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We present an analytical model, derived using the principle of virtual work, for closed and open thin-walled beams subjected to torsion. Nonclassical effects like primary and secondary torsional warping are taken into account. A closed-form expression for mode II stress-intensity factor for thin-walled beams with a longitudinal crack is derived. We start by finding analytical solutions based on Vlasov's torsional beam theory for thin-walled beams with any cross sections. We then use the calculated stress of a rectangular thin-walled beam to determine an analytical expression for mode II stress-intensity factor. Finally, we add a correction factor to account for complex behavior of long cracks. Examples are presented to illustrate the effectiveness of the current model, and it is validated by comparison with detailed finite element results obtained using ABAQUS. DOI: 10.2514/1.45393

DOI: 10.2514/1.30890 An analysis and parametric study of the flight dynamics of highly flexible aircraft are presented. The analysis extends previous work of the authors, used to predict the atypical flight dynamic characteristics of highly flexible flying wings, to conventional configurations with one or more fuselages, wings, and/or tails. The aircraft structure is represented as a collection of geometrically exact, intrinsic beam elements, with continuity conditions enforced where beams intersect. The structural model is coupled with an aerodynamic model consisting of two-dimensional, large-angle-of-attack, unsteady theory for the lifting surfaces, and a fuselage model based on application of slender-body theory to a cylindrical beam. Influences of various design parameters such as wing flexibility, horizontal/vertical tail aerodynamics, and offset are investigated for aeroelasticity and flight dynamics of highly flexible aircraft. Results for prototype configurations illustrate the relationships between its design parameters and flight dynamic behavior.

The paper presents a theory for flight-dynamic analysis of highly flexible flying-wing configurations. The analysis takes into account large aircraft motion coupled with geometrically nonlinear structural deformation subject only to a restriction to small strain. A large motion aerodynamic loads model is integrated into the analysis. The analysis can be used for complete aircraft analysis including trim, stability analysis linearized about the trimmed-state, and nonlinear simulation. Results are generated for a typical high-aspect-ratio 'flying-wing' configuration. The results indicate that the aircraft undergoes large deformation during trim. The flight-dynamic characteristics of the deformed aircraft are completely different as compared with a rigid aircraft. When the example aircraft is loaded sufficiently, the pair of complex-conjugate short-period roots merges to become two real roots, and the phugoid mode goes unstable. Furthermore, nonlinear flight simulation of the aircraft indicates that the phugoid instability leads to catastrophic consequences. DOI: 10.2514/1.17640

It has been shown in earlier work that the energy for flutter comes from propulsion, that is, flutter leads to an increase in drag. The present paper seeks to explain the effect of flutter-induced drag on aircraft response. It is shown that the aircraft can undergo limit-cycle oscillations even if the oscillations are in the linear structural and aerodynamic lift range. These limit-cycle oscillations occur as a result of the inability of the engine to support exponentially increasing oscillations. The limit-cycle oscillations are composed of variations in flight speed and amplitude of vibration. This modality of limit-cycle oscillations has not been presented in earlier literature and leads to better understanding of the limit-cycle oscillation problem.

A new paradigm is presented for understanding flutter and flapping flight. The framework for the investigation is based on conservation of energy. Energy produced, energy lost and/or work done due to structural vibration, aerodynamic wake, and propulsion are taken into account. It is shown that there exist three types of modes in an aeroelastic system, namely 1) unstable mode producing drag (flutter mode), 2) stable mode producing drag, and 3) stable mode producing thrust (flapping flight mode). The type of mode can be determined from the mode shape for a given reduced frequency. The regions (in the modal vector space) corresponding to the three types of modes are presented for a two-dimensional airfoil. It is shown that the flutter region is separate from the thrust-producing region and the boundaries of these regions are tangential to one another at a common neutral point. The neutral point corresponds to no energy transfer between the energy sources. The efficiency of flapping flight and occurrence of flutter is further investigated. Finally, the possibility of a limit-cycle oscillations due to constant thrust flight is presented.

The effect of thrust on the flutter of a high-aspect-ratio wing is investigated. The wing is represented by a beam using a nonlinear mixed finite element method. Aerodynamic forces are calculated using a finite state, two-dimensional unsteady aerodynamic model. The effect of thrust is modeled as a follower force of prescribed magnitude. Without the thrust force, the wing is shown to become unstable for freestream airspeeds greater than the flutter speed. On the other hand, in the absence of aerodynamic forces, the wing becomes unstable for values of the thrust in excess of a critical magnitude of the force. When both effects are present, the airspeed at which the instability occurs depends on the thrust magnitude. For validation, an analytical solution for the in vacuo case (accounting only for the effect of thrust) was developed and shown to match closely results from the numerical method. Parametric studies show that the predicted stability boundaries are very sensitive to the ratio of bending stiffness to torsional stiffness. Indeed, the effect of thrust can be either stabilizing or destabilizing, depending on the value of this parameter. An assessment whether or not the magnitude of thrust needed to influence the flutter speed is practical is made for one configuration.

A new, nonlinear aeroelastic study has been carried out on a complete aircraft model with geometric similarity to the existing high-altitude long-endurance aircraft.

Research is presented concerning the aeroelastic analysis of an entire aircraft flying in a subsonic manner. The amplitude of limit-cycle oscillations, flutter speed and nonlinearities on the trim are discussed.