Physics Informed Deep Neural Networks for Strength Evaluation Based on Shakedown Analysis

In the field of structural engineering and materials science, particularly in aerospace engineering, optimizing structural design for strength while minimizing material usage presents a complex challenge, especially under variable loading conditions. The current research for the first time introduces an approach to strength evaluation through the innovative application of Physics Informed Neural Networks (PINNs) in shakedown analysis. This paper presents a novel methodology that combines the principles of physics-informed machine learning with shakedown analysis's rigorous demands. Shakedown analysis offers a sophisticated framework for determining the safe load-bearing capacity of structures beyond the conventional elastic limit but within the plastic threshold, without the need to consider the history of loading conditions. This methodology enables engineers to design lighter, more material-efficient structures by safely harnessing the structure's capacity to withstand loads without reaching failure. Our approach leverages the concept of Physics Informed Neural Networks (PINNs), which integrates differential equations governing physical laws directly into the learning process of deep neural networks. PINNs are further advanced by incorporating self-equilibrating stress field relations, essential for shakedown analysis. This integration enables to accurately predict the shakedown limit strength, crucial for determining a structure's ability to endure repeated loading without failure. By adding these relations to the mechanical equilibrium equation and constitutive equations within the neural network architecture, it is now offer a comprehensive modeling capability, extending their application to more complex scenarios in solid mechanics, including accurate shakedown limit predictions. The proposed methodology introduces key innovations by extending PINNs to nonlinear problems for complex elastoplastic behavior through shakedown analysis and proposing a multi-network PINN model for more accurate structural response representation. To validate our approach, we employ synthetic data derived from analytical and numerical reference solutions, focusing on convergence behavior and accuracy. Our research highlights the robustness of PINNs in handling sparse data and extrapolating across a wide range of parameters, a critical aspect in the context of shakedown analysis where the design space is vast and complex. This ability to predict accurately under previously unseen conditions not only underscores the potential of PINNs in surrogate modeling but also in the further sensitivity analysis, providing a powerful tool for engineers to explore and optimize structural designs efficiently. Furthermore, the technique is used to determine the shakedown strength for a manned airtight module.