Elastic structural analysis based on graph neural network without labeled data

Artificial intelligence is gaining increasing popularity in structural analysis. However, at the structural system level, the appropriateness of data representation, the paucity of data, and the physical interpretability of results are rarely studied and remain profound challenges. To fill such gaps, a physics-informed model named StructGNN-E (i.e., structural analysis based on graph neural network [GNN]–elastic) based on the GNN architecture, which is capable of implementing the elastic analysis of structural systems without labeled data, is proposed in this study. The systems with structural topologies and member configurations are organized as graph data and later processed by a modified graph isomorphism network. Moreover, to avoid dependence on big data, a novel physics-informed paradigm is proposed to incorporate mechanics into deep learning (DL), ensuring the theoretical correctness of the results. Numerical experiments and ablation studies demonstrate the unique effectiveness of StructGNN-E against common DL models, with an average accuracy of 99% and excellent computational efficiency. Due to its differentiability, StructGNN-E is promising for bidirectionally linking structural parameters and analysis results, paving the way for a new end-to-end structural optimization method in the future.