Analysis of the Hessian for Aeroelastic Optimization

The symbol of the Hessian for an aeroelastic optimization model problem is analyzed. 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 computed. The result indicates that under some conditions, which are likely ful lled in most applications, the system is decoupled for the non-smooth components. The result also shows 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. This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), Mail Stop 132C, NASA Langley Research Center, Hampton, VA 23681.