Thermal design of functionally graded cellular structures with multiple microstructure configurations through topology optimization

Functionally graded cellular structures (FGCS) have attracted extensive attention in engineering due to their excellent performance and great flexibility. Focusing on thermal applications, this paper proposes a data -driven topology optimization (TO) approach for FGCS with multiple microstructure configurations. The design process is formulated as two distinct phases: lattice configuration determination at the microscale and material distribution at the macroscale. Specifically, a multi-cut level set method that can generate various graded microstructures (GMs) is performed firstly. For each type of GMs, microstructure instances are sampled by varying the relative densities, and the numerical homogenization algorithm is applied to compute their effective thermal conductivities. Then, a spectral decomposition-based interpolation model is constructed to predict the homogenized properties. After the model preparation at the microscale, a density-based TO method is modified to find the optimized macro-distribution of GMs. A multi-material interpolation approach is adopted to achieve the free selection of controllable types of base cells. At the geometry reconstruction stage, a post -processing method is suggested for improving the structural connectivity. Numerical examples and discussions demonstrate the effectiveness and versatility of the proposed design framework.