In the present study, a design methodology is developed for determining the optimal distribution of a limited amount of piezoelectric material and optimal skin for a conformable rotor airfoil section. The objective of the design optimization is to generate a conformable airfoil structure that produces significant trailing edge deflection under actuation loads, but minimal airfoil deflection under aerodynamic loads. Energy functions, Mutual Potential Energy (MPE) and Strain Energy (SE), are used as measures of the deflections created by the actuation and aerodynamic loads, respectively. The design objective is achieved by maximizing a multi-criteria objective function that represents a ratio of the MPE to SE. Several design optimization techniques are evaluated including geometry and concurrent geometry-topology optimizations. The results of the study indicate that the optimized conformable airfoil section obtained using the concurrent geometry-topology optimization can produce a significant downward trailing edge deflection, and the airfoil deformation due to the aerodynamic loads alone is small. However, the optimized airfoil design is extremely complex and contains intricate network of actuators, which may be difficult to fabricate. Systematic simplification of the structure is performed to obtain a conformable airfoil design that is simple and may be easy to build. Further parametric optimization is used to find optimal values of the skin axial and bending stiffness for an optimal conformable airfoil design. The airfoil can produce a downward trailing edge deflection equivalent to 3.7° of Effective Flap Angle from the actuation loads, with the peak-to-peak deflection being nearly twice the downward deflection, and the airfoil deformation due to the airload loads is less than 1°. The optimal skin should have less axial stiffness and much more bending stiffness as compared to a conventional skin.
Aerodynamic Optimization of Helicopter Blade Planform (I): Design Optimization Techniques