Shape optimization of a flexible flapping wing with hovering kinematics

Flapping wings demonstrate exceptional aerodynamic performance and the optimization of wing shape is an important issue within this field. A numerical optimization targeting wing lift maximization is conducted on a two-dimensional flapping wing with chordwise flexibility. A commonly used setup is to consider two rigid elliptical-section components connected by a torsional spring, providing chordwise flexibility. The leading body of the wing operates under specified hovering flapping kinematics, while the trailing body responds passively. Starting from this setup, the airfoil shape is parameterized using three parameters and optimized for maximum lift using the Simplex algorithm. Four configurations of the wing are evaluated, and the results indicate lift increase across all configurations, with a maximum increase in 10.6%. The optimized airfoil configuration adopts a teardrop profile, substantially narrower than the original elliptical section. According to further analysis, the lift increase can be primarily attributed to the enhancement of velocity circulation.