传热结构自适应拓扑优化准则法研究

合理的散热通道分布是提高小空间大热流密度传热结构散热性能最有效的手段。针对现有传热结构拓扑优化设计结果形态过于复杂，存在棋盘格、灰度单元等数值不稳定现象，提出一种基于基结构的散热通道分布的自适应拓扑优化方法。研究了适用于传热结构拓扑优化问题的基结构构建技术，建立满足库恩-塔克（Kuhn-Tucker，KKT）最优准则条件的迭代公式；以散热弱度最小为优化目标，以杆单元截面积为设计变量，对典型的二维和三维设计问题进行散热通道分布设计，并将设计结果与COMSOL软件优化结果进行对比。研究结果表明，提出的传热结构自适应拓扑优化方法产生的散热通道形态简单清晰，能满足散热性能，且优化过程收敛速度快，克服了现有优化方法产生的数值不稳定问题。

Adaptive Topology Optimization of Heat Transfer Structure by Optimality Criteria

Reasonable heat transfer channel layout is the most effective approach to improve the heat transfer performance of small space with high heat flux. Aiming at the excessively complicated shapes of the design results and numerical instabilities, such as checkerboard phenomenon and gray level units, which exist in the current topology optimization of heat transfer structure, an adaptive topology optimization method of heat transfer channel layout based on ground structure is suggested. Construction technology of ground structure that is suitable for topology optimization problems of heat transfer structure is studied and the iterative formula satisfied Kuhn Tucker optimal criterion condition is derived. The cross sectional areas of the bar units are selected to be the design variables and the minimum of dissipation of heat transport potential capacity is the design objective. The heat transfer channels of typical two dimensional and three dimensional design problems are studied and the designed results are compared with optimization results of COMSOL software. The results show that the produced layout of the heat transfer channels is simple and clear, and the heat transfer capability is better when the adaptive topology optimization method of heat transfer structure is used in optimization processes. The suggested method is more effective than other methods in the rate of convergence. The problems of numerical instabilities happened in current optimization methods are successfully solved by the adaptive topology optimization method of heat transfer structure.