Nonlinear analysis of glass panes under complex lateral pressures through physics informed neural networks

Abstract

Accurate prediction of large deflections in glass panes is crucial for economical and safe structural design, particularly under complex loading conditions. The Föppl-von Karman (FvK) equations are widely used to model their nonlinear behavior but pose significant computational challenges. Recent advancements in machine learning, especially Physics-Informed Neural Networks (PINN), offer a promising alternative for solving such complex partial differential equations (PDEs). However, standard PINN struggles to handle the computational demands of the FvK equations due to high-order derivatives and intricate boundary conditions.

To address these limitations, this study introduces a novel PINN framework tailored for the nonlinear analysis of glass panes. The proposed method integrates a reduced-order technique and imposed hard constraints both using auxiliary functions while mitigating training instabilities caused by high-order terms in the PDEs and potential conflicts in the loss function. An adaptive loss weighting strategy further enhances training stability and ensures robust convergence. Extensive validation examples and case studies demonstrate the improved accuracy and reliability of the proposed PINN approach.

As a practical application, a PINN-based surrogate model is developed for real-time simulation of glass pane behavior under catastrophic weather conditions, showcasing the method's computational efficiency and potential for in-time prediction during natural hazards. This study highlights a significant advancement in applying PINNs as a reliable and efficient solution for addressing the complexities of nonlinear glass pane analysis.