Homogenization based topology optimization of a coupled thermal fluid-structure problem

This article focuses on the topology optimization of a weakly coupled three physics problem. The structures are made of periodically perforated material, where the microscopic periodic cell is macroscopically modulated. The objective is to optimize the homogenized formulation of this system, where the coupling is weak because the three physics involved are solved consecutively: first, a coupled fluid flow is determined using the Biot-Darcy's law for the fluid domain, second, a thermal model using the convection-diffusion equation for the whole domain, and third, a three-physics problem by solving the linear poro-thermo elasticity problem in the solid domain. This approach allows low computational cost of evaluation of load sensitivities using the adjoint-state method. Two-dimensional and three-dimensional numerical problems are presented using the alternate directions algorithm. It is demonstrated how the implementation makes it possible to treat a variety of design problems.