# Dragonfly-Inspired 3D Bionic Folding Grid Structure Design
## 4 Structural Design Application  
Dragonfly wing structure is an efficient structure form, so this paper explores the combination of the genetic algorithm (GA) and the above simulation of the dragonfly wing 3D grid structure generation process applied to the bionic optimization design of the loaded structure. The whole process is shown in Figure 16. Step 1: branch structure is generated by taking the location of branch points and the direction vector of branches as parameters; step 2: centroid Voronoi grid is generated by taking the area of grid units as parameters; step 3: folding angle \(\theta\) and ratio of the section radius of the branch structure to the section radius of Voronoi grid R: r is used as the parameter to generate the folding grid structure; and step 4: analyze and optimize the structure. Table 1 shows the basic parameters of the material: elastic modulus (E1, E2, and E3), shear modulus (G12, G13, and G23), and [PERSON]'s ratio (v12 = v13 = 0.33). The load and support conditions of the two-dimensional plane design domain are shown in Figure 17a, the aspect ratio of the domain c:h = 1:5 and the load P = 1. Figure 17b shows the optimized grid structure of the two-dimensional design domain, the folds in the structure are shown in Figure 17c, and the ratio of the section radius R of the branch structure to r of the filled grid is 5:1. As shown in Figure 18, under the same load and support conditions, compared with the quadrilateral grid structure, the buckling load of the folded bionic dragonfly vein structure is 11% higher, and the buckling load is mainly borne by the branch structure. The filling grid structure can increase the first-order modal frequency of the whole structure by 2.6 times, which has a similar effect to the flexible structure. The grid structure simulating a dragonfly's wing has the effect of rigid and flexible coupling structure. \begin{table}
\begin{tabular}{c c} \hline \hline
**Material Parameters** & \\ \hline E1 [N/mm\({}^{2}\)] & 134,000 \\ E2 = E3 & 7900 \\ G12 = G13 [N/mm\({}^{2}\)] & 4620 \\ G23 & 3200 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters. Figure 16: Biomimetic grid structure design application process. The load and support conditions of ellipsoidal domain under distributed loading are shown in Figure 19a. Figure 19b shows the optimized grid structure in the design domain of the ellipsoidal surface, and almost no folding. The ratio of section radius R of the branch structure to that of the filled grid is 3:1. As shown in Figure 20, 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 by 1.7 times, and the first-order modal frequency of the structure increases by 1.3 times. Figure 17: Design of 2D cantilever thin plate grid structure: (**a**) One end is fixed, and the other end is applied a load P. (**b**) The cross-section structure obtained by simulating dragonfly wing vein, R is the radius of branch structure, r is the radius of filling grid. (**c**) The branch structure near Section 1 divides the region into five parts, and the generated fold structure is a corrugated structure with symmetry. Although the branch structure near Section 2 is increased, the overall fold pattern is similar to that near Section 1, and the folds near Section 3 are much gentler than those near Sections 1 and 2. Figure 19: Elliptic design domain: (**a**) ellipsoidal domain under a distributed loading; (**b**) the branch structure similar to the leaf vein is generated, and the branch nodes are staggered, which can reduce the stress of the nodes, the section radius R of the branch structure to the filled grid r is 3:1. Figure 18: The bionic vein grid structure is compared with the quadrilateral grid structure. The results show that the weight difference between the two structures is less than 3%, under the same load and support conditions.