Energy‑Based Physics‑Informed Neural Network for Linear Elastic Analysis of Multi‑patch Plate and Shell Structures

Machine learning provides a fast and accurate tool for the prediction of a physical model. In this paper， a machine learning framework based on the physics-informed neural network （PINN） was established to predict the linear elastic static deformation of plate and shell structures. In contrast to the purely data-driven neural network， PINN incorporates the physical laws into the training process， thus reducing the required amount of data. The loss functions of the PINN are constructed based on the total potential energy functions of the thin-walled structure. Besides， the proposed PINN can be easily extended to shell structures with multiple patches by adding interface compatibility constraints into the loss function. The performance of the PINNs with the energy-based loss functions was evaluated with different shell structures and compared with the finite element results. Numerical examples show that the highly accurate results can be achieved based on the proposed framework which significantly reduces the amount of required training data compared to the data-driven neural network.