PINN-Based Design of Cold Bent Monolithic Glass: A Novel Approach to Geometrically Nonlinear Plate Analysis

A Novel Approach to Geometrically Nonlinear Plate Analysis

Abstract

A novel method for the geometrically nonlinear plate analysis of cold bent monolithic glass using Physics-Informed Neural Networks (PINNs) is presented. The approach leverages the power of PINNs as solvers for the associated nonlinear partial differential equations of von Karman theory. Traditional methods for this type of analysis are computationally expensive and often require complex finite element modelling, while closed-form analytical solutions are seldomly found. We bypass these limitations by formulating the governing PDEs as loss functions for a neural network. We detail the complete modelling setup, including the incorporation of boundary conditions directly into the network's loss functions. The paper then outlines a systematic training methodology, exploring various neural network architectures and hyperparameter settings to optimize performance and convergence. We demonstrate the PINN's capability to accurately predict the deformed shape and stress distribution in cold bent glass plates under various loading conditions through comparison with FE solutions. The core contribution of this work is a practical and efficient framework for applying PINNs to a real-world structural engineering problem. Ultimately, the paper provides a clear outline on how the trained PINN can be used as a powerful and rapid design tool for cold bent glass, enabling architects and engineers to explore complex geometries and loading scenarios with unprecedented speed and accuracy.