A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate

TL;DR

This paper introduces a deep collocation method using neural networks to efficiently solve Kirchhoff plate bending problems, overcoming traditional continuity challenges and providing a mesh-free, flexible approach.

Contribution

The paper proposes a novel deep collocation method based on deep neural networks for Kirchhoff plate bending analysis, addressing continuity issues without mesh dependency.

Findings

Successfully models Kirchhoff plate deflections with high accuracy.

Handles complex geometries effectively.

Outperforms traditional mesh-based methods in continuity enforcement.

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.