Structural Analysis of 2D Frame Structures Using Physics Informed Neural Networks

Within the present paper, 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 results of the PINN framework are verified successfully with traditional finite element solutions for the presented examples. Nevertheless, the weighting of the individual loss function terms is the crucial point in the presented approach, which will be discussed in the paper.