A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate

• 作者: Hongwei Guo Timon Rabczuk Xiaoying Zhuang
• 来源期刊: 计算机、材料和连续体(英文)
• 学科: 数学
• 关键词: DEEP learning COLLOCATION method KIRCHHOFF plate HIGHER-ORDER PDES
• 年，卷（期）: 2019,（5）
• 页码范围: 433-456
• 页数: 24页
• 分类号: O17

摘要

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 C^1 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.