Aeroelastic Shape Optimization of a Pluging Plate

Abstract

In this paper, aeroelastic shape optimization is performed on flapping micro air vehicle (MAV) wings in forward flight. The aeroelastic model tightly couples the structural plate finite element model with an unsteady vortex lattice method aerodynamic model. A gradient-based optimizer is used to maximize the cycle-average thrust generated by the wing while minimizing the power requirements. The multiobjective optimization is performed using the -constraint method. The optimizer creates wings that maximize the span while the chord is limited by the power constraint. Nomenclatureα instantaneous angle of attack ∆t time step size η, ξ area coordinates of the DKT element Γ b vector of bound vorticies Γ w vector of wake vorticies ρ fluid density A b matrix of influence coefficients from the bound vorticity A e area of the e th finite element A w matrix of influence coefficients from the wake B DKT strain-displacement relationship matrix C s proportional structural damping D b DKT stress-strain relationship matrix F aero vecotr of aerodynamic forces acting on the wing F inertia vecotr of inertial forces acting on the wing g gravitational constant h rigid body motion at the nodes h CP vector of rigid-body velocity at the control points K s structural stiffness matrix for the DKT elements L lift m number of triangular elements in the structure M s structural mass matrix for the DKT elements m wing mass of the wing P in input power q vector of the global nodal degrees of freedom T thrust t h thickness of the plate T α,qmatrix that converts nodal deformation to control point rotations T a,cp matrix that converts pressure at the control points to nodal forces T V,q matrix that converts the nodal velocities to velocities at the control points V s velocity of the air acting on the wing due to the rate of the deformation V kin velocity of the air acting on the wing due to the prescribed kinematic motion

Multidisciplinary design optimization of the flapping wing system for forward flight

“…Many studies on optimization have been conducted considering aeroelasticity. Stewart et al 14 performed shape optimization of the wings in forward flight. The aeroelastic model tightly coupled a structural plate finite element model with an aerodynamic model for the unsteady vortex lattice method (UVLM), and a gradient-based optimization was used to maximize the average thrust.…”