Density-based topology optimization of high-fidelity fluid-structure interaction problems with large deformations

The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure interactions is still lagging behind, mainly due to the multidisciplinary and complex nature of such systems. In this work, we implement topology optimization of high-fidelity, fully-coupled fluid-structure interaction problems with large deformations. The fluid is incompressible and the flow conditions are steady-state and laminar with a Reynolds number of unity. We use the arbitrary Lagrangian–Eulerian approach to deform the fluid mesh as a pseudo-structural system such that structural deformations are completely reflected in the fluid flow mesh. The fluid-structure interaction problem is formulated using the three-field formulation (i.e., fluid, solid, and moving mesh) and the sensitivity analysis is derived using the discrete adjoint approach. The topology optimization problem is the compliance minimization of a column in channel standard benchmark problem with a constraint on the volume fraction of the structure. We show through numerical examples how the topology optimization of fluid-structure interaction problem with large deformations is highly sensitive to the selection of the projection and interpolation parameters, whose number increase with the inclusion of the fluid mesh field. On the positive side, we show the impact of considering structural deformations in the fluid mesh on the optimized design in comparison to the fixed mesh topology optimization of fluid-structure interaction problem.