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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.

Ce travail porte sur l’étude de l’environnement électromagnétique dans une chambre réverbérante à brassage mécanique de modes. Les chambres réverbérantes constituent un outil fondamental pour réaliser des mesures de compatibilité électromagnétique. Leur étude se focalise généralement sur les propriétés statistiques de la puissance du champ stationnaire. Cependant, d’autres études de ce champ stationnaire ont été faites sous un autre angle qui consiste à utiliser la décomposition en spectre d’ondes planes pour décrire ce champ. Les méthodes d’estimation spectrale à haute résolution constituent un outil puissant pour identifier les directions d’arrivée d’ondes planes. Ces méthodes réputées puissantes sont paramétriques, elles requièrent la connaissance a priori du nombre d’ondes planes à séparer. Une méthode complète basée sur le critère MDL (Minimum Description Length) pour l’estimation d’ordre et de l’algorithme MUSIC (MUltiple SIgnal Classification) a été codée pour l’estimation du nombre, des directions d’arrivée, des amplitudes et des phases des ondes planes. L’adaptation de l’estimateur du spectre d’ondes planes à l’environnement de la chambre réverbérante, qui est un milieu à forte corrélation, nécessite l’utilisation de la technique de lissage spatial pour décorréler les fronts d’onde. La simulation du fonctionnement de la chambre réverbérante par la méthode numérique FDTD (Finite Difference Time Domain) a permis d’avoir les cartographies du champ électrique pour réaliser l’étude de la variation du spectre angulaire par rotation du brasseur mettant en évidence l’effet du mouvement du brasseur sur les directions d’arrivée des ondes et sur leurs puissances respectives. Ce travail se termine par une étude statistique des directions d’arrivée et des amplitudes des ondes planes de la décomposition / This work deals with the study of electromagnetic environment in a mechanical stirred reverberation chamber. The reverberation chamber is a fundamental tool to perform measurements of electromagnetic compatibility. Its study is generally focused on the statistical properties of the stationary field power. However, other studies based on field decomposition on plane waves have been made to describe this environment. High resolution spectral methods are powerful tools to estimate the directions of arrival of plane waves. These parametric methods require a priori the knowledge of the number of plane waves to separate. A complete method based on MDL (Minimum Description Length) criterion and MUSIC algorithm (MUltiple SIgnal Classification) is developed for plane waves number, directions of arrival (DOA), amplitudes and phases estimation. To adapt the plane waves estimator to the environment of the reverberation chamber, which is a highly correlated medium, spatial smoothing technique is used for wavefronts decorrelation. The reverberation chamber is simulated by the FDTD (Finite Difference Time Domain) numerical method to obtain the electric field cartographies. They are then used to study the stirrer rotation effect on plane wave directions of arrival and their respective powers. This work concludes with a statistical study on the plane wave DOA and amplitudes