Evaluating Physics-Informed Neural Networks for Mesh-Free Structural Analysis

Predicting stress and deformation in engineering structures with high accuracy and efficiency remains a cornerstone challenge in computational mechanics. Physics‐informed neural networks (PINNs) have recently emerged as a mesh‐free alternative, capable of embedding governing partial differential equations (PDEs) directly into the training process. This study investigates the performance of PINNs on two canonical problems: a one-dimensional beam subjected to a uniform load, and a plane-stress scenario in metal plates featuring hole cutouts that introduce geometric irregularities. The PINN predicted solutions were benchmarked against analytical results and finite element method (FEM) simulations performed in Ansys Mechanical. Furthermore, transfer learning was explored by retraining pretrained PINNs on geometrically modified plates. The results demonstrate that PINNs can match FEM accuracy within a few percent error, though at a substantially higher computational cost. Importantly, PINNs yield continuous solution functions over the domain without requiring a mesh, and transfer learning substantially reduced training time for similar problems. These findings indicate that, while PINNs do not yet outperform traditional FEM in speed, their mesh‐free formulation and ability to leverage learned representations hold promise for adaptive, data‐driven structural‐analysis frameworks.