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为了实现基于宏观热传导条件的周期性材料微结构设计,建立了基于固体各向同性材料惩罚法的周期性结构拓扑优化模型.模型以体积比为约束,散热弱度最小为优化目标.为了满足周期性约束,将设计域划分为若干相同子区域,并重新分配散热弱度.基于偏微分方程的图像处理方式可以有效地消除棋盘格和网格依赖性现象.讨论并分析了不同子区域个数及不同载荷工况对拓扑优化构型的影响.数值实验结果表明:周期性结构的建模方式可以实现基于宏观稳态热传导条件的周期性材料微结构设计.子区域个数不同时,优化得到不同的微结构构型,这反映了尺寸效应对材料设计的影响.当子区域个数不断增加时,优化结果逐渐趋向收敛于均匀化方法对应的极限值.
In order to realize the microstructure design of periodic materials based on macroscopic heat conduction conditions, a periodic structural topology optimization model based on the solid isotropic material penalty method is established. The model is constrained by the volume ratio and the minimum heat dissipation weakness as the optimization objective. And the constraint of sex, the design domain is divided into several same sub-regions, and the heat dissipation weakness is redistributed. The image processing method based on partial differential equation can effectively eliminate the checkerboard grid and the grid-dependent phenomenon.We discuss and analyze the number of different sub-regions And the effect of different load conditions on the topology optimization.The numerical results show that the periodic structure modeling method can realize the periodic material microstructure design based on the macroscopic steady state heat conduction conditions.When the number of subregions is different, Different microstructure configurations, which reflects the effect of size effect on material design.When the number of sub-regions increases, the optimization results tend to converge to the corresponding limits of the homogenization method.