Design optimization is a method that can be used to automate the design process to obtain better results. When applied to aeroelastic structures, design optimization often leads to the creation of highly flexible aeroelastic structures. There are, however, a number of conventional design procedures that must be modified when dealing with highly flexible aeroelastic structures. First, the deformed geometry must be the baseline for weight, structural, and stability analyses. Second, potential couplings between aeroelasticity and rigid-body dynamics must be considered. Third, dynamic analyses must be modified to handle large nonlinear displacements. These modifications to the conventional design process significantly increase the difficulty of developing an optimization framework appropriate for highly flexible aeroelastic structures. As a result, when designing these structures, often either gradient-free optimization is performed (which limits the optimization to relatively few design variables) or optimization is simply omitted from the design process. Both options significantly decrease the design exploration capabilities of a designer compared to a scenario in which gradient-based optimization is used. This dissertation therefore presents various contributions that allow gradient-based optimization to be more easily used to optimize highly flexible aeroelastic structures. One of our primary motivations for developing these capabilities is to accurately capture the design constraints of solar-regenerative high-altitude long-endurance (SR-HALE) aircraft. In this dissertation, we therefore present a SR-HALE aircraft optimization framework which accounts for the peculiarities of structurally flexible aircraft while remaining suitable for use with gradient-based optimization. These aircraft tend to be extremely large and light, which often leads to significant amounts of structural flexibility. Using this optimization framework, we design an aircraft that is capable of flying year-round at \SI{35}{\degree} latitude at \SI{18}{\kilo\meter} above sea level. We subject this aircraft to a number of constraints including energy capture, energy storage, material failure, local buckling, stall, static stability, and dynamic stability constraints. Critically, these constraints were designed to accurately model the actual design requirements of SR-HALE aircraft, rather than to provide a rough approximation of them. To demonstrate the design exploration capabilities of this framework, we also performed several parameters sweeps to determine optimal design sensitivities to altitude, latitude, battery specific energy, solar efficiency, avionics and payload power requirements, and minimum design velocity. Through this optimization framework, we demonstrate both the potential of gradient-based optimization applied to highly flexible aeroelastic structures and the challenges associated with it. One challenge associated with the gradient-based optimization of highly flexible aeroelastic structures, is the ability to accurately, efficiently, and reliably model the large deflections of these structures in gradient-based optimization frameworks. To enable large-scale optimization involving structural models with large deflections to be performed more easily, we present a finite-element implementation of geometrically exact beam theory which is designed specifically for gradient-based optimization. A key feature of this implementation of geometrically exact beam theory is its compatibility with forward and reverse-mode automatic differentiation, which allows accurate design sensitivities to be obtained with minimal development effort. Another key feature is its native support for unsteady adjoint sensitivity analysis, which allows design sensitivities to be obtained efficiently from time-marching simulations. Other features are also presented that build upon previous implementations of geometrically exact beam theory, including a singularity-free rotation parameterization based on Wiener-Milenkovi\'c parameters, an implementation of stiffness-proportional structural damping using a discretized form of the compatibility equations, and a reformulation of the equations of motion for geometrically exact beam theory from a fully implicit index-1 differential algebraic equation to a semi-explicit index-1 differential algebraic equation. Several examples are presented which verify the utility and validity of each of these features. Another challenge associated with the gradient-based optimization of highly flexible aeroelastic structures is the ability to reliably track and constrain individual dynamic stability modes across the design iterations of an optimization framework. To facilitate the development of mode-specific dynamic stability constraints in gradient-based optimization frameworks we develop a mode tracking method that uses an adaptive step size in order to maintain an arbitrarily high degree of confidence in mode correlations. This mode tracking method is then applied to track the modes of a linear two-dimensional aeroelastic system and a nonlinear three-dimensional aeroelastic system as velocity is increased. When used in a gradient-based optimization framework, this mode tracking method has the potential to allow continuous dynamic stability constraints to be constructed without constraint aggregation. It also has the potential to allow the stability and shape of specific modes to be constrained independently. Finally, to facilitate the development and use of highly flexible aeroelastic systems for use in gradient-based optimization frameworks, we introduce a general methodology for coupling aerodynamic and structural models together to form modular monolithic aeroelastic systems. We also propose efficient methods for computing the Jacobians of these coupled systems without significantly increasing the amount of time necessary to construct these systems. For completeness we also discuss how to ensure that the resulting system of equations constitutes a set of first-order index-1 differential algebraic equations. We then derive direct and adjoint sensitivities for these systems which are compatible with automatic differentiation so that derivatives for gradient-based optimization can be obtained with minimal development effort.

Research into advanced wind turbine design has shown that load alleviation strategies like bend-twist coupled blades and coned rotors could reduce costs. However these strategies are based on nonlinear aero-structural dynamics providing additional benefits to components beyond the blades. These innovations will require Multi-disciplinary Design Optimization (MDO) to realize the full benefits. This research expands the MDO capabilities of Horizontal Axis Wind Turbines. The early research explored the numerical stability properties of Blade Element Momentum (BEM) models. Then developed a provincial scale wind farm siting models to help engineers determine the optimal design parameters. The main focus of this research was to incorporate advanced analysis tools into an aero-elastic optimization framework. To adequately explore advanced designs with optimization, a new set of medium fidelity analysis tools is required. These tools need to resolve more of the physics than conventional tools like (BEM) models and linear beams, while being faster than high fidelity techniques like grid based computational fluid dynamics and shell and brick based finite element models. Nonlinear beam models based on Geometrically Exact Beam Theory (GEBT) and Variational Asymptotic Beam Section Analysis (VABS) can resolve the effects of flexible structures with anisotropic material properties. Lagrangian Vortex Dynamics (LVD) can resolve the aerodynamic effects of novel blade curvature. Initially this research focused on the structural optimization capabilities. First, it developed adjoint-based gradients for the coupled GEBT and VABS analysis. Second, it developed a composite lay-up parameterization scheme based on manufacturing processes. The most significant challenge was obtaining aero-elastic optimization solutions in the presence of erroneous gradients. The errors are due to poor convergence properties of conventional LVD. This thesis presents a new LVD formulation based on the Finite Element Method (FEM) that defines an objective convergence metric and analytic gradients. By adopting the same formulation used in structural models, this aerodynamic model can be solved simultaneously in aero-structural simulations. The FEM-based LVD model is affected by singularities, but there are strategies to overcome these problems. This research successfully demonstrates the FEM-based LVD model in aero-elastic design optimization. / Graduate / 0548 / pilot.mm@gmail.com