Lightweight Structures and the Geometric Equilibrium in Dragonfly Wings
Lightweight Structures and the Geometric Equilibrium in Dragonfly Wings
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发表时间：
2021
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通讯作者：
S. Behnejad;G. Parke;O. Samavati;Hao Zheng;Márton HABLICSEKb;Masoud AKBARZADEHa
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作者：
S. Behnejad;G. Parke;O. Samavati;Hao Zheng;Márton HABLICSEKb;Masoud AKBARZADEHa
本研究探讨使用图形静力学在分析结构几何的自然现象，以了解其性能和相关的设计参数。大自然一直是设计师、工程师和科学家灵感的源泉。自然界中的结构系统不断地进化，以优化其边界条件。这种优化遵循某些设计规则，这些规则对于人类制定甚至理解都是相当具有挑战性的。机翼是一种高性能、轻质结构的例子，吸引了许多研究人员研究其几何形状和性能，作为自然界设计的最轻的结构之一。有大量的几何和分析研究的模式，机翼，但基本的设计逻辑是不清楚的。机翼内部构件的几何形状主要由凸单元组成，凸单元可以表示2D平面上的仅压缩网络。然而，这一属性还没有从这个角度进行几何分析，以证实这一假设。在本研究中，我们使用二维图形静力学的方法，从给定的机翼结构几何构造力图。我们使用代数和迭代的方法来报告的拓扑和几何性质的形式和力图，如网络的不确定度。对于样品机翼，我们分离内部和边界边缘，构建力图，最后重建结构形式。使用力图的边长将重构网络的力的大小与机翼的实际结构进行比较，将揭示结构的性能。将提供多项分析研究，以比较合成和天然网络的结果，并得出可靠的结论。利用图解静力学在预测自然结构模式中的力流方面的成功将扩大这些强有力的方法在许多工程和科学问题中用于再现自然结构系统的相似几何形状方面的用途。它也将最终帮助我们理解设计参数和边界条件，大自然创造了它的杰作。
This research investigates the use of graphic statics in analyzing the structural geometry of a natural phenomenon to understand its performance and its relevant design parameters. Nature has always been the source of inspiration for designers, engineers, and scientists. Structural systems in nature are constantly evolving to optimize themselves with their boundary conditions. This optimization follows certain design rules that are quite challenging for a human to formulate or even comprehend. A dragonfly wing is an instance of a high-performance, lightweight structure that has intrigued many researchers to investigate its geometry and its performance as one of the most light-weight structures designed by nature. There are extensive geometrical and analytical studies on the pattern of the wing, but the underlying design logic is not clear. The geometry of the internal members of the dragonfly wings mainly consists of convex cell which may represent a compression-only network on a 2D plane. However, this property has not been geometrically analyzed from this perspective to confirm the hypothesis. In this research, we use the methods of 2D graphic statics to construct the force diagram from the given structural geometry of the wing. We use algebraic and iterative methods to report the topological and geometric properties of the form and force diagrams such as the degrees of indeterminacies of the network. For sample wings, we separate the internal and the boundary edges, construct the force diagram, and finally reconstruct the structural forms. Comparing the magnitude of the forces of the reconstructed network with the actual structure of the wing using the edge lengths of the force diagram will shed light on the performance of the structure. Multiple analytical studies will be provided to compare the results in both synthetic and natural networks and drive solid conclusions. The success in predicting the force flow in the natural structural pattern using graphic statics will expand the use of these powerful methods in reproducing the similar geometry of the natural structural system for the use in many engineering and scientific problems. It will also ultimately help us understand the design parameters and boundary conditions for which nature produces its master-pieces.