Topology Optimization of Fluid-Structure Interaction Problems with Total Stress Equilibrium

TL;DR

This paper advances fluid-structure interaction topology optimization by incorporating total stresses, including viscous effects, and introduces a superconvergent patch recovery technique for improved sensitivity analysis, demonstrated through numerical examples.

Contribution

It extends force coupling to total stresses in FSI topology optimization and develops an analytical sensitivity method verified by complex-step approximation.

Findings

Designs differ when using pressure versus total stress coupling.

Superconvergent patch recovery effectively smooths velocity derivatives.

Numerical examples validate the impact of viscous stresses on optimized structures.

Abstract

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 vs. total stress coupling depending on the flow characteristics of the design problem.