Least-Squares, Continuous Sensitivity Analysis for Nonlinear Fluid-Structure Interaction

A least-squares, continuous sensitivity analysis method is developed for transient aeroelastic gust response problems to support computationally efficient analysis and optimization of aeroelastic design problems. A key distinction between the local and total derivative forms of the sensitivity system is introduced. The continuous sensitivity equations and sensitivity boundary conditions are derived in local derivative form which is shown to be superior for several applications. The analysis and sensitivity problems are both posed in a first-order form which is amenable to a solution using the least-squares finite element method. Several example and validation problems are presented and solved, including elasticity, fluid, and fluid-structure interaction problems. Significant contributions of the research include the first sensitivity analysis of nonlinear transient gust response, a local derivative formulation for shape variation that requires parameterizing only the boundary, and statement of sufficient conditions for using nonlinear "black box" software to solve the sensitivity equations. Promising paths for future investigation are presented and discussed.