稳态热传导下基于多相材料的一体化设计

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。

Concurrent topology optimization based on multiphase materials under steady thermal conduction

Based on multiphase materials, a concurrent optimization model of macrostructures and porous microstructures is proposed. In this model, the minimized heat compliance is taken as objective function. Structural volume fraction and microstructure mass are taken as constraints. Macro design variables and micro phase design variables are introduced into macrostructures and microstructures independently, and are integrated into one system with elemental phase density. The punishment relationship between elemental phase density and thermal conductive coefficient is built through uniform interpolation model, and the sensitivity of objective function is deduced. To eliminate the checkerboard pattern and mesh-dependence problem, the heat compliance is filtered using a partial differential equation. The effects of material characteristics, heat loads, volume fraction and microstructure mass constraints are discussed with 2D problems. The numerical results indicate that the proposed method is reliable and efficient to the concurrent topology optimization of macrostructures and porous microstructures based on multiphase materials.