Sequential Quadratic Programming and Dynamic Optimal Design of Rotating Blades

ABSTRACT By studying the Kuhn-Tucker conditions for a structural optimal design problem with multifrequency constraints, we show in this paper that the Optimality Criterion (OC) approach and Mathematical Programming (MP) can be unified. This unification leads to a new approach—Sequential Quadratic Programming (SQP)—which we combine with a technique of temporary relaxation of constraints and application of rational move-limits, based on deviations due to linearization of nonlinear constraints. The SQP algorithm is applied to solve the dynamic optimal design problem of rotating blades with prescribed multifrequency constraints on both flapping and chordwise vibration. A computer program based on the Finite Element Method and explicit design sensitivities is developed and a set of examples is tested. Numerical results for a variety of cross-sectional shapes are presented.