吉林大学学报(工学版) ›› 2024, Vol. 54 ›› Issue (10): 2754-2763.doi: 10.13229/j.cnki.jdxbgxb.20221624

• 车辆工程·机械工程 • 上一篇    

考虑几何非线性的多相多孔结构拓扑优化设计

周焕林1(),郭鑫1,王选1,2(),方立雪1,龙凯3   

  1. 1.合肥工业大学 土木与水利工程学院，合肥 230009
    2.天津大学 机械工程学院，天津 300072
    3.华北电力 大学 新能源电力系统国家重点实验室，北京 102206
  • 收稿日期:2022-12-25 出版日期:2024-10-01 发布日期:2024-11-22
  • 通讯作者: 王选 E-mail:zhouhl@hfut.edu.cn;xuanwang@hfut.edu.cn
  • 作者简介:周焕林（1973-），男，教授，博士. 研究方向：反问题与优化.E-mail： zhouhl@hfut.edu.cn
  • 基金资助:
    国家自然科学基金项目(12202129);中央高校科研业务费项目(JZ2022HGTB0291);中国博士后科学基金项目(2022M712358)

Topology optimization design of multiphase porous structures considering geometric nonlinearity

Huan-lin ZHOU1(),Xin GUO1,Xuan WANG1,2(),Li-xue FANG1,Kai LONG3   

  1. 1.College of Civil Engineering，Hefei University of Technology，Hefei 230009，China
    2.School of Mechanical Engineering，Tianjin University，Tianjin 300072，China
    3.State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources，North China Electric Power University，Beijing 102206，China
  • Received:2022-12-25 Online:2024-10-01 Published:2024-11-22
  • Contact: Xuan WANG E-mail:zhouhl@hfut.edu.cn;xuanwang@hfut.edu.cn

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摘要：

本文基于固体各向同性材料惩罚（solid lsotropic material with penalization，SIMP）插值模型提出一种考虑几何非线性效应的多相多孔结构拓扑优化设计方法。通过控制不同材料相的局部体积分数来形成多相多孔结构，利用p-范数将多个局部体积约束聚合为一个全局约束函数，以减少优化问题中的约束个数。采用附加超弹性技术避免几何大变形下的网格畸变问题。最后两个优化算例验证了本文方法的有效性，结果表明：本文方法可以实现不同材料相之间的合理分布，考虑几何非线性效应的多相多孔结构的位移、应力均更小。相比于单材料，考虑多相材料的多孔结构具有更好的性能。

关键词: 机械工程, 多孔结构, 几何非线性, 拓扑优化, 局部体积约束, 多相材料

Abstract:

A topology optimization method of multiphase porous structures considering geometric nonlinearity effects is proposed based on SIMP interpolation model. The multi-phase porous structure is formed by controlling the local volume fraction of different material phases. To reduce the number of constraints in the optimization problem， the p-norm is used to aggregate multiple local volume constraints into a global constraint function. The additional hyperelastic technique is used to avoid mesh distortion under large geometric deformation. Finally， two optimization examples are presented to verify the effectiveness of the proposed method. The optimization results show that the proposed method can achieve reasonable distribution among different material phases， and the displacement and stress of the porous structures considering the nonlinear effect are smaller. Compared with the single material structure， the porous structures composed of multi-materials has better mechanical properties.

Key words: mechanical engineering, porous structure, geometric nonlinearity, topology optimization, local volume constraint, multiphase materials

中图分类号: 

  • O342

图1

悬臂梁设计域"

图2

基于线弹性理论的两相材料多孔结构拓扑优化结果"

图3

考虑几何非线性的两相材料多孔结构拓扑优化果"

图4

考虑几何非线性的目标函数和体积分数的迭代史"

图5

非线性多孔结构的位移云图"

图6

线性多孔结构的位移云图"

图7

非线性多孔结构的应力云图"

图8

线性多孔结构的应力云图"

图9

不同局部体积过滤半径下的两相多孔结构拓扑优结果"

表1

不同局部体积过滤半径下的目标函数和体积分数值"

Casesre柔度实体体积分数材料2体积分数
Case 159.8320.4280.1993
Case 268.8420.4350.1973
Case 378.3570.4440.1986
Case 488.0860.4500.1999

图10

两点固定结构设计域"

图11

基于线弹性理论的两相材料多孔结构拓扑优化结果"

图12

考虑几何非线性的两相材料多孔结构拓扑优化果"

图13

基于线弹性理论的三相材料多孔结构拓扑优化果"

图14

考虑几何非线性的三相材料多孔结构拓扑优化果"

图15

考虑几何非线性的目标函数和体积分数的迭代史"

表2

不同材料相下的柔度值和最大位移值"

材料相数柔度实体体积分数最大位移/mm
单相1.0230.4004.100
两相0.8500.4003.405
三相0.7640.4003.055
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