Geometrically Nonlinear High-fidelity Aerostructural Optimization for Highly Flexible Wings
A. C. Gray, and J. R. R. A. Martins
Proceedings of the AIAA SciTech Forum, 2021
Over the past decade, advances in multidisciplinary design optimization (MDO) have enabled the optimization of aircraft wings using high-fidelity simulations of their coupled aerodynamic and structural behavior. However, as their aspect-ratios increase, these wings increasingly exhibit geometrically nonlinear behavior that cannot be correctly modeled by typical linear structural analysis methods. Although many low-fidelity aeroelastic analysis and optimization tools feature geometrically nonlinear finite element models, all examples to date of high-fidelity aerostructural optimization have been restricted to linear finite element models due to concerns over computational cost and complexity. In this work, we develop a tool for high-fidelity, geometrically nonlinear structural and aerostructural optimization and demonstrate it by performing detailed structural sizing optimization of a high aspect-ratio wingbox using high-fidelity RANS CFD and a geometrically nonlinear shell finite element formulation. By comparing the results of aerostructural analysis and optimization using both geometrically linear and nonlinear structural finite element formulations, we find that geometric nonlinearity results in a 5-10% increase in the bending stress and optimized structural mass of the wingbox. Geometrically nonlinear analysis not only results in deflected wing shapes and lift distributions which are more physically accurate, but also captures new loading phenomena within the wingbox, both of which lead to more realistic structural sizing. We also show that the increase in computational cost when optimizing with geometrically nonlinear analysis can be as low as 15%, meaning these formulations should not be viewed as prohibitively expensive.