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徐胜利 程耿东. 基于自适应网格的材料渗透系数设计[J]. 力学学报, 2010, 42(2): 238-244. DOI: 10.6052/0459-1879-2010-2-2008-730
引用本文: 徐胜利 程耿东. 基于自适应网格的材料渗透系数设计[J]. 力学学报, 2010, 42(2): 238-244. DOI: 10.6052/0459-1879-2010-2-2008-730
Shengli Xu, Gengdong Cheng. Material design of permeability coefficient based on adaptive mesh[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(2): 238-244. DOI: 10.6052/0459-1879-2010-2-2008-730
Citation: Shengli Xu, Gengdong Cheng. Material design of permeability coefficient based on adaptive mesh[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(2): 238-244. DOI: 10.6052/0459-1879-2010-2-2008-730

基于自适应网格的材料渗透系数设计

Material design of permeability coefficient based on adaptive mesh

  • 摘要: 采用基于单元(结点)密度为设计变量进行结构和材料的拓扑优化设计时,有限元网格的密度对优化设计有很大影响. 在以渗透系数为目标进行材料微结构设计时,为了较好地描述单胞中的流固边界,需要将单胞划分为很小的网格,进一步增加了有限元计算和优化分析的规模. 为了降低计算规模, 研究了基于自适应网格的逆均匀化方法,以最大化各向同性等效渗透系数为目标,进行材料微结构设计. 优化迭代过程中,对单胞中流固界面处的网格进行自适应加密,降低优化问题的计算规模. 采用这一算法,对不同初始密度分布得到的单胞优化结果虽然不同,但具有相同的材料微结构,一定程度上说明了该方法的有效性.

     

    Abstract: Finite element mesh size has considerable effect on theresult of optimum design when the topology optimization method based ondesign variable of element (node) is used to design structure and material.The cell should be divided into very small size grids for no-slip boundarycondition at fluid-solid interface in microstructure design of materialpermeability. Material microstructure design with inverse homogenizationmethod based on adaptive mesh is studied in this paper. The objectivefunction is maximizing isotropic permeability coefficient. The finiteelement mesh near fluid-solid interface will be refined adaptively duringoptimization iteration process for decreasing computing scale ofoptimization problem. With this algorithm, the material microstructure isobtained to be uniform from different initial density distributions. Theresult illustrates the effectiveness of our method.

     

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