Physics-informed neural networks for nonlinear bending of 3D functionally graded beam

Abstract

This paper proposes a framework for physics-informed neural networks (PINNs) in the nonlinear bending of 3D functionally graded (FG) beams. Utilizing the underlying physical rules governing a 3D FG porous beam resting on a Winkler-Pasternak foundation and motivated by the advancements in the research area of machine learning, this paper develops a PINN framework to predict the nonlinear bending of the beam system. PINNs need much less training data and can achieve high accuracy using a more straightforward network. The powerful tool presented in this work is general enough to handle any class of PDEs. We also take advantage of the recently developed deep learning platform TensorFlow with the company of DeepXDE library to design our network. In this study, the PINN framework takes information from the governing equations and the data from boundary conditions. We developed a mathematical model using the Euler-Bernoulli beam theory and inhomogeneous beam model and validated the results with those extracted from the finite difference method. Furthermore, PINN is presented to accurately predict the nonlinear bending of the system up to 37 times faster than the numerical method.