Geometry Optimization of a Highly Flexible Gradient Metamaterial Structure Using a Differential Evolution Algorithm

Gradient structures can offer great flexibility in parameter tuning, enabling the achievement of tailored mechanical properties for specific applications, and can even outperform their uniform counterparts. However, the design of such complex structures can be challenging, especially when many tunable geometric parameters are involved. To address this challenge, a simplified model that captures the main attributes and behavior of the structure can be employed. In this approach, a reduced number of parameters are optimized, while the remaining parameters are treated as constants throughout the structure. This also reduces the computational demands for simulating the structure with each iteration, thus accelerating the overall optimization process. A method for the geometry optimization of a highly flexible gradient metamaterial structure for the skin of a morphing aircraft wing's leading edge is proposed, utilizing a differential evolution algorithm. Initially, the basics of evolutionary algorithms and their representative, differential evolution, are introduced. Then, the flexible metamaterial skin with gradient bending stiffness, its simplified spring model, and the set of parameters for optimization are presented. Finally, the geometry parameters and the required acting loads are optimized using DE to achieve various deformed shapes that correspond to the morphing wing leading edge at different flight stages. Three levels of complexity of the optimized model are explored: a foundational version suitable for algorithm parameter tuning, an intermediate version for the optimization of geometric parameters and loading for one target shape, and an advanced version aimed at achieving multiple morphing shapes under different loading conditions.