Single-step tightening is simple and fast compared to multi-step tightening, and it is therefore frequently used during the tightening of bolts in flange structures. However, single-step tightening to maintain uniformity is more difficult to achieve. To address this problem, existing methods such as the Elastic Interaction Coefficient Method (EICM) and Tetraparametric Assembly Method (TAM) have been investigated for load uniformity in single-step tightening. In order to improve the computational efficiency and accuracy of the traditional methods, a new single-step tightening method is proposed in this paper. This method can realize the design of the initial preload force simply by measuring the change in bolt load in a specific sequence. It is verified by numerical simulation that this method can realize the uniform distribution of bolt load. In addition, this paper will provide suggestions for the optimal tightening sequence for the single-step tightening method.

Sequential tightening redistributes load among bolts and produces a residual preload field that depends on the complete operation history. This study presents a physics-informed graph-learning framework for a 60-bolt circular flange. The model receives initial preloads and tightening order and predicts the residual preload field on a complete causal directed graph. All 1770 admissible later-to-earlier edges are retained. Among them, 240 local edges carry non-zero Elastic Interaction Coefficient Method (EICM) attributes, while 1530 distant edges remain available to learned message passing. The multi-fidelity dataset combines online EICM responses, prescribed nonlinear-discrepancy labels, and repeated ultrasonic preload measurements. On the augmented development split, TransformerConv-L3 achieved an MAE of 138.3 N, an RMSE of 170.9 N, an NLL of 8.839, and 93.9% coverage for the nominal 95% prediction interval. Its RMSE was 56.9% lower than that of the strongest recurrent baseline evaluated under the same protocol. These results demonstrate the value of combining causal topology with mechanics-informed edge attributes for residual preload prediction.