Dimensional Synthesis of Urban Air Mobility Deployable Wings via Spectral Surrogate Modeling

The rapid evolution of Urban Air Mobility (UAM) necessitates high-performance morphing structures capable of seamless transitions between flight and ground modes. This research presents a rigorous structural optimization framework for a wing deployment mechanism, addressing the critical challenge of minimizing stress concentrations in cantilevered revolute joints. To overcome the computational prohibitive cost of traditional multibody dynamics, a Generalized Spectral Surrogate Model (GSSM) is introduced. This novel approach maps the mechanism’s geometric parameters to its kinetic response using polynomial-modulated Fourier series, reducing the evaluation time of 105 design configurations from 4.2 h to merely 0.8 s while maintaining a determination coefficient R2>0.995. Comparative analysis demonstrates that the GSSM outperforms Artificial Neural Networks and Kriging models in capturing periodic kinematic boundaries without spurious local minima. Through a weighted topological analysis, the study identifies a global optimum (L2=0.5 m, θ2=64.2∘) that effectively shunts 70.3% of the aerodynamic load to the robust vehicle chassis. The proposed solution deviates from the theoretical unconstrained minimum by only 0.24%, providing a validated mathematical basis for the rapid synthesis of reliable aerospace mechanisms.