Topology optimization of microstructures with maximum heat transfer and stiffness based on floating projection

Multi-functional microstructure design with high stiffness and thermal conductivity provides an effective solution to meet the lightweight and thermal management requirements of aerospace applications. A framework for multi-functional microstructure design is developed based on floating projection topology optimization. The energy-based homogenization methodology is employed to assess the equivalent macroscopic thermal conductivity and stiffness of microstructures. The weighting method is utilized to ascertain the relative importance of two normalized optimization objectives. The competition between the mechanical performance and thermal behavior of materials forming composites is considered. In the multi-material design, one material demonstrates a higher Young's modulus, while another exhibits higher thermal conductivity. The ambiguity of physical meaning and the challenge of convergence caused by material penalty are addressed by the linear material model. By systematically modifying the weight factor, a set of optimal Pareto solutions is generated. A comprehensive view of the trade-offs between mechanical and thermal properties is provided by the Pareto front which facilitates the design of microstructures with distinctive functional characteristics. This framework provides a scalable approach for optimizing multi-functional composite materials and can be extended to incorporate additional material properties or functional requirements.