基于联合仿真的曲面共形多孔结构拓扑优化方法

付君健; 徐勇; 周祥曼; 舒正涛; 田启华

doi:10.13700/j.bh.1001-5965.2022.0751

基于联合仿真的曲面共形多孔结构拓扑优化方法

doi: 10.13700/j.bh.1001-5965.2022.0751

付君健^{1, 2, 3},
徐勇²,
周祥曼^{1, 2, ,},
舒正涛²,
田启华^{1, 2}

1.
水电机械设备设计与维护湖北省重点实验室，宜昌 443002
2.
三峡大学机械与动力学院，宜昌 443002
3.
智能制造装备与技术全国重点实验室，武汉 430074

基金项目: 国家自然科学基金(51775308)；湖北省自然科学基金(2021CFB236)；智能制造装备与技术全国重点实验室开放基金(IMETKF2023016)

详细信息

通讯作者:
E-mail：zhouxman@ctgu.edu.cn

中图分类号: TH112
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- 文章访问数: 103
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- PDF下载量: 18
- 被引次数: 0
出版历程
- 收稿日期: 2022-08-31
- 录用日期: 2023-01-14
- 网络出版日期: 2023-02-28
- 整期出版日期: 2024-09-27

Topological optimization method for conformal cellular structures on surfaces based on co-simulation

FU Junjian^{1, 2, 3},
XU Yong²,
ZHOU Xiangman^{1, 2
, ,},
SHU Zhengtao²,
TIAN Qihua^{1, 2}

1.
Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance，Yichang 443002，China
2.
College of Mechanical & Power Engineering，China Three Gorges University，Yichang 443002，China
3.
Stale Key Laboratory of Intelligent Manufacturing Equipment and Technology, Wuhan 430074, China

Funds: National Natural Science Foundation of China (51775308); Natural Science Foundation of Hubei Province (2021CFB236); Open Fund of Stale Key Laboratory of Intelligent Manufacturing Equipment and Technology (IMETKF2023016)

More Information

Corresponding author: E-mail：zhouxman@ctgu.edu.cn

摘要

摘要:
针对宏观曲面结构上多孔结构单胞构型与设计域外形不匹配，导致曲面结构优化困难的问题，提出一种基于联合仿真的曲面共形多孔结构拓扑优化方法。基于三周期极小曲面隐式水平集函数，实现多孔结构的参数化建模。采用等参单元法理论，建立自然坐标系到笛卡儿坐标系的映射关系，实现曲面多孔结构的共形建模。构造线性插值函数，保证多孔结构单胞之间的C⁰连续。引入可变切割水平集函数，建立MATLAB与ANSYS联合仿真的多孔结构拓扑优化框架。数值算例表明：所提方法可有效实现曲面多孔结构的拓扑优化设计，确保多孔结构单胞与设计域外形的匹配，提升多孔结构的力学性能。
- 拓扑优化 /
- 多孔结构 /
- 共形建模 /
- 可变切割水平集函数 /
- 联合仿真
Abstract:
The optimization design for structures with surface is challenging due to the mismatch between cellular unit cell configuration and the design domain shape. Thus, a topological optimization design method for conformal cellular structures on surfaces based on co-simulation is proposed. The parametric modelling of cellular structures is achieved by utilising the implicit level set functions derived from triply periodic minimal surfaces. By using the isoparametric element method, the mapping relationship between the natural coordinate system and the cartesian coordinate is established to realize the conformal modeling of the cellular structures on surfaces. A linear interpolation function is constructed to ensure the C⁰ continuity of the cellular unit cell. An optimization framework for cellular structures is built by combining MATLAB and ANSYS with the use of variable cutting level set functions.Numerical examples show that this method can effectively realize the topological optimization design of cellular structures on surfaces. The method also ensures the matching of the cellular structures unit cell with the shape of the design domain, and improves the mechanical properties of the cellular structures.
- topology optimization /
- cellular structures /
- conformal modeling /
- variable cutting level set function /
- co-simulation

HTML全文

图 1 三周期极小曲面多孔结构

Figure 1. Triply periodic minimal surfaces based cellular structures

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图 2 P型单胞共形建模

Figure 2. Conformal modeling of P unit cell

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图 3 多孔结构建模过程

Figure 3. Modeling of cellular structures

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图 4 局部插值模型

Figure 4. Local interpolation model

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图 5 几何突变的梯度多孔结构

Figure 5. Graded cellular structures with abrupt geometric features

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图 6 几何连续的梯度多孔结构

Figure 6. Graded cellular structures with geometric continuity

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图 7 联合仿真程序流程

Figure 7. Flow of co-simulation program

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图 8 圆筒结构设计域

Figure 8. Design domain of cylinder structure

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图 9 圆筒结构有限元网格划分

Figure 9. Finite element meshing of cylinder structure

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图 10 圆筒结构优化迭代曲线

Figure 10. Optimize iterative curve of cylinder structure

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图 11 圆筒结构最优拓扑构型

Figure 11. The optimal configuration of cylinder structure

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图 12 预定义单胞及结构设计域

Figure 12. Predefined unit cell and structural design domains

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图 13 自由曲面结构有限元网格划分

Figure 13. Finite element meshing of free-form surface structure

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图 14 自由曲面结构优化迭代曲线

Figure 14. Optimize iterative curve of free-form surface structure

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图 15 自由曲面结构最优拓扑构型

Figure 15. Optimal configuration of free-form surface structure

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图 16 预定义单胞及结构设计域

Figure 16. Predefined unit cell and structural design domains

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图 17 曲面夹层结构有限元网格划分

Figure 17. Finite element meshing of curving sandwich structure

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图 18 曲面夹层结构优化迭代曲线

Figure 18. Optimize iterative curve of curving sandwich structure

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图 19 曲面夹层结构最优拓扑构型

Figure 19. Optimal configuration of curving sandwich structure

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图 20 未共形的曲面夹层结构

Figure 20. Non-conformal curving sandwich structure

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图 21 载荷-最大变形曲线

Figure 21. Load-maximum deformation curve

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图 22 3种结构最大变形位移云图

Figure 22. Maximum deformation nephogram of three structures

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