Three-dimensional topology optimization of a fluid-structure system using body-fitted mesh adaption based on the level-set method

作者：Li, Hao^*; Kondoh, Tsuguo; Jolivet, Pierre; Furuta, Kozo; Yamada, Takayuki; Zhu, Benliang; Izui, Kazuhiro; Nishiwaki, Shinji

来源：APPLIED MATHEMATICAL MODELLING, 2022, 101: 276-308.

DOI：10.1016/j.apm.2021.08.021

• Topology optimization
• Fluid-structure interaction
• Reaction-diffusion equation
• Body-fitted adaptive mesh
• Level-set method

We propose a new framework for the two-and three-dimensional topology optimization (TO) of the weakly-coupled fluid-structure system. The proposed design methodology uses a reaction-diffusion equation (RDE) for updating the level-set function based on the topological sensitivity. From the numerical point of view, two key ingredients are highlighted: (i) the body-fitted adaptive mesh strategy allows the disjoint reunion of a global mesh that contains several (fluid/solid) subdomains, whose interfaces can be described by an implicitly defined surface (zero level-set); (ii) our framework uses FreeFEM for finite element analysis (FEA) and PETSc for distributed linear algebra. Efficient preconditioner techniques are utilized to solve the large-scale finite element systems. From the engineering stand point, we propose a complete product development workflow including the pre-processing, TO, B-Rep conversion, and the numerical experiment. The performance of our methodology is demonstrated by solving three different optimization problems: compliance, power dissipation, and fluid-structure interaction (FSI). For comparison and for assessing our various techniques, we benchmark our designs against state-of-the-art works followed by showcasing a variety of practical engineering design examples.