PINN surrogate model for nonlinear equilibrium path analysis of von Mises shallow truss

This paper introduces the application of a surrogate physics-informed neural network (PINN) model for the comprehensive analysis of nonlinear equilibrium paths in Von Mises planar shallow trusses. Such studies are crucial in advancing the theory of stability for truss structures. Stability analysis is important in structural engineering since it can provide guidelines for designing safer, and more reliable structures. Conventional numerical modeling procedures based on the finite element method (FEM), apply incremental-iterative procedures, which often face significant challenges. They struggle with computational and time inefficiencies, difficulties in handling complex nonlinear behaviors, limitations in predicting post-critical responses, and convergence issues. This study upgrades the implementation of machine learning (ML) in structural analysis by showing the potential of physics-informed ML approaches to overcome the limitations of current numerical modeling techniques. Developed PINN is a mesh-free, unsupervised learning model, with integrated automatic identification of critical points along the equilibrium path. The developed model overcomes the limitations of existing solutions, does not require expert knowledge in the field of nonlinear structural analysis, and as such is more accessible to the wider community. The authors examined the influence of different spring stiffness, while also analyzing different geometrical and material properties of the bars. The PINN surrogate model has demonstrated exceptional adaptability to different structural configurations, which makes it a superior alternative for practical engineering applications.