins do not overlap each other. Less