Mechanically Constrained Graph Neural Networks for Linear Static Analysis of Planar Frame Structures with Member Loads

Artificial intelligence methods have attracted increasing interest in structural analysis. However, engineering applications still require reliable representation of irregular topology, actual member loads, mechanical consistency, and interpretable structural response quantities. This study develops a mechanically constrained graph neural network (GNN) method for 2D linear elastic static analysis of planar truss and building frame structures. The method represents the structural system as a graph and encodes nodes, members, boundary conditions, nodal loads, member stiffness, and actual member loads as graph features. A message-passing GNN predicts nodal DOF displacements, and the loss function includes free DOF equilibrium residuals and global equilibrium residuals to improve mechanical consistency. The workflow then recovers support reactions and member axial forces, shear forces, and bending moments from the predicted displacements through structural mechanics relations. Numerical examples show that the proposed method reduces equilibrium residuals and improves member force recovery compared with a displacement-supervised baseline. Ablation studies further confirm the roles of member load input, equilibrium constraints, and internal force recovery. The results show that graph representation, training constrained by equilibrium, and mechanics-based recovery can be integrated into an interpretable framework for structural static analysis.