A gradient-evolutionary coupled topology optimization for sheet reinforcement based on the mechanics of Voronoi pattern on dragonfly wings

The intricate network of veins on dragonfly wings has captured the attention of many researchers due to its fascinating configuration and excellent mechanical properties. In this paper, based on the observation of the layout of the vein domains on the hind wing of dragonfly, the types of domains were characterized from the aspects of area and shape. The numerical analysis revealed that different shaped domains enhance either stiffness or vibration stability of the wing. According to this feature, a multi-objective gradient optimization algorithm based on stiffness, mass transport efficiency and first order frequency was proposed. Associated by the size constraints, the optimal layout of the venation was obtained and subsequently used to generate the Voronoi patterns, whose positions and shapes could be further optimized by an evolutionary algorithm to match the mechanical analysis results. The effectiveness of this multi-cellular configuration was verified by testing the bending and vibration stability of the additive manufactured model. The aerodynamic simulation analysis of this flapping wing structure was also investigated. This study has important implications for understanding the evolutionary mechanisms of venation on biological wings and designing reinforcement for sheets.