Abstract This paper proposes a novel multi-scale topology optimization method to obtain a design that cannot be achieved by single-scale topology optimization for heat flux manipulation in heat conduction problems. The optimal designs are derived using a multi-scale topology optimization method for shielding, concentrating, and reversing the heat flux over the objective domain. A single variable formulation is proposed to avoid underestimating the material property. The micro-scale design variables are updated by the method of moving asymptotes with design sensitivity derived by the adjoint variable method. The validity and effectiveness of this method are shown by comparing the performance measure and the computing time to the single-scale topology optimization method. The results show that the multi-scale approach achieved better performance over the various composition ratios of the high-conductive material than the single-scale method and converged about 20 times faster.

中文翻译：

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使用单变量公式化多尺度拓扑优化方法控制热通量

摘要 本文提出了一种新的多尺度拓扑优化方法，以获得单尺度拓扑优化无法实现的热传导问题中热通量操纵的设计。优化设计是使用多尺度拓扑优化方法导出的，用于屏蔽、集中和反转目标域上的热通量。提出了单一变量公式以避免低估材料特性。微尺度设计变量通过移动渐近线的方法更新，设计灵敏度由伴随变量方法导出。通过将性能指标和计算时间与单尺度拓扑优化方法进行比较，证明了该方法的有效性和有效性。