Facilitating digital assembly: A physics-informed graph learning framework for prediction of assembly deviations in bolted flange connections

Rapid and high-fidelity prediction of assembly deviations is critical for the digital assembly of high-precision products. In the assembly of bolted flange connections, bolt preload induces micro-scale deformations that are intrinsically coupled with complex contact mechanics. However, resolving these deformations via Finite Element Analysis (FEA) is computationally intensive, while purely data-driven models often lack physical consistency and generalization robustness. To address this, we propose a Physics-Informed Graph Neural Network (PI-GNN) framework for rapid displacement field prediction. This architecture explicitly encodes the topological dependencies of unstructured meshes via graph learning while embedding Navier–Cauchy equilibrium residuals into the loss function to enforce physical validity. Crucially, to address the sharp stress gradients inherent in contact surface, a distance-weighted supervision mechanism is introduced to stabilize training on sparse datasets. Comprehensive benchmarks on L-block assemblies demonstrate that the proposed method achieves simulation-grade fidelity with minimal data dependence. Compared to the purely data-driven baseline, the PI-GNN exhibits superior extrapolation robustness, reducing the axial Mean Absolute Error (MAE) by up to 48.8% in OOD regimes. Finally, the method is applied to the assembly deviation prediction of a two-stage flange connection. Experimental validation focusing on physical end-face tilt measurements confirms the model's ability to accurately characterize macroscopic assembly posture variations, verifying its potential as a reliable framework for intelligent assembly and in-process quality monitoring.