Homogenization Based Topology Optimization of a Coupled Thermal Fluid-Structure Problem
Optimisation Topologique basée sur l'Homogénéisation d'un Problème Hydraulique, Thermique et Mécanique Couplées
Résumé
Homogenization method is applied to topology optimization of a weakly coupled three physics problem, where structures are made of periodically perforated material. The microscopic periodic cell is macroscopically modulated, where the design is characterized by the material density and its homogenized Hooke's law at each point of the domain. The coupling is weak because the three physics involved are solved consecutively: first, the coupled fluid flow is determined using Biot-Darcy's law, second, the thermal model using the convection-diffusion equation and third, the three-physic problem by solving the linear poro-thermo elasticity system; our aim is to optimize the homogenized formulation of this system. This approach permits a computationally low cost of evaluation of load sensitivities using the adjoint-state method. Numerical two-dimensional and moderately large-scale three-dimensional two or three-physic problems are presented using the alternate directions algorithm. It is demonstrated how the implementation can address a variety of design problems.
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