A deep collocation method for the bending analysis of Kirchhoff plate

verfasst von: Hongwei Guo, Xiaoying Zhuang, Timon Rabczuk
Abstract: 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.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Externe Organisation(en): Tongji University
Ton Duc Thang University
Typ: Artikel
Journal: Computers, Materials and Continua
Band: 59
Seiten: 433-456
Anzahl der Seiten: 24
ISSN: 1546-2218
Publikationsdatum: 2019
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Biomaterialien, Modellierung und Simulation, Werkstoffmechanik, Angewandte Informatik, Elektrotechnik und Elektronik
Elektronische Version(en): https://doi.org/10.32604/cmc.2019.06660 (Zugang: Offen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{0d3b589c88234b3d8c041e02b0b45575,
title = "A deep collocation method for the bending analysis of Kirchhoff plate",
abstract = "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.",
keywords = "Collocation method, Deep learning, Higher-order PDEs, Kirchhoff plate",
author = "Hongwei Guo and Xiaoying Zhuang and Timon Rabczuk",
year = "2019",
doi = "10.32604/cmc.2019.06660",
language = "English",
volume = "59",
pages = "433--456",
journal = "Computers, Materials and Continua",
issn = "1546-2218",
publisher = "Tech Science Press",
number = "2",
}