Second-order analysis of beam-columns by machine learning- based structural analysis through physics-informed neural

The second-order analysis of slender steel members could be challenging, especially when large deflection is involved. This paper proposes a novel machine learning-based structural analysis (MLSA) method for second-order analysis of beam-columns, which could be a promising alternative to the prevailing solutions using over-simplified analytical equations or traditional finite-element-based methods. The effectiveness of the conventional machine learning method heavily depends on both the qualitative and the quantitative of the provided data. However, such data are typically scarce and expensive to obtain in structural engineering practices. To address this problem, a new and explainable machine learning-based method, named Physics-informed Neural Networks (PINN), is employed, where the physical information will be utilized to orientate the learning process to create a self-supervised learning procedure, making it possible to train the neural network with few or even no predefined datasets to achieve an accurate approximation. This research extends the PINN method to the problems of second-order analysis of steel beam-columns. Detailed derivations of the governing equations, as well as the essential physical information for the training process, are given. The PINN framework and the training procedure are provided, where an adaptive loss weight control algorithm and the transfer learning technic are adopted to improve numerical efficiency. The practicability and accuracy of which are validated by four sets of verification examples.