Structural analysis of 2D frame structures using Physics Informed Neural Networks : Calculation files and result data

Within the present study, a framework for Physics Informed Neural Networks (PINN) is formulated for the analysis of frame structures in two dimensions. The individual structural elements are represented by Euler-Bernoulli beams with additional axial stiffness. The transverse and axial displacements are approximated by individual neural networks and the differential equations are considered by minimizing a global loss function within the simultaneous training process.
As a novelty, the boundary conditions at the supports of the structure and the coupling conditions at the element connections are considered in a joined loss function and specific weighting factors are defined and tuned within the training.
Several examples have been investigated: first a simple beam structure with varying cross section properties and second with a concentrated discrete load in order to investigated the applicability of the PINNs for structural analysis. Two more sophisticated examples with several elements connected at rigid corners were analyzed, where the fulfillment of the consistency of the displacements and the equilibrium conditions of the internal forces is a crucial condition within the loss function of the network training.

The presented examples were implemented in Python using the PyTorch framework, with the Adam optimizer commonly employed to perform gradient-based updates of the network parameters. For the investigated structures, learning rate schedulers were employed to facilitate convergence by systematically adjusting the learning rate as training progressed. In the final example, the use of a scheduler was omitted. Instead, an additional optimization phase was executed using the L-BFGS algorithm following a phase using the Adam optimizer to further refine the solution and promote convergence.