1. A method of performing aeroelastic analyses, comprising the steps of: providing a mathematical model for a plurality of structural modes of a flexible structure; providing a nonlinear aerodynamic model for generating a plurality of unsteady aerodynamic responses based on said plurality of structural modes for conditions defining an aerodynamic condition of said flexible structure; performing a single execution of said nonlinear aerodynamic model for said plurality of structural modes using a family of orthogonal functions as inputs thereto; converting said plurality of unsteady aerodynamic responses generated during said step of performing to a linear state-space model; and generating static and dynamic aeroelastic solutions using computational interaction between said mathematical model and said linear state-space model for a plurality of periodic points in time.