Modern Optimization Methods for Structural Optimization under Flutter Constraints

Abstract

One of the goals in the design of aircraft wings is to attain a design which is safe of flutter. The flutter analysis leads to a solution of a quadratic parameter dependent eigenvalue problem. The stability is described by the real parts of the eigenvalues. The optimization problem consists of finding design parameters which satisfy certain criteria, for example minimal weight under the restriction of stability. This is reduced to a semi-infinite optimization problem where constraints are posed on the eigenvalues. It turns out that the method of local reduction is closely connected with a concept of hump modes used in aeroelasticity. In this paper new numerical methods from positive definite programming are applied to the problem. In order to achieve this, the original problem has to be rewritten as a semi-infinite positive definite programming problem. The numerical solution is carried out with a barrier method. The minimization of the mass of a wing segment is numerically worked out for a model problem with this method.