Lightweight Structures and the Geometric Equilibrium in Dragonfly Wings

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.