基于各向异性亥姆霍兹方程的空腔连通性约束拓扑优化设计方法

doi:10.3901/JME.2022.13.240

机械工程学报 ›› 2022, Vol. 58 ›› Issue (13): 240-250.doi: 10.3901/JME.2022.13.240

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基于各向异性亥姆霍兹方程的空腔连通性约束拓扑优化设计方法

王天赐¹, 刘龙¹, 李智忠¹, 向继方², 易兵¹

1. 中南大学交通运输工程学院长沙 410075;
2. 湖南长城海盾光纤科技有限公司长沙 410006

收稿日期:2021-07-08 修回日期:2022-04-07 出版日期:2022-07-05 发布日期:2022-09-13
通讯作者: 易兵(通信作者),男,1987年出生,博士,副教授,博士研究生导师。主要研究方向为数字样机、虚拟现实和结构拓扑优化。E-mail:bingyi@csu.edu.cn
作者简介:王天赐,男,1997年出生。主要研究方向为结构拓扑优化。E-mail:tianciwang@csu.edu.cn;刘龙,男,1995年出生,博士研究生。主要研究方向为拓扑优化、计算几何。E-mail:dragon_liu@csu.edu.cn;李智忠,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:zhizhongli@csu.edu.cn;向继方,男,高级工程师。主要研究方向光纤传感器结构、减振降噪结构设计与优化。E-mail:xjf1900@yeah.net

Structural Topology Optimization with Connectivity Constraints Based on Anisotropic Helmholtz Equation

WANG Tianci¹, LIU Long¹, LI Zhizhong¹, XIANG Jifang², YI Bing¹

1. School of Traffic and Transportation Engineering, Central South University, Changsha 410075;
2. Hunan Great Wall Haidun Optical Fiber Technology Co., Ltd., Changsha 410006

Received:2021-07-08 Revised:2022-04-07 Online:2022-07-05 Published:2022-09-13

摘要/Abstract

摘要： 针对增材制造加工拓扑优化结构存在的内部空腔难以加工和支撑材料无法去除的问题，提出一种基于各向异性亥姆霍兹方程的拓扑优化方法，能够简单有效地实现考虑空腔连通性约束的结构拓扑优化。首先，根据封闭空腔结构特点，定义了结构连续性作为结构连通性的等效描述，便于在拓扑优化框架内添加连通性约束；然后，采用各向异性亥姆霍兹方程，通过设置各向异性参数保证实体结构在特定方向上的连续性，构建了包含空腔连通性限制的拓扑优化模型；最后，采用MMA算法求解拓扑优化模型，实现了考虑空腔连通性约束的结构拓扑优化。多个优化算例结果表明，相比于传统方法，该方法能够在不添加新的约束条件和中间变量的基础上，即可抑制拓扑优化设计中封闭空腔结构的产生，构成面向增材制造的拓扑优化结构。同时，该方法很容易拓展到考虑传统制造约束的拓扑优化模型中，避免设计中出现封闭空腔结构。

关键词: 拓扑优化, 增材制造, 空腔连通性, 结构连续性, 各向异性亥姆霍兹

Abstract: With the framework for topology optimization via Solid Isotropic Material with Penalization method (SIMP), a novel and simple method for topology optimization based on Helmholtz equation is constructed to solve the problem of cavity connectivity in the topology optimization design for additive manufacturing. First, the structure continuity is defined as a new equivalent description of structural connectivity according to the characteristics of enclosed void in order to encapsulate connectivity constraints into the framework of topology optimization. Then, the anisotropic Helmholtz equation is used to ensure the continuity of the entity structure in a specific direction by setting different parameters, and the topology optimization model considering the cavity connectivity constraint is constructed. Finally, the MMA algorithm is used to solve the topology optimization model, and the limit of cavity connectivity is realized. Several optimization examples prove the performance of the proposed method for topology optimization of continuum structure with connectivity constraints for additive manufacturing without adding new constraints and intermediate variables compared with conventional methods. This method can also be easily extended to the topology optimization of continuum structure with conventional manufacturing methods to avoid enclosed void.

Key words: topology optimization, additive manufacturing, connectivity constraints, structural continuity, anisotropic Helmholtz equation

中图分类号:

TH122

王天赐, 刘龙, 李智忠, 向继方, 易兵. 基于各向异性亥姆霍兹方程的空腔连通性约束拓扑优化设计方法[J]. 机械工程学报, 2022, 58(13): 240-250.

WANG Tianci, LIU Long, LI Zhizhong, XIANG Jifang, YI Bing. Structural Topology Optimization with Connectivity Constraints Based on Anisotropic Helmholtz Equation[J]. Journal of Mechanical Engineering, 2022, 58(13): 240-250.

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基于各向异性亥姆霍兹方程的空腔连通性约束拓扑优化设计方法

Structural Topology Optimization with Connectivity Constraints Based on Anisotropic Helmholtz Equation

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