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高承载梯度分层点阵结构的拓扑优化设计方法

黄垲轩 丁喆 张严 李小白

黄垲轩, 丁喆, 张严, 李小白. 高承载梯度分层点阵结构的拓扑优化设计方法. 力学学报, 2023, 55(2): 294-305 doi: 10.6052/0459-1879-22-363
引用本文: 黄垲轩, 丁喆, 张严, 李小白. 高承载梯度分层点阵结构的拓扑优化设计方法. 力学学报, 2023, 55(2): 294-305 doi: 10.6052/0459-1879-22-363
Huang Kaixuan, Ding Zhe, Zhang Yan, Li Xiaobai. Topological optimization design method of layer-wise graded lattice structures with high load-bearing. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 294-305 doi: 10.6052/0459-1879-22-363
Citation: Huang Kaixuan, Ding Zhe, Zhang Yan, Li Xiaobai. Topological optimization design method of layer-wise graded lattice structures with high load-bearing. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 294-305 doi: 10.6052/0459-1879-22-363

高承载梯度分层点阵结构的拓扑优化设计方法

doi: 10.6052/0459-1879-22-363
基金项目: 国家自然科学基金(52205280, 51805383), 湖北省自然科学基金(2022CFB632), 中国博士后科学基金(2021M692486, 2022M722484)和数字制造装备与技术国家重点实验室开放基金(DMETKF2022017)资助项目
详细信息
    通讯作者:

    丁喆, 副教授, 主要研究方向为阻尼结构系统动力学分析及优化研究. E-mail: dingzhe@wust.edu.cn

  • 中图分类号: O342

TOPOLOGICAL OPTIMIZATION DESIGN METHOD OF LAYER-WISE GRADED LATTICE STRUCTURES WITH HIGH LOAD-BEARING

  • 摘要: 随着增材制造技术的迅速发展, 点阵结构由于其高比强度、高比刚度等优异力学性能受到广泛关注, 但其单胞分布设计大多基于均布式假设, 导致其承载能力相对较差. 基于拓扑优化技术提出了一种梯度分层的点阵结构设计方法. 首先, 基于水平集函数建立点阵单胞几何构型的显式描述模型, 引入形状插值技术实现点阵单胞的梯度构型生成; 其次, 构建基于Kriging的梯度点阵单胞宏观等效力学属性预测模型, 建立宏观有限单元密度与微观点阵单胞等效力学属性的内在联系; 然后, 以点阵结构刚度最大为优化目标, 结构材料用量和力学控制方程为约束条件, 构建点阵结构的梯度分层拓扑优化模型, 并采用OC算法进行数值求解. 算例结果表明, 所提方法可实现点阵结构的最优梯度分层设计, 充分提高了点阵结构的承载性能, 同时可保证不同梯度点阵单胞之间的几何连续性. 最后, 开展梯度分层点阵结构与传统均匀点阵结构和线性梯度点阵结构的准静态压缩仿真分析, 仿真结果表明, 与传统均匀点阵结构和线性梯度点阵结构相比, 梯度分层点阵结构的承载能力明显提高. 研究结果可为高承载点阵结构设计提供理论参考.

     

  • 图  1  梯度分层点阵结构

    Figure  1.  Structure with layer-wise graded lattices

    图  2  二维点阵微结构

    Figure  2.  2D lattice microstructure

    图  3  三维水平集函数及等值面

    Figure  3.  3D level set function and contour

    图  4  三维点阵微结构

    Figure  4.  3D lattice microstructure

    图  5  四维水平集函数及等值面

    Figure  5.  4D level set function and contour

    图  6  梯度点阵结构拓扑优化设计流程图

    Figure  6.  Flowchart of topology optimization for the design of graded lattice structures

    图  7  均布载荷的二维设计域

    Figure  7.  2D design domain under uniformly distributed load

    图  8  设计域30 cm × 15 cm目标函数及体积分数迭代图

    Figure  8.  Iterations of objective function and volume fraction for design domain 30 cm × 15 cm

    图  9  MBB点阵结构设计域

    Figure  9.  3D design domain of the MBB lattice structure

    图  10  设计域40 cm × 15 cm × 10 cm目标函数及体积分数迭代图

    Figure  10.  Iterations of objective function and volume fraction for design domain 40 cm × 15 cm × 10 cm

    图  11  均布斜载荷下的柱状设计域

    Figure  11.  3D design domain of a culumn under uniformly distributed oblique load

    图  12  15 cm × 20 cm × 10 cm立体构型及微结构

    Figure  12.  The structure and microstructure of example 15 cm × 20 cm × 10 cm

    图  13  迭代步时间

    Figure  13.  Time of an iteration step

    图  14  750 mm × 750 mm点阵结构应力云图及变形图

    Figure  14.  Stress and deformation diagrams of lattice structures 750 mm × 750 mm

    图  15  二维应力应变曲线

    Figure  15.  2D stress-strain curves

    图  16  90 mm × 120 mm × 60 mm点阵结构应力云图及变形图

    Figure  16.  Stress and deformation diagrams of lattice structures 90 mm × 120 mm × 60 mm

    图  17  三维应力应变曲线

    Figure  17.  3D stress-strain curves

    表  1  设计域30 cm × 15 cm结构图及柔度

    Table  1.   The structure and compliance of design domain 30 cm × 15 cm

    UniformLinear gradedTopology gradedRelative density
    structure
    compliance124.24 N·cm88.84 N·cm60.55 N·cm
    下载: 导出CSV

    表  2  设计域15 cm × 15 cm结构图及柔度

    Table  2.   The structure and compliance of design domain 15 cm × 15 cm

    UniformLinear gradedTopology gradedRelative density
    structure
    compliance293.04 N·cm229.45 N·cm172.34 N·cm
    下载: 导出CSV

    表  3  设计域40 cm × 15 cm × 10 cm结构图及柔度

    Table  3.   The structure and compliance of design domain 40 cm × 15 cm × 10 cm

    UniformLinear gradedTopology gradedRelative density
    structure
    compliance10171.05 N·cm13759.11 N·cm4979.70 N·cm
    下载: 导出CSV

    表  4  设计域15 cm × 20 cm × 10 cm结构图与柔度

    Table  4.   The structure and compliance of design domain 15 cm × 20 cm × 10 cm

    UniformLinear gradedTopology gradedRelative density
    structures
    compliance8165.04 N·cm7708.78 N·cm6945.11 N·cm
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-08-08
  • 录用日期:  2023-01-02
  • 网络出版日期:  2023-01-03

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