一种基于共形映射与神经网络的拓扑优化方法  

A topology optimization method based on conformal mapping and neural networks

作　　者：农卫航 曾梓洋 邢志 吴飞 丁江 NONG Weihang;ZENG Ziyang;XING Zhi;WU Fei;DING Jiang(School of Mechanical Engineering,Guangxi University,Nanning 530004,China;Guangxi Key Laboratory of Manufacturing System&Advanced Manufacturing Technology,Guangxi University,Nanning 530004,China;State Key Laboratory of Featured Metal Materials and Life-cycle Safety for Composite Structures,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学机械工程学院,广西南宁530004 [2]广西制造系统与先进制造技术重点实验室,广西南宁530004 [3]省部共建特色金属材料与组合结构全寿命安全国家重点实验室,广西南宁530004

出　　处：《广西大学学报(自然科学版)》2025年第1期137-148,共12页Journal of Guangxi University(Natural Science Edition)

基　　金：国家自然科学基金项目(52475096);广西科技重大专项项目(桂科AA22068055);广西自然科学基金项目(2021GXNSFAA220095);广西自然科学基金项目(2025GXNSFFA069009)。

摘　　要：针对神经网络驱动的拓扑优化方法难以优化非结构化网格中优化对象的问题,本文提出了一种基于共形映射与神经网络的拓扑优化方法,通过共形映射将非结构化网格保角地映射到一个有界的二维平面上。在二维平面上重新划分规则的矩形网格;通过重心插值算法将非结构化网格上的信息插值到矩形网格中,通过神经网络对这些矩形网格进行处理就能得到优化的结构拓扑。数值实验结果显示,该方法能有效且准确地优化不同非结构化网格对象。To address the challenge that neural network-driven topology optimization methods face when optimizing design targets on unstructured meshes,this paper proposes a topology optimization approach based on conformal mapping and neural networks.Initially,unstructured grids are conformally mapped onto a bounded two-dimensional plane,preserving angles.Subsequently,regular rectangular grids are redefined on this two-dimensional plane.By interpolating the information on unstructured grids to rectangular grids using the barycentric interpolation algorithm,the optimized structural topology can be obtained by processing these rectangular grids through a neural network.Numerical experimental results indicate that the proposed method can naturally optimize different unstructured grid objects while maintaining both efficiency and accuracy.

关 键 词：拓扑优化 共形映射 非结构化网格 神经网络 重心插值 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]