PHYSICS-INFORMED NEURAL NETWORKS FOR ELASTIC PLATE PROBLEMS WITH BENDING AND WINKLER-TYPE CONTACT EFFECTS

Abstract

Kirchhoff plate bending and Winkler-type contact problems with different boundary conditions are solved with the use of physics-informed neural networks (PINN). The PINN is built on the base of mechanics laws and deep learning. The idea of the technique includes fitting the governing partial differential equations at collocation points and then training the neural network with the use of optimization techniques. Training of the neural network is performed by numerical optimization using Adam’s method and the L-BFGS (Limited-Broyden–Fletcher–Goldfarb– Shanno) algorithm. The error loss function and the computational error of the approximate solution (output of the neural network) of the bending problem and contact problem with Winkler type elastic foundation are shown on examples. The predictions of the NN are investigated for different values of the foundation’s constants. The effectiveness of the proposed framework is demonstrated through numerical experiments with different numbers of epochs, hidden layers, neurons and numbers of collocation points. The Tensorflow deep learning and scientific computing package of Python is used through a Jupyter Notebook.