This paper presents topology optimization of nonlinear heat conduction problems with multiple domains and multiple constraints, including regional temperature and material volume for reducing temperature. Maximum approximation temperatures in the constraint regions are accurately and dynamically calculated, though temperature and temperature-dependent thermal conductivity change with the update of material distribution. A temperature measure with constant error to approximate regional maximum temperature is adaptive to different temperature ranges. A strategy of hole nucleation generation combined with the regional temperature constraints is presented for the level set-based topology optimization. The solid isotropic material with penalization (SIMP) and parametrized level set methods are compared for the temperature-constrained topology optimization. Finally, several numerical examples are solved by the SIMP and parametrized level set methods. The results demonstrate that the proposed approach can obtain intricate topological details and reduce regional temperatures for the nonlinear heat conduction problems.

中文翻译：

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非线性热传导问题的温度约束拓扑优化

本文介绍了具有多域和多约束的非线性热传导问题的拓扑优化，包括区域温度和用于降低温度的材料体积。尽管温度和温度相关的热导率随着材料分布的更新而变化，但约束区域中的最大近似温度会被准确且动态地计算出来。近似区域最高温度的具有恒定误差的温度测量适用于不同的温度范围。针对基于水平集的拓扑优化，提出了一种结合区域温度约束的空穴成核策略。比较了带惩罚的固体各向同性材料 (SIMP) 和参数化水平集方法，用于温度约束拓扑优化。最后，通过SIMP和参数化水平集方法求解了几个数值例子。结果表明，所提出的方法可以获得复杂的拓扑细节并降低非线性热传导问题的区域温度。