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基于变体积约束的阻尼材料微结构拓扑优化研究

张东东 栾福强 赵礼辉 郑玲

张东东,栾福强,赵礼辉,郑玲. 基于变体积约束的阻尼材料微结构拓扑优化研究 [J]. 应用数学和力学,2022,43(6):648-659 doi: 10.21656/1000-0887.420206
引用本文: 张东东,栾福强,赵礼辉,郑玲. 基于变体积约束的阻尼材料微结构拓扑优化研究 [J]. 应用数学和力学,2022,43(6):648-659 doi: 10.21656/1000-0887.420206
ZHANG Dongdong, LUAN Fuqiang, ZHAO Lihui, ZHENG Ling. Research on Topology Optimization of Damping Material Microstructures With Varied Volume Constraints[J]. Applied Mathematics and Mechanics, 2022, 43(6): 648-659. doi: 10.21656/1000-0887.420206
Citation: ZHANG Dongdong, LUAN Fuqiang, ZHAO Lihui, ZHENG Ling. Research on Topology Optimization of Damping Material Microstructures With Varied Volume Constraints[J]. Applied Mathematics and Mechanics, 2022, 43(6): 648-659. doi: 10.21656/1000-0887.420206

基于变体积约束的阻尼材料微结构拓扑优化研究

doi: 10.21656/1000-0887.420206
基金项目: 上海市青年科技英才扬帆计划(18YF1418500)
详细信息
    作者简介:

    张东东(1986—),男,副教授,博士,硕士生导师 (通讯作者. E-mail:dongdongzhang@usst.edu.cn

  • 中图分类号: TB53

Research on Topology Optimization of Damping Material Microstructures With Varied Volume Constraints

  • 摘要:

    阻尼复合结构的抑振性能取决于材料布局和阻尼材料特性。该文提出了一种变体积约束的阻尼材料微结构拓扑优化方法,旨在以最小的材料用量获得具有期望性能的阻尼材料微结构。基于均匀化方法,建立阻尼材料三维微结构有限元模型,得到阻尼材料的等效弹性矩阵。逆用Hashin-Shtrikman界限理论,估计对应于期望等效模量的阻尼材料体积分数限,并构建阻尼材料体积约束限的移动准则。将获得阻尼材料微结构期望性能的优化问题转化为体积约束下最大化等效模量的优化问题,建立阻尼材料微结构的拓扑优化模型。利用优化准则法更新设计变量,实现最小材料用量下的阻尼材料微结构最优拓扑设计。通过典型数值算例验证了该方法的可行性和有效性,并讨论了初始微构型、网格依赖性和弹性模量等对阻尼材料微结构的影响。

  • 图  1  含阻尼材料微结构的夹层阻尼结构示意图:(a) 夹层阻尼结构;(b)阻尼材料变形图;(c)阻尼材料三维微结构

    Figure  1.  Schematic drawings of a sandwich damping structure with a damping core microstructure: (a) the sandwich damping structure; (b) the deformation of the damping core; (c) the 3D microstructure of the damping core

    图  2  阻尼材料单胞初始构型A

    Figure  2.  Initial configuration A of the damping material unit cell

    图  3  基于初始构型A获得阻尼材料单胞微结构拓扑优化结果

    Figure  3.  Topology optimization results of the damping material unit cell microstructure for initial configuration A

    图  4  阻尼材料初始构型:(a) 阻尼材料初始构型B; (b) 阻尼材料初始构型C

    Figure  4.  The initial configurations of the damping material unit cell:(a) initial configuration B of the damping material unit cell; (b) initial configuration C of the damping material unit cell

    图  5  基于初始构型B获得阻尼材料单胞微结构拓扑优化结果

    Figure  5.  Topology optimization results of the damping material unit cell microstructure for initial configuration B

    图  6  基于初始构型C获得阻尼材料单胞微结构拓扑优化结果

    Figure  6.  Topology optimization results of the damping material unit cell microstructure for initial configuration C

    图  7  单胞初始构型A优化结果(15 × 15 × 15)

    Figure  7.  Topology optimization results of initial configuration A (15 × 15 × 15)

    图  8  单胞初始构型A优化结果(25 × 25 × 25)

    Figure  8.  Topology optimization results of initial configuration A (25 × 25 × 25)

    图  9  单胞初始构型A优化结果(30 × 30 × 30)

    Figure  9.  Topology optimization results of initial configuration A (30 × 30 × 30)

    图  10  基于初始构型A的拓扑优化结果(Ev=10 MPa)

    Figure  10.  Topology optimization results of initial configuration A (Ev=10 MPa)

    图  11  基于初始构型A的拓扑优化结果(Ev=15 MPa)

    Figure  11.  Topology optimization results of initial configuration A (Ev=15 MPa)

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出版历程
  • 收稿日期:  2021-07-06
  • 修回日期:  2021-11-27
  • 网络出版日期:  2022-05-26
  • 刊出日期:  2022-06-30

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