We propose a physics-informed elastic structural analysis framework based on graph neural network: StructGNN-E, which is capable of digitalizing the topological features and member composition information of structure systems with high fidelity, and performing elastic structural analysis on arbitrary structures of bar systems without labeled dataset to produce theoretically correct results. We summarize the main characteristics of the problem concerned and the limitations of typical neural networks on capturing static features on system level, and introduce the graph neural network (GNN) to describe the non-seriality and non-transitional-invariance of structural systems. By considering the scarcity of available dataset and inadequacy of typical deep learning methods which ignores mechanical interpretations, we build up a physics-informed framework imbedded with mechanical theories including equilibrium and constitutive equations as prior information, which offer an innovative solution to structural analysis on neural networks without labeled dataset. Numerical experiments demonstrated that StructGNN-E is able to obtain results with high accuracy on the system level, and we observe a 36% increase on the efficiency for elastic analysis of large-scale frame structures. By comparison tests, we show the inefficiency of typical neural networks and data-driven models on the system level, and further demonstrate the validity and rationality of StructGNN-E.