Aero-Structural Wing Planform Optimization

During the last decade, aerodynamic shape optimization methods based on control theory have been intensively developed. The methods have proved to be very effective for improving wing section shapes for fixed wing-planforms. Building on this success, extension of the control theory approach to variable planforms has yielded further improvement. This paper describes the formulation of optimization techniques based on control theory for aerodynamic shape design in inviscid compressible flow modeled by the Euler equations. The design methodology has been expanded to include wing plan-form optimization. It extends the previous work on wing planform optimization based on simple wing weight estimation. A more realistic model for the structural weight, which is sensitive to both planform variations and wing loading, is included in the design cost function to provide a meaningful design. A practical method to combine the structural weight into the design cost function is studied. An extension of a single to a multiple objective cost function is also considered. Results of optimizing a wing-fuselage of a commercial transport aircraft show a successful trade-off between the aerodynamic and structural cost functions, leading to meaningful wing planform designs. The results also support the necessity of including the structural weight in the cost function. Furthermore, by varying the weighting constant in the cost function, an optimal set called " Pareto front " can be captured, broadening the design range of optimal shapes. Introduction W HILE aerodynamic prediction methods based on CFD are now well established, quite accurate , and robust, the ultimate need in the design process is to find the optimum shape which maximizes the aerodynamic performance. One way to approach this objective is to view it as a control problem, in which the wing is treated as a device which controls the flow to produce lift with minimum drag, while meeting other requirements such as low structural weight, sufficient fuel volume, and stability and control constraints. In this paper, we apply the theory of optimal control of systems governed by partial differential equations with boundary control, in this case through changing the shape of the boundary. Using this theory, we can find the Frechet derivative (infinitely dimensional gradient) of the cost function with respect to the shape by solving an adjoint problem, and then we can make an improvement by making a modification in a descent direction. For example, the cost function might be the drag coefficient at a fixed lift, …