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

Abstract

SUMMARYThis 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.

Topology optimization for submerged buoyant structures

“…These works showed that pressure loading problems can be efficiently solved with density-based topology optimization by using different pressure boundaries modeling techniques. The idea of using mixed element formulations by Sigmund and Clausen (2007) could be further applied in a range of different multiphysics problems (Yoon, Jensen and Sigmund 2007;Yoon and Sigmund 2008;Yoon 2010).…”

Topology optimization of inertia driven dosing units

“…heat (Yoon, 2010a;Marck et al, 2013;Alexandersen et al, 2016). Models for including the fluid structure interaction have been developed as demonstrated in Yoon (2010b) and Kreissl et al (2010). In this work, the deformations of the component are assumed negligible, and thus the solid is assumed infinitely stiff and no interaction is modeled.…”

Multiscale modeling and topology optimization of poroelastic actuators

“…The application of topology optimization to fluid structure interaction problems has only recently been approached. Yoon (2010) presented a method for converting the interface stresses to a volume integral which is suited for a monolithic formulation. Kreissl et al (2010) presented a one way coupling used for the design of flexible micro-fluidic devices.…”