| Citation: | JIA Guanghui, YU Yunrui, WANG Danet al. Solving finite element stiffness matrix based on convolutional neural network[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(3): 481-487. doi: 10.13700/j.bh.1001-5965.2019.0134(in Chinese)
|
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.
| [1] |
GOLOVKO V A.Deep learning:An overview and main paradigms[J].Optical Memory and Neural Networks, 2017, 26(1):1-17. http://cn.bing.com/academic/profile?id=269ac3d9f6001d015e05a978bb2983a5&encoded=0&v=paper_preview&mkt=zh-cn
|
| [2] |
孙道恒, 罗萍平, 胡俏, 等.有限元单刚矩阵计算的神经网络法[J].东北大学学报(自然科学版), 1997, 18(4):431-434. doi: 10.3321/j.issn:1005-3026.1997.04.005
SUN D H, LUO P P, HU Q, et al.Neural network method for finite element single stiffness matrix calculation[J].Journal of Northeastern University(Natural Science), 1997, 18(4):431-434(in Chinese). doi: 10.3321/j.issn:1005-3026.1997.04.005
|
| [3] |
孙道恒, 胡俏.弹性力学的实时神经计算原理与数值仿真[J].力学学报, 1998, 30(3):348-353. doi: 10.3321/j.issn:0459-1879.1998.03.012
SUN D H, HU Q.The principle and numerical simulation of real-time neural computing for elastic mechanics[J].Chinese Journal of Theoretical and Applied Mechanics, 1998, 30(3):348-353(in Chinese). doi: 10.3321/j.issn:0459-1879.1998.03.012
|
| [4] |
丁耀武.线弹性结构静动态有限元法[M].沈阳:东北工学院出版社, 1990:31-54.
DING Y W.Static and dynamic FEM for linear elastic structural analysis[M].Shenyang:Northeastern University Press, 1990:31-54(in Chinese).
|
| [5] |
蒋维城.固体力学有限元分析[M].北京:北京理工大学出版社, 1989:308-312.
JIANG W C.Finite element analysis of solid mechanics[M].Beijing:Beijing Institute of Technology Press, 1989:308-312(in Chinese).
|
| [6] |
姜晋庆, 张铎.结构弹塑性有限元分析法[M].北京:宇航出版社, 1990:1-10.
JIANG J Q, ZHANG D.Structural elastoplastic finite element analysis method[M].Beijing:Aerospace Publishing House, 1990:1-10(in Chinese).
|
| [7] |
曾攀.材料的概率疲劳损伤特性及现代结构分析原理[M].北京:科学技术文献出版社, 1993:140-141.
ZEN P.Probabilistic fatigue damage properties of materials and modern structural analysis principle[M].Beijing:Science and Technology Literature Press, 1933:140-141(in Chinese).
|
| [8] |
YOSHIOKA T, KARITA S, NAKATANI T.Far-field speech recognition using CNN-DNN-HMM with convolution in time[C]//IEEE International Conference on Acoustics, Speech and Signal Processing.Piscataway, NJ: IEEE Press, 2015: 15361744.
|
| [9] |
YOSHIOKA T, OHNISHI K, FANG F, et al.Noise robust speech recognition using recent developments in neural networks for computer vision[C]//IEEE International Conference on Acoustics, Speech and Signal Processing.Piscataway, NJ: IEEE Press, 2016: 16021176.
|
| [10] |
GLOROT X, BENGIO Y.Understanding the difficulty of training deep feedforward neural networks[C]//Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 2010: 249-256.
|
| [11] |
ZHANG X, ZOU Y, SHI W.Dilated convolution neural network with LeakyReLU for environmental sound classification[C]//International Conference on Digital Signal Processing.Piscataway, NJ: IEEE Press, 2017: 1-5.
|
| [12] |
ZHAO P, ZHANG T.Accelerating minibatch stochastic gradient descent using stratified sampling[EB/OL].(2014-05-13)[2019-03-28].https://arxiv.org/abs/1405.3080.
|
| [13] |
NG A Y.Feature selection, L1 vs.L2 regularization, and rotational invariance[C]//Proceedings of the Twenty-first International Conference on Machine Learning.New York: ACM, 2004: 78.
|
| [14] |
KINGMA D, BA J.Adam: A method for stochastic optimization[EB/OL].(2014-12-22)[2019-03-28].https://arxiv.org/abs/1412.6980.
|
| [15] |
陈国荣.有限单元法原理及应用[M].北京:科学出版社, 2016:91-116.
CHEN G R.Principle and application of finite element method[M].Beijing:Science Press, 2016:91-116(in Chinese).
|
Figures(10) / Tables(1)
Copyright © Journal of Beijing University of Aeronautics and Astronautics
Address: Editorial Department of Journal of Beijing University of Aeronautics and Astronautics, 37 Xueyuan Road, Haidian District, Beijing Post Code: 100191 Email: jbuaa@buaa.edu.cn
Supported by:
Beijing Renhe Information Technology Co., Ltd.
DownLoad:
