# Dragonfly-Inspired 3D Bionic Folding Grid Structure Design
## 3 Generate a 3D Model of Dragonfly Wing  
The process of generating a dragonfly fold grid structure by using the above method is shown in Figure 9. Since the real dragonfly vein is a curve, it is necessary to turn the branch line into a curve. The transformation method is to regard the branch line as an elastic line with fixed end points, define a group of normal phase vectors on the branch line, and the curve will deform along these vectors. By adjusting the position and direction of the normal phase vector, the curve will gradually approach the shape of the real wing vein curve. Figure 8: In the process of a plane grid structure changing into a fold grid structure: (**a**) in order to quickly make the grid structure reach a balanced and stable state in the folding process, the gravity direction load is increased at the nodes; and (**b**) the section diagram of the folded grid structure. The dragonfly wings in Figure 9c are divided into many different areas, and the centroid Voronoi grid is filled in these areas, as shown in Figure 10. The finally generated two-dimensional wing grid structure is shown in Figure 10d. The whole structure contains 354 polygonal grid units, among which triangles account for 1.4%, quadrilateral for 12.15%, pentagonal and hexagon for 30.23%, and 56.21%. During the generation of the dragonfly wing grid structure fold, the average load gave obtained from Equation 3 is added to the node, as shown in Figure 11. The forewing two-dimensional model generated in Figure 12 has 13 main veins, which are divided into six Mountain lines (M) and seven Valley lines (V). According to the divided M-V folding lines, the fold structure is generated, as shown in Figure 12e. After the definition of folding lines, the forewing model prepares to generate the fold structure. The folding process continues until the entire grid structure reaches a stable state, and the grid structure in this state is the final forewing three-dimensional model, as shown in Figure 13a. Folding structures in different regions have different forms. There is a large amount of filling grid between the two folding lines in Figure 13c, so the fold change in this area is not as obvious as that in Figure 13b. Figure 14 shows the cross-section of the forewing 3D model. The simpler the grid units on both sides of the fold line, the more obvious the fold is, otherwise, the grid structure is more flattened. The three-dimensional forewing model generated in this paper for finite element analysis is shown in Figure 15. The weight of the dragonfly is \(m=865.3\) mg, the wing area is \(A_{f}=713.32\) mm\({}^{2}\), and the average load on the wing surface is \(q_{ave}\), \(q_{ave}=\frac{mg}{A_{f}}=1.21\) Pa.  
Figure 9: To generate the dragonfly vein, (**a**) divides the wing into different regions with the vein line generated by the above method, and the red dot is the starting point for generating the branch structure; (**b**) adds the normal phase vector offset to the straight vein line and turns it into a curve form; and (**c**) adjusts the position and direction of the normal phase vector to make the vein line close to the real vein form. Figure 11: The average load obtained from Equation 3 is added to the node, and the red arrow is the direction of the load distribution: (**a**) near the wing root region; and (**b**) near the edge region. Figure 12: The process of forewing model folding structure: (**a**) The wing veins are defined as folding lines: M = 6, V = 7. (**b**) After the definition of the folding line is completed, the folding begins, the deformation force generated by the folding is small, and the grid structure is still in a two-dimensional stable state. (**c**) During the folding process, the folding force increased and the folds became obvious. Although the grid structure at this time became similar to the grid structure of dragonfly wings, the structure did not reach the final stable state.