On the Application of Total Traction Equilibrium in Topology Optimization of Fluid-Structure Interactions
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This work investigates the different techniques of enforcing traction equilibrium in topology optimization of fluid-structure interaction problems. In literature, force coupling between the solid and the fluid domains is usually achieved using internal volume integrals of hydrostatic stresses. In this work, we extend the traction equilibrium condition to include the viscous stress components as well as the hydrostatic components in what is termed the total stress formulation. We also investigate the different force calculation techniques, and how the mixed finite element formulation results in two conflicting approaches; external surface vs. internal volume integrals. Lastly, a numerical experiment reveals the effects of the different force coupling techniques on the optimized designs with commentary on complexity of implementation and convergence behaviour.
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