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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. Using RANS CFD and detailed structural finite element models, the aerodynamic shape and internal structural sizing of a wing can be optimized concurrently to tailor the wing’s aeroelastic behavior and optimally trade-off drag and structural mass. This capability makes MDO a key enabling technology for the next generation of efficient high-aspect-ratio transport aircraft. However, as their aspect ratios increase, these wings increasingly exhibit geometrically nonlinear behavior that linear structural analysis methods cannot model correctly. The purpose of this dissertation is both to address some of the challenges of including these nonlinear structural models in large scale wing design problems, and to investigate whether doing so is really necessary.
To enable this, I first develop a benchmark model and series of aerostructural optimization problems. The model is intended to be a simpler and more accessible alternative to the more complex uCRM benchmark model. I also define a set of three optimization problems with increasing complexity, progressing from structural sizing with a fixed geometry, to fuel burn minimization with both a fixed and variable wing planform. This benchmark has enabled researchers from across different countries and institutions have been able to compare their aerostructural optimization tools on the same problem for the first time. The optimal wing designs produced by solving the third benchmark problem feature high aspect ratios and in-flight deflections that are larger than those of current commercial aircraft, making them suitable for investigating the impact of geometric nonlinearity on optimal wing design.
I then implement a series of methods to enable high-fidelity aerostructural optimization using geometrically nonlinear static and dynamic aeroelastic analyses. In the finite element library TACS, I implement an efficient and robust nonlinear static solver based on the Newton-Raphson method and a predictor-corrector continuation algorithm. I also implemented a shell constitutive model that balances design freedom with the ability to consider the variety of failure modes necessary for sizing stiffened composite panels. Using the MPhys multiphysics coupling framework, I couple these capabilities with a high-fidelity RANS CFD solver using a geometrically nonlinear load and displacement transfer scheme, enabling fully geometrically nonlinear aeroelastic analysis, gradient computation, and optimization.
I then extend an “appropriate-fidelity” method for high-fidelity aerostructural optimization considering the effect of geometric nonlinearity on a wing’s flutter stability boundary. The geometrically nonlinear flutter constraint is evaluated by condensing a detailed structural model to a simpler, but geometrically nonlinear beam model. The resulting low-fidelity aeroelastic model captures the impact of in-flight deflections on the flutter boundary with computational effort and robustness adequate for optimization, while other quantities of interest, such as cruise range and peak stress levels, are evaluated by using the detailed model. The flutter constraint is differentiated using the adjoint method to enable large-scale gradient-based optimization with large numbers of structural sizing and geometric design variables.
Using these capabilities, I perform a series of analysis and optimization studies to investigate when and how geometric nonlinearity affects the optimal design of high-aspect-ratio wings. I find that the nonlinear static aeroelastic effects have surprisingly small impact on the optimal trade-off between cruise drag and structural mass for high-aspect-ratio wings, even at deflection levels where nonlinear is traditionally thought necessary. However, I also find that geometric nonlinearity can have a significant impact on when and how a wing will flutter, and how it should be designed to avoid such instabilities. This is the case even when the wing’s in-flight deflections are well predicted by a linear model.