Integrating perimeter constraints into topology optimization of thermal conduction structures considering the manufacturing efficiency

Abstract

Topology optimization has the advantages of large design freedom and optimization searching space. Hence, it has been introduced into the topology optimization of structures with excellent thermal conductive properties with given volume constraints. However, the optimized structures contain a lot of complex geometry, which increases the difficulty and cost of manufacturing. To address these challenges by balancing the manufacturing cost and thermal conductivity property, a perimeter-constrained topology optimization method for thermal conduction structures is proposed. First, the structural boundaries are extracted by using the modified two-step filter and projection process, which directly relates to the manufacturing costs. Subsequently, the perimeter constraint is integrated into the formulation of the topology optimization model based on Solid Isotropic Material with Penalization (SIMP), and the thermal compliance is set as the objective function. Then, the sensitivity analysis is derived for both the constraints and objective function, and the method of moving asymptotes (MMA) is used to solve the model iteratively. Finally, several numerical examples are conducted to show the performance of the proposed method for topology optimization of heat conduction structure under various boundary conditions. The average temperature of the examples only improved by 2–3 K under the condition that the perimeter is reduced by 50 % of the conventional results. The results validate the effectiveness of the proposed method for the ability to balance the manufacturing costs and the thermal conductivity property of the optimized structure according to the requirements of the designers.