Shape sensitivity analysis of strongly coupled fluidstructure interaction problems

The analysis and design sensitivity analysis (DSA) of steady, strongly coupled fluidstructure interaction problems are considered. Nonlinearities in the analysis arise from both the solid behaviour, the fluid behaviour, and from the deformed interface, where the deformation of the interface is large enough to significantly alter the flow of the fluid. A solution for state is obtained using a Galerkin finite element discretization, which is based on a consistent weak formulation for the fluid-structure interaction problem. The resulting nonlinear equations are solved using an approximate Newton method. Sensitivity analysis is done by the direct differentiation method, and the resulting linear equations are solved very efficiently by an incremental iterative method. The methods for analysis and design sensitivity analysis are illustrated in two examples involving large displacements.