Application of a Neural Network to Computing the Stress Fields in a Bridge Cross-Section

The accurate prediction of stress fields in bridges is crucial for their design, maintenance, and safety. Unfortunately, solving for stress in bridge cross-sections can be computationally intensive and time-consuming, especially if the resolution is high. This is because we typically examine the stress at steady-state, which requires the use of implicit methods involving many iterations over large matrices. To optimize the bridge design process, we need a more efficient approach than that afforded by implicit methods. This paper introduces a novel approach utilizing tensorized Fourier Neural Operators (TFNOs) to predict the Airy stress, tension, and compression inside diverse bridge cross-sections. TFNOs do well in predicting partial differential equations (PDEs), which is used to compute the stress in bridges. TFNOs demonstrate promise in capturing the nuanced stress fields within bridges, aiding in identifying potential failure points, optimizing material usage, and ensuring safe load-bearing capac-ities. Using a relatively small number of data points, this paper proves the effectiveness of TFNOs by presenting predictions that match closely with the ground values. The integration of TFNOs into stress analysis can allow for greater accuracy, efficiency, and safety in the design and maintenance of critical infrastructure.