Topology optimization of fluid-structure interaction problems with total stress equilibrium

This work extends force coupling in the topology optimization of fluid-structure interaction problems from hydrostatic to total stresses through the inclusion of viscous stress components. The superconvergent patch recovery technique is implemented to remove the discontinuities in velocity derivatives over the finite elements boundaries. The sensitivity analysis is derived analytically for the superconvergent patch recovery approach and further verified through the use of the complex-step derivative approximation method. Numerical examples demonstrate a differentiation in the optimized designs using pressure versus total stress coupling depending on the flow characteristics of the design problem.