Design of Elastic Wind Tunnel Models via Level-Set Topology Optimization of Eigenvalue Ratios and Compliance

This paper presents a novel level-set-based topology optimization framework for designing elastic wind tunnel models that accurately replicate the static and dynamic characteristics of full-scale aircraft structures. In aeroelastic wind tunnel testing, scaling laws require the reduced-scale model to match the mass and stiffness distributions of the full-scale target; however, achieving these simultaneous requirements with traditional structural design methods is challenging. To address this, we propose a topology optimization method that optimizes the internal structure of the model to match target eigenvalue ratios and a reduced-order compliance matrix. The proposed framework employs a conforming mesh approach to ensure high-fidelity structural analysis and integrates a hybrid computational scheme using JAX for automatic differentiation and MSC Nastran for robust eigenvalue analysis. To ensure manufacturability via additive manufacturing (3D printing), penalty functions for overhang angles and sharp edges are introduced. The method is applied to the design of a high-aspect-ratio wing model using PLA material. Numerical results demonstrate that the optimized structure achieves a high degree of similarity to the target model, with a reduced compliance matrix similarity exceeding 99.9\% and minimal deviation in lower-order natural frequencies, while satisfying manufacturing constraints. The study validates the effectiveness of the proposed framework in automating the design of complex aeroelastic models.