Physics-informed neural networks for solving elasticity problems - Almeida, Estevão Fuzaro [UNESP]; Silva, Samuel da [UNESP]; Cunha Júnior, Americo (Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM), 2023)
Computational mechanics has seen remarkable progress in recent years due to the integration of machine learning techniques, particularly neural networks. Traditional approaches in solid mechanics, such as the finite element method (FEM), often require extensive manual labor in discretization and mesh generation, making them time-consuming and challenging for complex geometries. Moreover, these methods heavily rely on accurate and complete data, which may not always be readily available or prone to measurement errors. On the other hand, Physics-Informed Neural Networks (PINNs) are a machine learning technique that can learn from data and physics equations, allowing accurate and physically consistent predictions. Through this study, we aim to demonstrate the effectiveness of PINNs in accurately predicting the stress distribution in a triangular plate, showcasing their potential as a valuable tool in solving real-world solid mechanics problems. Combining the elasticity conservation laws and boundary conditions into the neural network architecture creates a PINN and is trained on a coarse mesh of points over the plate domain and evaluated on a fine mesh using a data-free approach, compared with the Airy analytical solution.
The first author would like to thank São Paulo Research Foundation (FAPESP) for providing financial support under grant number 2022/16156-9.
Keywords: Solid mechanics; Physics-informed neural networks; Stress distribution; Data-free modeling