# Dragonfly-Inspired 3D Bionic Folding Grid Structure Design
## 4 Structural Design Application
Compared with the quadrilateral grid structure, the buckling load of the grid structure biomimetic dragonfly wing vein increases 11%, and the first-order modal frequency of the structure increases by 2.6 times: (**a**) buckling of biomimetic vein grid structure; (**b**) buckling of quadrilateral grid structure; (**c**) the first mode of biomimetic vein grid structure; and (**d**) the first mode of quadrilateral grid structure. Different from the plane design domain, the beam elements obtained in the elliptic design domain mainly bear axial loads, and from the obtained grid structure, it can be seen that there are no obvious folds like the grid structure mainly bearing bending loads, as shown in Figure 19. Therefore, whether the grid structure needs to be strengthened by folding is related to the angle between the axial direction of the beam element and the load direction. In general, by combining the branching structure, the Voronoi grid and folding method can simulate the three-dimensional fold structure of the dragonfly wing. When the structure mainly suffers from torsion and bending deformation, the structure will improve its resistance to torsion and bending by generating a fold structure. The load and support conditions in the design domain of the thin-walled shell are shown in Figure 21a, the ratio of section radius to length r:h = 1:10, and the load P = 1. Figure 21b shows the optimized grid structure in the design domain of the airfoil surface, and the folding in the structure is shown in Figure 21c. The ratio of section radius R of the branch structure to that of the filled grid is 3:1. As can be seen from Figure 21, the entire structure is wrapped around the thin-walled shell. As shown in Figure 22, under the same load and support conditions, compared with the quadrilateral grid structure, the buckling load of the folded grid structure biomimetic dragonfly wing vein increases by 1.5 times, and the first-order modal frequency of the structure increases by 1.4 times. The load and support conditions in the design domain of the airfoil surface are shown in Figure 23a, the chord to length ratio ch = 1:5, and the load P = 1. Figure 23b is the optimized grid structure in the design domain of the airfoil surface, and the folding in the structure is shown in Figure 23c. The ratio of the section radius R of the branch structure to that of the filled grid r is 3:1. The whole structure is wrapped around the surface of the wing like a rattan man. As shown in Figure 24, under the same load and support conditions, compared with the quadrilateral grid structure, the buckling load of the folded bionic dragonfly vein structure is nearly four times higher, and the buckling load is mainly borne by the branch structure. The filling grid structure increases the first-order modal frequency of the whole structure by 1.8 times. This grid structure design structure by simulating a dragonfly's wing veins can provide a new idea for the design of airfoil structure. Figure 20: Comparing the bionic vein grid structure with the quadrilateral grid structure, the weight difference between the two structures is less than 4%, under the same load and support conditions. Compared with the quadrilateral grid structure, the buckling load of the grid structure biomimetic dragonfly wing vein increases 74.2%, and the first-order modal frequency of the structure increases by 32%: (**a**) bionic vein grid structure; (**b**) quadrilateral grid structure buckles; (**c**) bionic vein grid structure first-order mode; and (**d**) quadrilateral grid structure first-order mode. Figure 21: Design domain of the thin-walled shell. (**a**) Thin-walled cylinder design domain; (**b**) thin-walled cylinder grid structure of biomimetic dragonfly wing veins; and (**c**) cross-section diagram of thin-walled cylinder grid structure of biomimetic dragonfly wing vein in which R is the radius of main structure and r is the radius of filling grid. The branch structure near Section 1 of the constrained end is densely distributed, and the folds are relatively deep.