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This paper presents a method to model the coupled nonlinear flight dynamics and aeroelasticity of highly flexible flying wings, as well as analyze their nonlinear characteristics. A low-order, nonlinear, strain-based finite element framework is used, which is capable of assessing the fundamental impact of structural nonlinear effects in a computationally effective formulation target for preliminary vehicle design and control synthesis. The crosssectional stiffness and inertia properties of the wings are calculated along the wing span, and then incorporated into the 1-D nonlinear beam model. A proposed model for the effects in the torsional stiffness of skin wrinkling due to large bending curvature of the wing is also presented. Finite-state unsteady subsonic aerodynamic loads are incorporated to complete the aeroelastic representation of a flying wing. In studying flying wing dynamic response, a spatially-distributed discrete gust model is introduced and its impact on the time-domain solutions is investigated.

Blended-wing-body (BWB) aircraft with high-aspect-ratio wings is an important configuration for high-altitude long-endurance unmanned aerial vehicles (HALE UAV). Recently, Northrop Grumann created a wind tunnel model under the Air Force's High Lift over Drag Active (HiLDA) Wing program to study the aeroelastic characteristics of blended-wing-body for a potential Sensorcraft concept. This paper presents a study on the coupled aeroelastic / flight dynamics stability and response of a BWB aircraft that is modified from the HiLDA experimental model. An effective method is used to model very flexible BWB vehicles based on a low-order aeroelastic formulation that is capable of capturing the important structural nonlinear effects and couplings with the flight dynamics degrees of freedom. A nonlinear strain-based beam finite element formulation is used. Finite-state unsteady subsonic aerodynamic loads are incorporated to be coupled with all lifting surfaces, including the flexible body. Based on the proposed model, body-freedom flutter is studied, and is compared with the flutter results with all or partial rigid-body degrees of freedom constrained. The applicability of wind tunnel aeroelastic results (where the rigid-body motion is limited) is discussed in view of the free flight conditions (with all 6 rigid-body degrees of freedom). Furthermore, effects of structural and aerodynamic nonlinearities as well as wing bending/torsion rigidity coupling on the stability and gust response are also studied in this paper. H

a b s t r a c tThis paper introduces a strain-based geometrically nonlinear beam formulation for structural and aeroelastic modeling and analysis of slender wings of very flexible aircraft. With beam extensional strain, twist, and bending curvatures defined as the independent degrees of freedom, the equations of motion are derived through energy methods. Some special treatments are applied to the formulation to effectively model split-beam systems and beam configurations with multiple nodal displacement constraints. Using the strain-based formulation, solutions of different beam configurations under static loads and forced dynamic excitations are compared against ones from other geometrically nonlinear beam formulations.

This paper introduces an approach to effectively model the nonlinear aeroelastic behavior of fully flexible aircraft. The study is conducted based on a nonlinear strainedbased finite element framework in which the developed low-order formulation captures the nonlinear (large) deflection behavior of the wings, and the unsteady subsonic aerodynamic forces acting on them. Instead of merely considering the nonlinearity of the wings, the paper will allow all members of the vehicle to be flexible. Due to their characteristics of being long and slender structures, the wings, tail, and fuselage of highly flexible aircraft can be modeled as beams undergoing three dimensional displacements and rotations. The cross-sectional stiffness and inertia properties of the beams are calculated along the span, and then incorporated into the 1-D nonlinear beam model. Finite-state unsteady subsonic aerodynamic loads are incorporated to be coupled with all lifting surfaces, so as to complete the state space aeroelastic model. Different Sensorcraft concepts are modeled and studied, including conventional single-wing and joined-wing aircraft configurations with flexible fuselage and tail. Based on the proposed models, roll responses and stabilities are studied and compared with linearized and rigidized models. At last, effects of the flexibility of the fuselage and tail on the roll maneuver and stability of the aircraft are presented.