Efficient Representation and Optimization of TPMS-Based Porous Structures for 3D Heat Dissipation

Abstract Triply periodic minimal surfaces (TPMSs) have been widely used in many engineering fields, including tissue engineering, lightweight manufacturing, and biomedicine. Although TPMSs have many nice properties that make them very suitable for thermal property analysis, there has been little work that has applied TPMSs in this important field due to the high complexity of representation and optimization. This paper presents an efficient representation and optimization of TPMS-based porous structures for heat dissipation. First, the porous structure is established by a function representation that is derived by the function representations of TPMSs. It inherits the good properties of TPMSs, such as high surface-to-volume ratio, full connectivity, high smoothness, and controllability. Then, according to the steady-state heat conduction equation, the heat dissipation problem can be formulated into a minimization problem dealing with the mean temperature distribution using the given constraints. Next, to solve the problem directly on function representation without remeshing, an efficient optimization method with global–local interpolation is exploited. Finally, we obtain the optimized porous shell structures with smooth period and wall-thickness changes. Different from traditional TPMS-based methods, the proposed approach provides both efficient function representation and optimization of TPMS-based porous shell structures for heat dissipation. Various experiments were conducted showing that the proposed porous structures have obvious advantages in terms of efficiency and effectiveness.