Topology optimization of multi-material for the heat conduction problem based on the level set method
Topology optimization of multi-material for the heat conduction problem based on the level set method
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DOI：
10.1080/03052150903443780
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发表时间：
2010-06
影响因子：
2.7
通讯作者：
Chungang Zhuang;Z. Xiong;H. Ding
中科院分区：
文献类型：
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作者：
Chungang Zhuang;Z. Xiong;H. Ding
提出了一种多材料热传导问题的拓扑优化数值方法。多相水平集模型用于隐式描述不同电导率材料区域的几何边界。多材料表示模型没有中间密度的出现。优化的目标是构造出最佳的导热路径，以提高传热效率。以热输运势容耗散为目标函数。灵敏度分析采用伴随变量法，这是构造水平集方程速度场的基础。优化结果通过多材料边界的演化逐步实现，拓扑变化在优化过程中得到自然处理。最后通过数值算例验证了该方法在热传导问题拓扑优化中的可行性和有效性。
This article presents a numerical approach of topology optimization with multiple materials for the heat conduction problem. The multiphase level set model is used to implicitly describe the geometric boundaries of material regions with different conductivities. The model of multi-material representation has no emergence of the intermediate density. The optimization objective is to construct the optimal heat conductive paths which improve the efficiency of heat transfer. The dissipation of thermal transport potential capacity is taken as the objective function. The sensitivity analysis is implemented by the adjoint variable method, which is the foundation of constructing the velocity field of the level set equation. The optimal result is gradually realized by the evolution of multi-material boundaries, and the topological changes are naturally handled during the optimization process. Finally, the numerical examples are presented to demonstrate the feasibility and validity of the proposed method for topology optimization of the heat conduction problem.