# Triangular Position Multi-Bolt Layout Structure Optimization
## 4 Conclusions  
This paper applies the gray wolf algorithm to optimize the structural layout of multi-bolt positioning in triangular configurations. By analyzing the forces, the objective function is formulated based on the fitted functions of hole perimeter stress for nickel steel plates, maximum shear stress for bolts and bending stress for nickel steel plates. The value range for bolt diameter and spacing is determined according to design specifications. The optimal solutions calculated using the fruit fly optimization algorithm, particle swarm optimization algorithm, gray wolf optimization algorithm, multi-verse optimization algorithm and wind driven optimization algorithm are compared. ABAQUS simulation software is used to model and compare the stress on nickel steel plates and bolts before and after optimization, thereby verifying the correctness of the algorithm application. Through analysis, the following conclusions can be drawn:  
1. Before optimization, a traditional design method was used with a bolt spacing of 60 mm and a bolt diameter of 8 mm. After optimization, the bolt spacing is chosen as 108.5629 mm and bolt diameter is 9.0233 mm. The stress distribution of the newly  
Figure 13: Comparison chart for optimisation of different force cases. arranged nickel steel plate is more uniform, and the local stress values have also been reduced, resulting in a more stable overall stress state. 2. Through this layout optimization, under pressures and tensions of 15 KN, the hole perimeter stress on the upper nickel steel plate decreased by 73.1 MPa, with an optimization rate of 24%. The hole perimeter stress on the lower nickel steel plate decreased by 8.7 MPa, with an optimization rate of 2.8%. The maximum equivalent stress on the bolts decreased by 47.7 MPa, with an optimization rate of 12.5%. 3. When the load is less than 18 KN, the optimization effect of both the upper nickel steel plate and bolt assembly is above 10%. However, when the load exceeds 18 KN, the optimization effect decreases. When the load exceeds 21 KN, the nickel steel plate has exceeded its yield limit. The upper nickel steel plate shows significant optimization, but the optimization effect on the lower nickel steel plate is not obvious due to the existence of fixed constraints that restrict pressure. 4. The chosen material for the connecting structure in this article is nickel steel plates, which are widely used in the load-bearing connection structures of large and complex equipment and aerospace and other complex mechanical fields. By optimizing the structural layout, fatigue damage of bolt holes or plastic deformation of connectors caused by excessive hole perimeter stress can be effectively prevented. This enhances the safety, reliability and stability of load-bearing connection structures. 5. This article studied the non-symmetrical triangular structure of bolt connections, providing an effective method and ideas for the layout optimization of non-symmetrical bolt configurations, enriching the research achievements in related fields. This paper proves the correctness of applying algorithms to optimize bolt layouts. However, it only focuses on a specific equilateral triangular multi-bolt structure. In future studies, the layout optimization of randomly positioned multi-bolt structures should be further analyzed. Moreover, this article only conducts simulations on nickel steel plates, and subsequent experiments and simulations should cover different metal materials to enhance the applicability of this article. [PERSON] conducted experiments, data collection and analysis, and study design. [PERSON] designed and conceived the project. [PERSON] wrote and edited the manuscript to verify the correctness of the method. [PERSON] reviewed and edited the manuscript. [PERSON] and [PERSON] investigated the research background and conducted a literature search. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.