On the Coupling of Aerodynamic and Structural Design

The symbol of the Hessian for a static aeroelastic optimization model problem is analyzed for the optimization of a plate's shape and rigidity distribution with respect to a given cost function. The ow is modeled by the small-disturbance full-potential equation and the structure is modeled by an isotropic (von K arm an) plate equation. The cost function consists of both aerodynamic and structural terms. In the new analysis the symbol of the cost function Hessian near the minimum is approximated for the non-smooth error components in the shape and rigidity. The result indicates that the system can be decoupled to two single discipline sub-minimization problems which will e ectively converge to the multidisciplinary optimal solution. The result also indicates that the structure part in the Hessian is well-conditioned while the aerodynamic part is ill-conditioned. Applications of the result to optimization strategies are discussed and demonstrated numerically.