• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2022, Vol. 58 ›› Issue (5): 136-143.doi: 10.3901/JME.2022.05.136

• 机械动力学 • 上一篇    下一篇

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基于贴体网格的高分辨率三维结构拓扑优化研究

张横1, 李昊2, 丁晓红1, 胡天男1, 潘晟3, 朱本亮4, 倪维宇1, 徐世鹏1   

  1. 1. 上海理工大学机械工程学院 上海 200093;
    2. 京都大学大学院工学研究科 京都 6158540 日本;
    3. 大连理工大学运载工程与力学学部 大连 116024;
    4. 华南理工大学机械与汽车工程学院 广州 510640
  • 收稿日期:2021-05-27 修回日期:2021-11-22 出版日期:2022-03-05 发布日期:2022-04-28
  • 通讯作者: 李昊(通信作者),男,1994年出生,博士研究生,日本学术振兴会特别研究员-DC2。主要研究方向为多物理场拓扑优化,高性能计算。E-mail:lihao71862b@sina.com E-mail:lihao71862b@sina.com
  • 作者简介:张横,男,1988年出生,讲师。主要研究方向为多尺度拓扑优化,高性能计算。E-mail:zhanghengsh@usst.edu.cn
  • 基金资助:
    国家自然科学基金(51975380,52005337);中国博士后科学基金(2020M681346);日本学术振兴会(JSPS)(JP21J13418)资助项目。

Numerical Study on the Body-fitted Topology Optimization for Three-dimensional High Resolution Structure Design

ZHANG Heng1, LI Hao2, DING Xiao-hong1, HU Tian-nan1, PAN Sheng3, ZHU Ben-liang4, NI Wei-yu1, XU Shi-peng1   

  1. 1. School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093;
    2. Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto, Japan 6158540;
    3. Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024;
    4. School of Mechanical & Automotive Engineering, South China University of Technology, Guangzhou 510640
  • Received:2021-05-27 Revised:2021-11-22 Online:2022-03-05 Published:2022-04-28

摘要: 针对高分辨率三维结构拓扑优化中计算成本高的问题,提出一种基于水平集方法融合自适应贴体网格的拓扑优化并行计算新框架。通过水平集函数零等值面,清晰描述优化结果边界,实现了“所见即所得”的拓扑优化设计结果;并在每一迭代步中基于该等值面进行网格重构,加密边界周围网格,稀疏其余区域内网格,从而大幅减少了网格数量,有效降低计算成本;在计算过程中通过对网格进行分割,并指派给不同的CPU进行计算,实现并行计算,可以有效处理大规模计算问题。该框架基于开源软件FreeFEM,Mmg和PETSc进行开发,以经典的刚度问题为例,在工作站平台上,求解网格规模达380万的数值算例,验证该方法的高效性。

关键词: 拓扑优化, 贴体网格, 并行计算, 高分辨率, 水平集

Abstract: To solve a high-resolution 3D topology optimization problem, a new parallel distributed framework integrated with the body-fitted mesh adaptation technique is proposed. The solid-void interface can be described explicitly by a zero-level-set isosurface.The mesh is refined iteratively, the areas near boundaries have dense grids while other areas have sparse grids. This feature can save a huge amount of unneeded computation cost. In the computing process, the computational domain is decomposed, and submit them to different processors to realize parallel computing. Thus, the proposed method can deal with large-scale topology optimization problems. The proposed numerical implementation relies on FreeFEM, Mmg and PETSc open-source software packages. The problem at hand is the classical compliance maximization problem. The proposed framework is scalable to 3.8 million tetrahedral elements and can be performed on a standard workstation. Several numerical examples support these remarkable features.

Key words: topology optimization, body-fitted mesh, parallel computing, high resolution, level-set

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