# Dragonfly-Inspired 3D Bionic Folding Grid Structure Design
## 4 Structural Design Application
The fold becomes complicated due to the increase in branches near Section 2, and the folds of Section 3 away from the constrained end become uniform. The whole branch structure is distributed in a spiral pattern. Figure 22: Comparing the bionic vein grid structure with the quadrilateral grid structure, the weight difference between the two structures is less than 5%, 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 52%, and the first-order modal frequency of the structure increases by 39.3%. (**a**) Bionic vein grid structure buckles; (**b**) quadrilateral grid structure buckles; (**c**) bionic vein grid structure first-order mode; and (**d**) quadrilateral grid structure first-order mode. Through the simulation of the dragonfly wing grid structure application design process, it can be found that the direction of branch structure generation is from the constraint end to the loading position. The form of the branch structure determines the shape of the filling grid, and the fold form of the grid structure is basically determined. In the initial design state, when the ratio of the section radius of the branch structure to the filling grid radius is 1, the section radius of the branch and filling grid is relatively small, and the grid fold depth is maximum at this time. As the ratio increases from 1 to 2, the fold depth changes significantly; when the ratio exceeds 2, the fold depth significantly decreases, and the fold filling grid basically reaches the stable state, as shown in Figure 25. When the radius ratio is greater than 2, the mechanical properties of the structure can be improved by adjusting the ratio of the radius of the branch structure to the radius of the filled grid, as well as the change in the depth of the small fold, as shown in Figure 16:0 Due to the limitation of the design area, the radius of the branch structure cannot be increased  
Figure 16:1 Design domain of the airfoil surface: (**a**) airfoil design domain; (**b**) the wing surface grid structure of biomimetic dragonfly wing veins; and (**c**) section diagram of curved grid structure of biomimetic dragonfly wing vein, where R is the radius of main structure and r is the radius of filling grid. The branch structure near the root of Section 1 is simple and the fold depth is larger. With the increase in the branch structure and filling grid near Section 2, the fold becomes complicated and the fold depth is close to that near Section 1. The fold depth decreases near Section 3.  
indefinitely, so when the radius ratio exceeds a certain value, the radius of the filled grid will become small, and the fold depth will also decrease, then the structural performance will decline. Therefore, appropriate radius ratio and structure depth can work together to obtain the best mechanical properties of the spatial grid structure. Figure 16:2 The comparison between the bionic vein grid structure and quadrilateral grid structure shows that the weight difference between the two structures is less than 5%, 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: (**a**) the buckling of the biomimetic vein grid structure mainly occurs in the filled grid; (**b**) quadrilateral grid structure buckling; (**c**) simulates the first-order mode of vein grid structure; and (**d**) quadrilateral grid structure. Figure 16:3 Change in maximum depth of fold. In the initial state, the ratio between the radius of the main structure and the radius of the filled grid is 1, the radius of the section is the smallest, and the fold depth is the largest at this time. As the proportion of the radius gradually increases, the fold depth also decreases.