北京航空航天大学学报 ›› 2020, Vol. 46 ›› Issue (3): 481-487.doi: 10.13700/j.bh.1001-5965.2019.0134

• 论文 • 上一篇    下一篇

卷积神经网络求解有限元单元刚度矩阵

贾光辉1, 于云瑞1, 王丹2   

  1. 1. 北京航空航天大学 宇航学院, 北京 100083;
    2. 北京空间飞行器总体设计部, 北京 100094
  • 收稿日期:2019-04-01 发布日期:2020-03-28
  • 通讯作者: 贾光辉 E-mail:jiaguanghui@buaa.edu.cn
  • 作者简介:贾光辉,男,博士,副教授,硕士生导师。主要研究方向:飞行器结构分析与撞击动力学响应;于云瑞,男,硕士研究生。主要研究方向:深度学习与传统结构分析的结合;王丹,女,博士,高级工程师。主要研究方向:飞行器总体设计。

Solving finite element stiffness matrix based on convolutional neural network

JIA Guanghui1, YU Yunrui1, WANG Dan2   

  1. 1. School of Astronautics, Beihang University, Beijing 100083, China;
    2. Beijing Institute of Spacecraft System Engineering, Beijing 100094, China
  • Received:2019-04-01 Published:2020-03-28

摘要: 随着深度学习在众多领域的成功应用与快速发展,将深度学习与传统的结构分析相融合已经成为了新的研究方向。在求解有限元单元刚度矩阵的具体问题上,研究了卷积神经网络在结构分析上的应用。以四边形平面应力单元为例,基于卷积神经网络,提出了一个求解有限元总体刚度矩阵的神经网络模型;同时分析了网络的学习效果与网络卷积核数目、训练样本数目之间的关系。计算实例表明,在一定范围内,网络的学习能力随着卷积核数目、训练样本数目的增加而不断提升。在现实应用时,可以根据具体的精度要求而设定相应的卷积神经网络。卷积神经网络训练完成后,单元刚度矩阵的计算具有实时性,且精度满足工程要求。

关键词: 卷积神经网络, 有限元, 刚度矩阵, 卷积核数, 总样本数, 实时计算

Abstract: With the successful application and rapid development of deep learning in many fields, the integration of deep learning with traditional structural analysis has become a new research direction. In terms of solving the finite element stiffness matrix problem, the application of convolutional neural network in structural analysis is studied. Taking the quadrilateral plane stress element as an example, based on the convolutional neural network, a neural network model for solving the finite element global stiffness matrix is proposed. Moreover, the relationship between the learning effect of the network and the number of network convolution kernels and the number of training samples is analyzed. The calculation example shows that, within a certain range, the learning ability of the network increases with the number of convolution kernels and the number of training samples. In practical applications, the corresponding convolutional neural network can be set according to specific accuracy requirements. After the convolutional network training is completed, the calculation of the element stiffness matrix is real-time, and the accuracy meets the engineering requirements.

Key words: convolutional neural network, finite element, stiffness matrix, convolution kernel number, total sample number, real-time calculation

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