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提出一种基于多相多孔材料的一体化模型。模型以结构散热弱度最小为目标,以结构体积比与材料微结构质量为约束。引入独立的宏观设计变量和微观相设计变量,通过单元相密度建立两类变量间的联系;基于对等混合材料插值模型建立单元相密度与热传导系数间的惩罚关系;推导得到目标函数灵敏度表达式。求解偏微分方程实现单元散热弱度过滤,消除棋盘格及网格依赖性现象。通过二维数值算例讨论并分析了材料特性、热载荷、体积比约束以及质量约束对一体化优化结果的影响。数值实验结果表明,该建模方法在多相材料/结构一体化稳态热传导优化设计中具有可行性和有效性。
An integrated model based on multiphase porous materials was proposed. The model takes the minimum heat dissipation of the structure as the target, and takes the volume ratio of the structure and the microstructure quality as the constraint. Independent macroscopic design variables and micro-phase design variables are introduced to establish the relationship between the two types of variables through the phase density of cells. The penalty relationship between the phase density and thermal conductivity is established based on the equivalent mixed material interpolation model. The objective function sensitivity expression . Solving Partial Differential Equation to Filter Unit Heat Dissipation, Eliminate Checkerboard and Grid Dependency. The effects of material properties, thermal load, volume ratio constraints and mass constraints on the integration optimization results are discussed and analyzed through two-dimensional numerical examples. The numerical results show that the proposed method is feasible and effective in the optimal design of steady-state heat conduction in multiphase materials / structures.