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.