A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate

In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning. Besides, the proposed DCM is based on a feedforward deep neural network (DNN) and differs from mos...

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Vydáno v:Computers, materials & continua Ročník 59; číslo 2; s. 433 - 456
Hlavní autoři: Guo, Hongwei, Zhuang, Xiaoying, Rabczuk, Timon
Médium: Journal Article
Jazyk:angličtina
Vydáno: Henderson Tech Science Press 2019
Témata:
Algorithms
Artificial neural networks
Back propagation
Bending
Collocation methods
Deep learning
Initial conditions
Machine learning
Neural networks
Partial differential equations
Thin plates
ISSN:1546-2226, 1546-2218, 1546-2226
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Shrnutí:In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning. Besides, the proposed DCM is based on a feedforward deep neural network (DNN) and differs from most previous applications of deep learning for mechanical problems. First, batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries. A loss function is built with the aim that the governing partial differential equations (PDEs) of Kirchhoff plate bending problems, and the boundary/initial conditions are minimised at those collocation points. A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters. In Kirchhoff plate bending problems, the C1 continuity requirement poses significant difficulties in traditional mesh-based methods. This can be solved by the proposed DCM, which uses a deep neural network to approximate the continuous transversal deflection, and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.
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ISSN:1546-2226
1546-2218
1546-2226
DOI:10.32604/cmc.2019.06660