Aeroelastic Shape Optimization of a Flapping Wing

Abstract

This paper presents the theory and results for the shape and structural optimization of a platelike flapping wing. The aeroelastic system is analyzed by coupling an unsteady vortex lattice aerodynamics model with a plate finite element model. The assumptions in the aerodynamic model allow the system of equations to be calculated with the inversion of a single matrix, greatly reducing the computational cost. The design variables are the shape parameters from the modified Zimmerman method and the polynomial coefficients that describe the wing thickness. The wing shape and structure are optimized using two multiobjective optimization formulations. The first optimization minimizes the input power while maximizing the cycle-averaged thrust. The input power is the secondary objective function and is treated as a nonlinear constraint, whereas the cycle-averaged thrust is the primary objective function. A second multiobjective formulation that treats wing mass as the secondary objective function is also performed. The power-thrust-optimal wing designs minimize the contribution of the wing deformation to the input power over the flapping cycle. The mass-optimal shapes maximize the wingspan and tailor the wing thickness such that the wing deformation adds to the thrust. It is shown that, although thrust benefits from added wing deformation, it also adds to the power required to flap the wing.