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考虑表面层厚度不确定的稳健性拓扑优化方法

李冉 刘书田

李冉, 刘书田. 考虑表面层厚度不确定的稳健性拓扑优化方法[J]. 力学学报, 2021, 53(5): 1471-1479. doi: 10.6052/0459-1879-20-419
引用本文: 李冉, 刘书田. 考虑表面层厚度不确定的稳健性拓扑优化方法[J]. 力学学报, 2021, 53(5): 1471-1479. doi: 10.6052/0459-1879-20-419
Li Ran, Liu Shutian. ROBUST TOPOLOGY OPTIMIZATION OF STRUCTURES CONSIDERING THE UNCERTAINTY OF SURFACE LAYER THICKNESS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1471-1479. doi: 10.6052/0459-1879-20-419
Citation: Li Ran, Liu Shutian. ROBUST TOPOLOGY OPTIMIZATION OF STRUCTURES CONSIDERING THE UNCERTAINTY OF SURFACE LAYER THICKNESS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1471-1479. doi: 10.6052/0459-1879-20-419

考虑表面层厚度不确定的稳健性拓扑优化方法

doi: 10.6052/0459-1879-20-419
基金项目: 1)国家自然科学基金(U1808215)
详细信息
    作者简介:

    2)刘书田, 教授, 主要研究方向: 结构与多学科优化. E-mail: stliu@dlut.edu.cn

    通讯作者:

    刘书田

  • 中图分类号: O343.1

ROBUST TOPOLOGY OPTIMIZATION OF STRUCTURES CONSIDERING THE UNCERTAINTY OF SURFACE LAYER THICKNESS

  • 摘要: 采用增材制造工艺制备结构件时, 较差的成型精度和表面粗糙度会导致结构表面层异质, 引起表面层厚度的不确定性. 为了研究不确定性对拓扑优化结构性能的影响, 进而获得对不确定性具有更低敏感性的结构构型, 提出了考虑结构表面层厚度不确定性的稳健性拓扑优化方法. 首先, 采用一种基于腐蚀操作的表面层识别技术, 通过基于Helmholtz偏微分方程的PDE光滑过滤和基于Heaviside过滤、tanh函数的离散映射两个过程实现表面层异质等效模型的建立. 其次, 将表面层厚度作为服从高斯分布的随机变量, 基于摄动有限元方法开展了不确定性传播的分析和系统随机响应的预测; 以结构柔顺性均值和标准差的加权和作为优化目标, 建立了考虑表面层厚度不确定性的拓扑优化模型, 并推导了目标函数关于设计变量的敏度. 最后, 通过数值算例验证了该方法的有效性. 数值结果表明, 在设计过程中考虑表面层厚度不确定性对结构性能的影响, 可以得到具有更强抵抗不确定性能力的结构构型, 有效提升了结构性能的稳健性.

     

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出版历程
  • 收稿日期:  2020-12-19
  • 刊出日期:  2021-05-18

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