Physics-informed neural network for nonlinear analysis of cable net structures

In this study, a Physics-Informed Neural Network (PINN) framework is extended and applied to predict the geometrically nonlinear responses of pretensioned cable net structures without utilizing any incremental-iterative algorithms as well as Finite Element Analyses (FEAs). Instead of solving nonlinear equations as in existing numerical models, the core idea behind this approach is to employ a Neural Network (NN) that minimizes a loss function. This loss function is designed to guide the learning process of the network based on Total Potential Energy (TPE), pretension forces, and Boundary Conditions (BCs). The NN itself models the displacements given the corresponding coordinates of joints as input data, with trainable parameters including weights and biases that are regarded as design variables. Within this computational framework, these parameters are automatically adjusted through the training process to get the minimum loss function. Once the learning is complete, the nonlinear responses of cable net structures can be easily and quickly obtained. A series of numerical examples is investigated to demonstrate the effectiveness and applicability of the PINN for the geometrically nonlinear analysis of cable net structures. The obtained results indicate that the PINN framework is remarkably simple to use, robust, and yields higher accuracy.