• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2022, Vol. 58 ›› Issue (17): 249-260.doi: 10.3901/JME.2022.17.249

• 数字化设计与制造 • 上一篇    下一篇

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功能梯度多孔结构拓扑优化的混合水平集方法

付君健1,2, 舒正涛2, 田启华1,2, 杜义贤1,2, 周祥曼1,2, 徐勇2   

  1. 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
  • 收稿日期:2021-05-12 修回日期:2022-02-13 发布日期:2022-11-07
  • 作者简介:付君健,男,1987年出生,博士,讲师,硕士研究生导师。主要研究方向为结构拓扑优化、超构材料设计、结构缺陷识别。E-mail:fjj@ctgu.edu.cn;舒正涛,男,1997年出生,硕士研究生。主要研究方向为结构拓扑优化。E-mail:1045969497@qq.com;田启华,男,1962年出生,博士,教授,博士研究生导师。主要研究方向为智能制造、CAD/CAE/CAM。E-mail:tqh@ctgu.edu.cn;周祥曼,男,1983年出生,博士,副教授,硕士研究生导师。主要研究方向为增材制造、CAD/CAE/CAM。E-mail:zhouxman@ctgu.edu.cn;徐勇,男,1995年出生,硕士研究生。主要研究方向为结构拓扑优化。E-mail:2449689455@qq.com

A Hybrid Level Set Method for Topology Optimization of Functionally Graded Cellular Structures

FU Junjian1,2, SHU Zhengtao2, TIAN Qihua1,2, DU Yixian1,2, ZHOU Xiangman1,2, XU Yong2   

  1. 1. Hubei Key Laboratory of Hydroelectric Machinery Design& Maintenance, Yichang 443002;
    2. College of Mechanical& Power Engineering, China Three Gorges University, Yichang 443002
  • Received:2021-05-12 Revised:2022-02-13 Published:2022-11-07
  • Contact: 国家自然科学基金(51775308)、湖北省自然科学基金(2021CFB236)、湖北省教育厅科学技术研究项目(Q20201205)、水电机械设备设计与维护湖北省重点实验室开放基金(2020KJX04)资助项目。

摘要: 为解决传统功能梯度多孔结构单胞分布形式单一、几何连续性差的问题,提出了一种功能梯度多孔结构拓扑优化的混合水平集方法。引入权重系数构造隐式水平集函数的仿射,实现了梯度微结构单胞与宏观结构隐式建模。建立全局更新-局部插值的设计变量更新策略,将几何连续性嵌入拓扑优化模型。以权重系数作为设计变量,结构体积分数为约束,建立了功能梯度多孔结构刚度拓扑优化模型,并采用优化准则算法进行求解。数值算例表明,本方法可有效实现功能梯度多孔结构拓扑优化,丰富了多孔结构单胞的梯度变化形式,保证了不同多孔结构之间的连续性。

关键词: 拓扑优化, 功能梯度多孔结构, 混合水平集法, 几何连续性

Abstract: To enrich the distribution ways of the cellular cells and improve the geometric continuity in traditional functionally graded cellular structures (FGCS), a hybrid level set method (HLSM) for topology optimization of FGCS is proposed. By introducing the affine concept of convex optimization theory, the affine of implicit level set function is constructed to realize the implicit modeling of graded micro and macrostructures. A global update-local interpolation strategy is proposed to update design variables, and then the geometric continuity is embedded into the topology optimization model. The weight coefficient is the design variable and the volume fraction of the structure is the constraint condition. A HLSM-based FGCS topology optimization model is established with the maximum stiffness. The optimality criteria (OC) is used to solve the model to obtain a FGCS with superior continuity. Numerical examples show that the proposed method can effectively realize topology optimization of the FGCS, which enriches the graded varying form of the cellular cell and ensures the continuity between the different cellular structures.

Key words: topology optimization, functionally graded cellular structures, hybrid level set method, geometric continuity

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