A deep collocation method for the bending analysis of Kirchhoff plate

authored by
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.

Organisation(s)
Institute of Continuum Mechanics
External Organisation(s)
Tongji University
Ton Duc Thang University
Type
Article
Journal
Computers, Materials and Continua
Volume
59
Pages
433-456
No. of pages
24
ISSN
1546-2218
Publication date
2019
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Biomaterials, Modelling and Simulation, Mechanics of Materials, Computer Science Applications, Electrical and Electronic Engineering
Electronic version(s)
https://doi.org/10.32604/cmc.2019.06660 (Access: Open)
 

Details in the research portal "Research@Leibniz University"