Aerostructural Optimization of Nonplanar Lifting Surfaces

Nonplanar lifting surfaces can lower the induced drag relative to planar surfaces by redistributing vorticity. Other sources of drag, such as viscous drag, as well as nonaerodynamic considerations, such as structural weight, also play an important role in assessing the overall efficiency of such lifting surfaces. In this paper we solve a series of problems to find optimal nonplanar lifting surfaces and to explain the various factors and tradeoffs at play. A panel method and an equivalent beam finite-element model are used to explore nonplanar lifting surfaces, while taking into account the coupling and design tradeoffs between aerodynamics and structures. Both single-discipline aerodynamic optimization and multidisciplinary aerostructural optimization problems are investigated. The design variables are chosen to give the lifting-surface arrangement as much freedom as possible. This is accomplished by allowing a number of wing segments to vary their area, taper, twist, sweep, span, and dihedral, with the constraint that they must not intersect each other. Because of the complexity of the resulting design space and the presence of multiple local minima, an augmented Lagrangian particle swarm optimizer is used to solve the optimization problems. When only aerodynamics are considered, closed lifting-surface configurations, such as the box wing and joined wing, are found to be optimal. When aerostructural optimization is performed, a winglet configuration is found to be optimal when the overall span is constrained, and a wing with a raked wingtip is optimal when there is no such constraint.