考虑拓扑相关热载荷的散热结构多相材料拓扑优化设计

doi:10.3969/j.issn.1004-132X.2020.20.002

摘要/Abstract

摘要： 针对热传导拓扑优化设计过程中拓扑相关热载荷问题，以结构散热弱度为目标函数，体积分数为约束条件，构建了多相材料散热结构拓扑优化数学模型。采用一种基于变密度理论的有序固体各向同性微结构材料惩罚模型法构建多相材料插值模型，分别进行拓扑相关热载荷与拓扑独立热载荷作用下的灵敏度分析，借助优化准则法推导设计变量的迭代格式，引入偏微分方程过滤方法抑制优化过程中出现的数值不稳定现象。通过2D与3D数值模型计算，获得考虑拓扑相关热载荷、拓扑独立热载荷以及耦合拓扑独立/相关热载荷在不同边界条件下对拓扑优化结果的影响规律。结果证明了所提方法在解决拓扑相关热载荷作用下散热结构多相材料拓扑优化设计问题方面的有效性与可行性。

关键词: 多相材料, 热传导, 拓扑优化, 拓扑相关, 散热弱度

Abstract: Considering the topology-dependent heat source problems in the heat conduction topology optimization design, the mathematical model of multi-phase material topology optimization of heat dissipation structures was constructed. The objective function was assigned to dissipation of heat potential capacity, combined with volume fraction constraint conditions. The variable density theory was introduced to represent the multi-phase material interpolation model based on ordered-solid isotropic microstructures with penalization (Ordered-SIMP) methodology. Then the sensitivity analysis of topology-dependent and topology-independent heat sources was executed respectively, and the iteration format of design variables were solved by optimization criterion. The partial differential equation filter method was implemented to suppress numerical instability in the optimization processes. Through the 2D/3D numerical models, the meaningful conclusions of topology-dependent heat sources, topology-independent heat sources and coupled heat sources were illustrated under different boundary conditions. The proposed method is effective and feasible in solving the multi-phase material topology optimization problem of topology-dependent heat sources.

Key words: multi-phase material, heat conduction, topology optimization, topology dependent, dissipation of heat potential capacity

中图分类号:

TH122
O39

赵清海1,2;张洪信2;蒋荣超2;华青松1,2;袁林2. 考虑拓扑相关热载荷的散热结构多相材料拓扑优化设计[J]. 中国机械工程, DOI: 10.3969/j.issn.1004-132X.2020.20.002.

ZHAO Qinghai1,2;ZHANG Hongxin2;JIANG Rongchao2;HUA Qingsong1,2;YUAN Lin2. Multi-phase Material Topology Optimization Design of Heat Dissipation Structures Considering Topology-dependent Heat Sources[J]. China Mechanical Engineering, DOI: 10.3969/j.issn.1004-132X.2020.20.002.

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