Spectral Formulation-Based FSI and Coupled Sensitivity Analysis for Dyanmic Aeroelastic Problems

Efficient computational methods for fluid-structure interaction and corresponding coupled sensitivity analysis based on spectral formulation are introduced to solve dynamic aeroelastic problems. A time-spectral method is used for computational fluid dynamics and a modal analysis based finite element method is employed for computational structural dynamics. One of the advantages is computational efficiency by eliminating transient flow solutions to reach a periodic steady state, through the solution approximation of a discrete Fourier series. Through the spectral formulation of the FSI problems, dynamic aeroelastic problems are solved by the solution methods for the static aeroelastic problems. The biggest advantage is the availability of the steady form of the adjoint sensitivity analysis for the dynamically coupled system. Computational time and memory requirement for the unsteady adjoint sensitivity analysis are avoided in the current study by directly using the steady adjoint formulation in the spectral form of the governing equations of both fluids and structures. In this study, a practical threedimensional problem of wing flutter is be solved to show the validity of the proposed coupled-sensitivity analysis method in terms of solution accuracy and computational efficiency as well as optimality achieved for the design cases.

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