Aerodynamics-driven topology optimization of compliant airfoils considering stability

Abstract

Airfoil structures optimized solely for stiffness can suffer from buckling instabilities under realistic aerodynamic loads. We present the first topology optimization framework to improve the stability of aerodynamic structures. For a clear representation of structure, this work employs the topology optimization of binary structures with geometry trimming. Reynolds-averaged Navier-Stokes turbulence model is employed to accurately predict the turbulent aerodynamic loading under realistic flight conditions. Fluid–structure interaction and buckling analysis are conducted using an elastic formulation with geometrical nonlinearities to allow for large deformations. The numerical model system is solved through the finite element method and the Arbitrary Lagrangian-Eulerian method is applied. The sensitivities are calculated using semi-automatic differentiation and interpolated to the optimization mesh. Kreisselmeier-Steinhauser aggregation function is used and augmented Lagrangian multipliers are developed for buckling constraints. Numerical examples demonstrate that the proposed method can effectively improve the airfoil stability to different constraint levels across various configurations with minimal parameter tuning. Additionally, the algorithm produces designs that are conducive to manufacturing.