Alexandra A. Gomes

Aero-structural Design Optimization of a Morphing Wingtip

Over the past few years, better knowledge of aerodynamics and structures and the permanent need to improve the performance and efficiency of aircraft have led to the generalized adoption of wingtip devices. The requirements faced by wingtip devices throughout the various flight conditions are, however, different. A static wingtip device (as is the case with existing designs) must be a compromise of these various conflicting requirements, resulting in less than optimal effectiveness in each flight condition. A morphing device, on the other hand, can adapt to the optimum configuration for each flight condition, leading to improved effectiveness. This article presents a morphing wingtip mechanism based on a servo-actuated articulated winglet, able to rotate about two different axes: vertical axis (toe angle) and aircraft’s longitudinal axis (cant angle). These can be controlled independently by servo-actuators. The wingtip behavior is a function of aerodynamic and structural loads which, in turn, are interdependent, requiring a multidisciplinary design optimization procedure in order to determine the ideal wingtip configuration for each case. The proposed concept is applied to a multi-mission unmanned aerial vehicle and the results show that a morphing wingtip can outperform an optimum fixed design. The optimum geometries for the different flight missions are presented and the feasibility of such a morphing wingtip is confirmed by a prototype. The performance metrics of the morphing wingtip are compared to those of a fixed wingtip to quantify the gain associated with the use of the morphing concept and it is seen that the improvement can reach 25%.

Topology Optimization of a Reinforced Wing Box for Enhanced Roll Maneuvers

In this paper, the aileron reversal speed of a wing torsion box is maximized by reinforcing its upper skin. We propose a topology optimization approach using the spectral level set methodology. This is based on the level set methods,which represent theinterface describing thereinforcements asthe zerolevel setofafunction. Accordingto the proposed methodology, this function is discretized using its Fourier coefficients. These coefficients become the design variables of the optimization problem assigned to define the reinforcing layout. Results show that approximately the sameoptimal reinforcement layout isobtained from topologically different initialconfigurations. The two underlying ideas of the present work are to propose the spectral level set methodology as a framework for topology optimization, given its potential for reducing the design space dimension, and, considering the possibilities of new custom-made materials, to readdress the reinforcement perspective in aircraft structures without the weight penalty. Nomenclature ai,bi = problem domain boundaries corresponding to componenti ofx at = � t smoothness parameter aV = � V smoothness parameter a0 = lift curve slope bt = minimum thickness C = positive constant Cl� = derivative of the rolling moment coefficient of the rigid airplane with respect to� C �� � y;n� = twist aty produced by a unit moment at�

Design and Analysis of an Adaptive Wingtip

Wingtip devices are a common component of most modern aircraft, improving the overall aerodynamic behaviour of the wing and thus improving performance and reducing operating costs and pollutant emissions. Unfortunately, given the wide range of different flight conditions encountered by an aircraft throughout the flight (and between flights with different characteristics), no single wingtip design can perform optimally at all times. The design of wingtip devices is therefore a problem of determining the best compromise between the various (often conflicting) requirements of the various flight conditions. If, however, the wingtip device can adapt (by changing shape and/or orientation) to each condition encountered throughout the flight, optimum performance can be achieved at all times. This concept is analysed and a variable orientation wingtip device is presented, consisting of a winglet able to rotate relative to the wing about two different axes (cant and toe). A multidisciplinary computational model of the proposed concept is described and the results show the potential to outperform conventional, fixed wingtip devices. The practical aspects of the construction and implementation of this novel design are also discussed.

Study of an Articulated Winglet Mechanism

The recognition that a fixed aircraft design cannot perform optimally across the wide range of flight stages and missions has sparked a great interest in morphing aircraft, able to adapt their configuration to the prevailing conditions in each moment. Many different concepts of morphing wings have been proposed but widespread adoption is hampered by actuation difficulties and reliability and safety concerns. Replacing such all-encompassing wing morphing ideas with smaller, localised geometry changes can overcome these limitations. Wingtip devices are a particularly interesting candidate in that, in spite of their small size and limited loads, they play an important role in the overall wing aerodynamics. Indeed, computational work previously carried out by the authors demonstrated the appeal of adaptive winglets and paved the way for further development of the concept. This paper describes the design, construction and testing of a prototype of the proposed adaptive winglet, with the testing focussing on two major aspects: the actuation capabilities and the system’s dynamic response. The results presented in this paper confirm the viability of the variable orientation winglet design.

SPECTRAL LEVEL SET METHODOLOGY IN TOPOLOGY OPTIMIZATION

This paper proposes a new framework to perform topology optimization. As in the level set methodology, the interface is described as the zero level set of a function. We expand the level set function in a finite Fourier series, and then use the Fourier coefficients as design variables of the optimization problem. We show that every interface can be approximated implicitly by the sum of finitely many Fourier modes. We provide an estimate for the truncation error, which is inversely proportional to the number of Fourier modes. Preliminary results are presented for the constraint design of a short cantilever. The final designs show that topological changes were described by the proposed methodology with a significant reduction in the number of design variables. This is in fact the main advantage: when compared to real domain discretization methods, our approach reduces the number of degrees of freedom necessary to describe the boundary.

Advancement of a Robust and Reliability Based Design Optimization Framework for Wing Design

This paper outlines an architecture for simultaneous analysis and robustness and reliability calculations in aircraft design optimization. Robust Design Optimization and Reliability Based Design Optimization are merged into a unied formulation which streamlines the setup of optimization problems and aims at preventing foreseeable implementation issues. The code in development expands upon and, in some cases, completely rewrites a previous version of a Multidisciplinary Design Optimization tool that was solely oriented to deterministic problems.

Spectral Level Set Methodology in MDO

A desirable feature in multidisciplinary design optimization (MDO) is to achieve an acceptable preliminary or initial design in an expeditiously fashion. One way to pursue this goal is to describe the structural boundary using a small number of design variables. We propose an approach to structural optimization that enhances the performance of multidisciplinary design tools because it greatly decreases the number of design variables assigned to structural definition. This approach is based on the Level Set Methods and uses the coefficients of the Fourier series expansion of the level set function as design variables. The global character of these coefficients and the fact that the level set function is realvalued provide the means to reduce the design space dimension. Within the level set framework, the structure is confined to the region in which the level set function is negative. In this way, the zero level set of this function implicitly describes the structural boundary, which can undergo topological changes during the optimization process as the function evolves. The proposed methodology also averts successive mesh generation. We show that an interface can be described to any desirable accuracy using finitely many Fourier modes of the signed distance to the interface. The total error is inversely proportional to the number of Fourier modes. We present and discuss two application examples in topology optimization, namely the design of short and long cantilevers subject to a pontual load. In these cases, we analyze the results obtained with the Spectral Level Set formulation for different parameter values.

Spectral Level Set Methodology in the Design of a Morphing Airfoil

In this paper, we consider the design of a morphing airfoil for improved aileron effectiveness using the spectral level set methodology. This methodology is a framework to formulate topology optimization of interfaces based on the level set methods, which represent the interface as the zero level set of a function. As this function evolves, during the optimization process, topological changes of the interface are easily described. According to our formulation, the Fourier coefficients of the level set function are the design variables of the optimization problem. An advantage of the proposed methodology, for a sufficiently smooth interface, is to admit an error asymptotically smaller than the one for non-adaptive spacial discretizations of the level set function. In this case, the methodology could lead to a reduction of the design space dimension. Another advantage is the nucleation of holes in the interior of the interface.

Optimization of Aircraft Aeroelastic Response Using Level Set Methods

In this paper, we propose a new approach to the optimization of aircraft aeroelastic response that greatly reduces the number of design variables, thus enhancing the performance of multidisciplinary design tools. The current method is an extension of the Level Set Methods, which represent an interface as the zero level set of a function. According to the proposed formulation, the Fourier coefficients of the level set function are the design variables assigned to describe the interface. Two structural topology optimization examples and two applications to aircraft structures are presented. The first two examples deal with the optimal configuration of short and long cantilevered beams for maximum stiffness. In the first application, a system of actuators provides morphing capability to an airfoil by operating on its camber to increase lift. The problem consists in determining the airfoil profile that minimizes the power consumption while improving the airfoil effectiveness. In the second application, the aileron reversal speed is maximized by applying reinforcements to the upper skin of a wing torsion box. These four problems demonstrate that the proposed methodology is able to modify the topology of the interface while using a reduced number of design variables. Other advantages of this methodology include the partial avoidance of local non-global minima, by providing a mechanism for nucleation of new holes, and avoidance of checkerboard-like designs and sucessive remeshing.

Topology Optimization of a Wing Including Self-Weight Load

In this work is presented a material model to include self-weight loads in topology optimization. The proposed approach is focused in the optimization of lifting structures and aims not only to eliminate numerical instabilities due to the weight load but also to improve the solution quality. The algorithm is tested in a two-dimensional benchmark, which is also solved with a conservative formulation of the self-weight problem for comparison of results and validation purposes. Results of this problem shows that the method implemented improves the discreteness of the design of structures subjected to load cases similar to lifting structures and that it finds also efficient designs for conventional load cases in topology optimization problems. After validation, it is optimized the full interior body of a wing where the skin is left out of the design domain. The aerodynamic load is computed assuming a rigid wing and it is also considered the self-weight load. In a first approach, the aerodynamic load is much larger than the wing weight, simulating an airliner wing and the results shows the merits of the code implemented. Then, the wing is optimizing assuming an aerodynamic load matching the wing weight in order to simulate a flying wing aircraft configuration.