Shape design optimization of steady fluid-structure interaction problems with large displacements

The objective of this work is to develop and implement efficient numerical procedures for gradient based shape design optimization of steady, strongly coupled fluid-structure interaction problems. 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 response. The solution for state is obtained using finite element residual formulations based on a consistent weak formulation of the fluid-structure interaction problem. The resulting nonlinear equations are solved using an approximate Newton method. Design sensitivity analysis (DSA) is performed by the direct differentiation method, and the resulting sensitivity equations are solved very efficiently by an incremental iterative method. Gradient based shape optimization is illustrated for finding the shape of a body with smallest drag in a flow governed by the two-dimensional steady Navier-Stokes equations for an infinitely stiff body but also for a very flexible body in strong interaction with the surrounding fluid. The shape optimization examples illustrate the potential of the described methods to solve nonlinear multidisciplinary design problems involving strongly coupled fluid-structure interaction.