Design of a conformable rotor airfoil using distributed piezoelectric actuators

In the present study, several design methodologies are developed for determining the optimal distribution of a limited amount of piezoelectric material aft of the spar in a conformable rotor airfoil section. The design objectives are to maximize the trailing-edge deflection under actuation loads and simultaneously minimize the airfoil deflection under aerodynamic loads. Energy-like 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 objectives are achieved by maximizing a multicriteria objective function that represents a ratio of the MPE to SE. Several design optimization techniques are evaluated including topology, geometry, sequential topology-geometry, and concurrent topology-geometry optimizations. The results of the study indicate that the optimized conformable airfoil section obtained using the concurrent topology-geometry optimization can produce a downward trailing-edge deflection equivalent to 4.24 deg of effective flap angle from the actuation loads, with the peak-to-peak deflection being nearly twice the downward deflection. The airfoil deformation caused by the aerodynamic loads alone is extremely small (less than 0.24 deg). Key features of the optimized airfoil are arrangement of actuators near the spar that act to stretch and shrink the skin and a bimorph like mechanism from midchord to the trailing edge. Additional results include a strain analysis, aerodynamic lift-and-drag increment study, and an examination of the effects of skin thickness and volume constraint of the active material.