Implementation of physics informed neural networks for geometrically nonlinear analysis of non-prismatic members

Advancements in manufacturing techniques, such as wire and arc additive manufacturing, have enabled the efficient production of non-prismatic members. These members, characterized by varying cross-sectional geometries, offer superior structural efficiency. However, they present significant challenges for geometrically nonlinear analysis, a persistent problem for decades, as conventional methods often result in oversimplified equations or time-consuming finite-element-based approaches. This paper introduces a novel method leveraging machine-learning techniques, specifically Physics-Informed Neural Networks (PINNs), to tackle this analysis problem. The new PINNs method employs a self-supervised learning process, integrating physical laws into the machine learning model to accurately determine equilibrium conditions under varied loads and boundary conditions. The paper provides a detailed explanation of the governing equations, the PINNs framework, and the training procedure. The accuracy and effectiveness of the proposed approach are validated through a series of validation examples, demonstrating the potential of PINNs in handling geometrically nonlinear analysis problems of non-prismatic members. This research provides a new direction in solving challenging structural analysis problems, potentially promoting the application of emerging machine learning techniques in the field.