Exploring the Potential of Physics-Informed Neural Networks for the Structural Analysis of 2D Frame Structures

Within the present paper, Physics-Informed Neural Networks (PINN) are investigated 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 joined global loss function within the simultaneous training process. The boundary conditions at the supports of the structure and the coupling conditions at the element connections are considered in the global loss function and specific weighting factors are defined and tuned within the training. The combination of several structural elements within one analysis by training a set of neural networks simultaneously by a joined loss function is the main novelty of the current study. The formulation of coupling conditions for different scenarios is illustrated. Additionally, a nondimensionalization approach is introduced in order to achieve an automatic scaling of the individual loss function terms. Several examples have been investigated as follows: a simple beam structure first with quadratic load and second with varying cross-section properties is analyzed with respect to the convergency of the networks accuracy compared to the analytical solutions. Two more sophisticated examples with several elements connected at rigid corners were investigated, 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.