Modeling Methodologies for Nonlinear Aeroelasticity

Conventional methodologies for aeroelastic analysis and design are typically based on linear assumptions and neglect any interaction with flight dynamics. If adequate for traditional relatively stiff configurations, which experience small deflections under normal operating load conditions and show high-frequency natural vibration modes, these methodologies may not be capable of capturing the behavior of next-generation vehicles. Higher-performance requirements on both transport and unmanned Aircraft are leading to explore innovative, increasingly light and flexible design solutions, which in turn calls for the development of more advanced models, computational methods, and software tools appropriate to evaluate the effects of large-amplitude displacements and couplings between rigid-body and elastic degrees of freedom. This thesis addresses the modeling of nonlinear aeroelasticity at the two-dimensional level of a wing cross-section and at the three-dimensional level of a complete aircraft, for which couplings with the vehicle motion as a whole are also considered. The first part of the thesis presents a geometrically exact semi-analytical formulation of the unsteady aerodynamics of a flexible thin airfoil undergoing arbitrary motion in incompressible potential flow. The proposed model extends traditional closedform linearized solutions to the case of large-amplitude displacements and provides a nonlinear theoretical benchmark for solver validation as well as a low-order simulation tool to gain physical insight into the aeroelastic behavior of very flexible wings. The second part of the thesis zooms out to study the fully coupled flight dynamics and aeroelasticity of free-flying flexible aircraft. An integrated formulation of nonlinear rigid-body motion and linear structural dynamics applicable to complex configurations described by detailed models is linearized around steady maneuvers and a computational environment for stability and response studies in presence of inertial and aerodynamic couplings is implemented using data from commercial finite element solvers. The prediction capabilities of the developed tool are demonstrated by analyzing the unique flight dynamic/aeroelastic stability of two existing experimental vehicles: the University’s of Michigan X-HALE and the Lockheed Martin’s Body Freedom Flutter research drones. The integrated linearized formulation of rigid-body and structural dynamics is next extended by allowing arbitrary static elastic displacements in order to study small perturbations around trim points at which the structure may experience a large aeroelastostatic response, as typically occurs for very flexible vehicles. As the first step to implement the obtained statically-nonlinear dynamically-linear model, a novel high-fidelity algorithm for trim analysis of very flexible aircraft is formulated, implemented by coupling off-the-shelf solvers, and validated by analyzing the X-HALE. The two parts of this work adopt different perspectives: the relative simple description of two-dimensional problems allows to obtain a fully theoretical nonlinear airfoil model, whereas the complexity of a complete flexible vehicle in free flight motivates to develop a formulation that can be readily implemented to analyze generic configurations by exploiting the advanced modeling capabilities of commercially available software tools. The theoretical and computational points of view adopted in the two parts of the thesis are not in contrast, but complementary and both necessary to the development of nonlinear aeroelasticity, as they both played a crucial role in the formulation of state-of-the-art linear aeroelastic models and analysis methods. Indeed, the common aim shared by the methodologies presented in this work is to contribute to the understanding and simulation of nonlinearities and couplings in aircraft aeroelasticity, in order to prevent possible negative effects and exploit potential benefits in the design of high-performance tomorrow’s aircraft.