Topology optimization for stationary fluid–structure interaction problems using a new monolithic formulation

TLDR

Current topology optimization methods struggle with alternating between separate fluid and structural equations and enforcing coupling boundary conditions. The study proposes a monolithic topology optimization procedure for steady‑state fluid–structure interaction problems, replacing alternating fluid and structural domains with a unified domain. The method transforms fluid and structural differential operators to an undeformed configuration using the deformation gradient, inserts pressure divergence and Darcy damping for coupling, and enables topology optimization by interpolating Young's modulus, modified solid pressure, and inverse permeability as design variables. The approach was validated on multiple benchmark problems. © 2009 John Wiley & Sons, Ltd.

Abstract

Abstract This paper outlines a new procedure for topology optimization in the steady‐state fluid–structure interaction (FSI) problem. A review of current topology optimization methods highlights the difficulties in alternating between the two distinct sets of governing equations for fluid and structure dynamics (hereafter, the fluid and structural equations, respectively) and in imposing coupling boundary conditions between the separated fluid and solid domains. To overcome these difficulties, we propose an alternative monolithic procedure employing a unified domain rather than separated domains, which is not computationally efficient. In the proposed analysis procedure, the spatial differential operator of the fluid and structural equations for a deformed configuration is transformed into that for an undeformed configuration with the help of the deformation gradient tensor. For the coupling boundary conditions, the divergence of the pressure and the Darcy damping force are inserted into the solid and fluid equations, respectively. The proposed method is validated in several benchmark analysis problems. Topology optimization in the FSI problem is then made possible by interpolating Young's modulus, the fluid pressure of the modified solid equation, and the inverse permeability from the damping force with respect to the design variables. Copyright © 2009 John Wiley & Sons, Ltd.