Helicopter aeroelastic analysis is highly complex and multidisciplinary in nature; the flexibility of main rotor blades is coupled with aerodynamics, dynamics and control systems. A key component of an aeroelastic analysis is the vehicle trim procedure. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which cause the six steady forces and moments about the helicopter center of gravity to be zero. Trim simulates steady level flight of the helicopter. The trim equations are six nonlinear equations which depend on blade response and aerodynamic forcing through finite element analysis. Simulating the behavior of the helicopter in flight requires the solution of this system of nonlinear algebraic equations with unknowns being pilot controls and vehicle attitude angles. The nonlinear solution procedure is prone to slow convergence and occasional divergence causing problems in optimization and stochastic simulation studies. In this thesis, an attempt is made to efficiently solve the nonlinear equations involved in helicopter trim. Typically, nonlinear equations in mathematical physics and engineering are solved by linearizing the equations and forming various iterative procedures, then executing the numerical simulation. Helicopter aeroelasticity involves the solution of systems of nonlinear equations in a computationally expensive environment. The Newton method is typically used for the solution of these equations. Due to the expensive nature of each aeroelastic analysis iteration, Jacobian calculation at each iteration for the Newton method is not feasible for the trim problems. Thus, the Jacobian is calculated only once about the initial trim estimate and held constant thereafter. However, Jacobian modifications and updates can improve the performance of the Newton method. A comparative study is done in this thesis by incorporating different Jacobian update methods and selecting appropriate damping schemes for solving the nonlinear equations in helicopter trim. A modified Newton method with varying damping factor, Broyden rank-1 update and BFGS rank-2 update are explored using the Jacobian calculated at the initial guess. An efficient and robust approach for solving the strongly coupled nonlinear equations in helicopter trim based on the modified Newton method is developed. An appropriate initial estimate of the trim state is needed for successful helicopter trim. Typically, a guess from a simpler physical model such as a rigid blade analysis is used. However, it is interesting to study the impact of other starting points on the helicopter trim problem. In this work, an attempt is made to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of trim solution in the aeroelastic analysis of helicopter are proposed.

A supercavitating vehicle, a next-generation underwater vehicle capable of changing the paradigm of modern marine warfare, exploits supercavitation as a means to reduce drag and achieve extremely high submerged speeds. In supercavitating flows, a low-density gaseous cavity entirely envelops the vehicle and as a result the vehicle is in contact with liquid water only at its nose and partially over the afterbody. Hence, the vehicle experiences a substantially reduced skin drag and can achieve much higher speed than conventional vehicles. The development of a controllable and maneuvering supercavitating vehicle has been confronted with various challenging problems such as the potential instability of the vehicle, the unsteady nature of cavity dynamics, the complex and non-linear nature of the interaction between vehicle and cavity. Furthermore, major questions still need to be resolved regarding the basic configuration of the vehicle itself, including its control surfaces, the control system, and the cavity dynamics. In order to answer these fundamental questions, together with many similar ones, this dissertation develops an integrated simulation-based design tool to optimize the vehicle configuration subjected to operational design requirements, while predicting the complex coupled behavior of the vehicle for each design configuration. Particularly, this research attempts to include maneuvering flight as well as various operating trim conditions directly in the vehicle configurational optimization. This integrated approach provides significant improvement in performance in the preliminary design phase and indicates that trade-offs between various performance indexes are required due to their conflicting requirements. This dissertation also investigates trim conditions and dynamic characteristics of supercavitating vehicles through a full 6 DOF model. The influence of operating conditions, and cavity models and their memory effects on trim is analyzed and discussed. Unique characteristics are identified, e.g. the cavity memory effects introduce a favorable stabilizing effect by providing restoring fins and planing forces. Furthermore, this research investigates the flight envelope of a supercavitating vehicle, which is significantly different from that of a conventional vehicle due to different hydrodynamic coefficients as well as unique operational conditions.

The primary research objective was to develop a methodology to support conceptual design of the Hybrid Wing Body (HWB) configuration. The absence of a horizontal tail imposes new stability and control requirements on the planform, and therefore requiring greater emphasis on control authority assessment than is typical for conceptual design. This required investigations into three primary areas of research. The first was to develop a method for designing an appropriate amount of redundancy. This was motivated widely varying numbers of trailing edge elevons in the HWB literature, and inadequate explanations for these early design decisions. The method identifies stakeholders, metrics of interest, and synthesizes these metrics using the Breguet range equation for system level comparison of control surface layouts. The second area of research was the development trim analysis methods that could accommodate redundant control surfaces, for which conventional methods performed poorly. A new measure of control authority was developed for vehicles with redundant controls. This is accomplished using concepts from the control allocation literature such as the attainable moment subset and the direct allocation method. The result is a continuous measure of remaining control authority suitable for use during HWB sizing and optimization. The final research area integrated performance and control authority to create a HWB sizing environment, and investigations into how to use it for design space exploration and vehicle optimization complete the methodology. The Monte Carlo Simulation method is used to map the design space, identify good designs for optimization, and to develop design heuristics. Finally, HWB optimization experiments were performed to discover best practices for conceptual design.