Advances in Aerospace Engineering

Volume 2015, Article ID 613962, 11 pages

http://dx.doi.org/10.1155/2015/613962

## On the Importance of Nonlinear Aeroelasticity and Energy Efficiency in Design of Flying Wing Aircraft

^{1}University of California, Los Angeles, CA 90095, USA^{2}Georgia Institute of Technology, Atlanta, GA 30332-0150, USA

Received 17 August 2014; Accepted 4 December 2014

Academic Editor: Jens N. Sorensen

Copyright © 2015 Pezhman Mardanpour and Dewey H. Hodges. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Energy efficiency plays important role in aeroelastic design of flying wing aircraft and may be attained by use of lightweight structures as well as solar energy. NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft) is a newly developed computer program which uses a nonlinear composite beam theory that eliminates the difficulties in aeroelastic simulations of flexible high-aspect-ratio wings which undergoes large deformation, as well as the singularities due to finite rotations. NATASHA has shown that proper engine placement could significantly increase the aeroelastic flight envelope which typically leads to more flexible and lighter aircraft. The areas of minimum kinetic energy for the lower frequency modes are in accordance with the zones with maximum flutter speed and have the potential to save computational effort. Another aspect of energy efficiency for High Altitude, Long Endurance (HALE) drones stems from needing to minimize energy consumption because of limitations on the source of energy, that is, solar power. NATASHA is capable of simulating the aeroelastic passive morphing maneuver (i.e., morphing without relying on actuators) and at as near zero energy cost as possible of the aircraft so as the solar panels installed on the wing are in maximum exposure to sun during different time of the day.

#### 1. Introduction

Over the last decade, Hodges and coworkers [1–3] at Georgia Tech have been extensively involved in aeroelastic simulation of very light and thus highly flexible aircraft for development of the next generation of unmanned aerial vehicles (UAVs) and/or High-Altitude, Long Endurance (HALE) aircraft, including flying wings. Such aircraft typically have high-aspect-ratio wings with high flexibility, which leads to large deformation. Consequently, linear aeroelastic analyses are incapable of predicting the stability characteristics of such aircraft. They successfully proved that only nonlinear aeroelastic analysis provides correct information regarding the aeroelastic flight envelope of this class of aircraft [1, 4, 5].

Nonlinear aeroelastic trim and stability of HALE aircraft, NATASHA, is a computer program developed by the authors of references [1, 4, 5] that accommodates modeling of large deformation of high-aspect-ratio flying wings. The theory behind NATASHA is based on the geometrically exact, nonlinear, composite beam theory of Hodges [6], along with the finite-state induced flow model of Peters et al. [7].

Previous comparisons by [2] showed that results from NATASHA are in excellent agreement with well-known beam stability solutions [8, 9], the flutter problem of [10], experimental data presented by [11], and results from well-established computer codes such as DYMORE [12, 13] and RCAS [14]. Mardanpour et al. [3] considered the classical cantilever wing model of Goland and Luke [15] and verified NATASHA for the behavior of the eigenvalues as well as the effect of sweep on divergence and flutter characteristics and it was shown that gravity and load factor play an important role in aeroelasticity of high-aspect-ratio wings [16].

A principal determinant of energy consumption in aircraft is drag, which must be opposed by engine thrust for the aircraft to fly. Flying wings may achieve significant drag reduction due to a smooth outer surface and the lack of a vertical tail [3]. Consequently, the performance of such aircraft may increase significantly, relative to conventional configurations of the same size. The potential increase of performance for this class of aircraft has inspired aeroelasticians to design new generation of aircraft based on a flying wing configuration [3]. Typical aeroelastic instability of these aircraft is body-freedom flutter when the short-period mode of the aircraft couples with the elastic bending-torsion modes [3, 17–24].

In another context, a morphing solar-powered flying wing can maximize the energy absorption of solar panels on the wing surfaces by changing its configuration such that the panels have highest exposure to the sun. This change in the geometry of the flying wing is highly effective in energy absorption during times just before sunset and just after sunrise, and consequently the aircraft can sustain longer flight [25]. Use of solar energy is a novel method that eliminates one of the design constraints to a considerable extent by removing the limitation on the source of energy. The morphing concept could be based on either wing morphing systems or airfoil morphing systems, or a combination of both [26]. So far in the literature, several morphing concepts and systems have been developed based on altering various geometric parameters of the wing (such as span, chord, camber, sweep, twist, and even airfoil thickness distribution) to make the aircraft suitable for different missions and flight conditions [19, 26, 26, 26–37]. The folding wing configuration has been analyzed using linear aeroelastic models [38–40] and nonlinear aeroelastic models [41, 42]. In all the mentioned works the weight of actuators and the actuation power that the morphing mechanisms require performing their task are the problematic parts of the design [26], in particular when it comes to morphing of flying wing and/or HALE aircraft.

In this paper, after a brief outline of the theory behind NATASHA, energy efficiency in aeroelastic design and simulation for flying wing configuration will be assessed as (a) a feature of the design (i.e., engine placement), which attains instability at higher speed with lighter aircraft structure, (b) a methodology that helps to decrease computational effort required for determining favorable locations for engine placement with the potential of higher flutter speed, and (c) a scheme to passively morph a solar-powered flying wing, so that exposure to the sun of solar panels distributed on the wings is maximized for higher absorption of solar energy at specific times of the day.

#### 2. Theory

##### 2.1. Nonlinear Composite Beam Theory

The fully intrinsic nonlinear composite beam theory [6] is based on geometrically exact first-order partial differential equations of motion for the beam that are independent of displacement and rotation variables. They contain variables that are expressed in the bases of the reference frames of the undeformed and deformed beams, and , respectively; see Figure 1. These geometrically exact equations are written in terms of force, moment, velocity, and angular velocity, and they contain no nonlinearities higher than second degree in the unknowns. The equations of motion are where the generalized strains and velocities are related to stress resultants and moments by the structural constitutive equations and the inertial constitutive equations Finally, strain- and velocity-displacement equations are used to derive the intrinsic kinematical partial differential equations [6], which are given as