Topological design of thermal conductors using functionally graded materials

This study presents a novel method for the structural design of thermal conductors using functionally graded materials (FGMs). The effective thermal conductivity tensor components of the unit structure of the FGM composite were obtained using the representative volume element (RVE) homogenization method under periodic boundary conditions. In addition, a machine learning method of neural network fitting was applied to the dis-cretized RVE data to build a prediction module that derives the effective thermal conductivity corresponding to the continuous shape change of the unit structure. In this study, thermal-conduction optimization problems are considered for various dimensions of the design domain and thermal boundary conditions to minimize the thermal compliance and constraints of volume fractions for each material constituting the composite. Through the optimization process, the overall topological layout of the composite and local layout of the fibrous material were simultaneously optimized to maximize the thermal-conduction performance of the structure. Several nu-merical examples were used to validate the proposed method. Finally, the de-homogenization projection method was applied to the obtained topology optimization results to convert the complex micro-scale structures to a manufacturable level.