# Triangular Position Multi-Bolt Layout Structure Optimization
## Materials and Methods
### Finite Element Modeling and Boundary Conditions  
The bolt specifications in this paper refer to GB/T191-197-2003 [27], and M8 bolts with a pitch of 1.25 mm and a screw length of 50 mm are selected. Nickel steel has important properties such as formability, weldability and ductility, and has good corrosion resistance. It is an important material, and widely used in large equipment, aerospace and other complex assemblies in the field of connection structures. At present, there is little research in the field of nickel steel plates, so the bolt role of the plate in this paper is selected from nickel steel material. The modulus of elasticity of both the bolt and nickel steel plate is 210,000 MPa, the Poisson's ratio is 0.283 and the density is 7999 kg\(\cdot\)m\({}^{-3}\); the maximum stress limit of the bolt is 640 MPa and maximum stress limit of the nickel steel plate is 340 MPa.  
To verify the accuracy of the objective function as well as the algorithm, parametric modeling of the bolt and nickel steel flat plate was carried out based on ABAQUS with Python-3.90 software. Due to the difficulty of meshing the threads in ABAQUS and non-convergence of the calculations, the paper uses a simplified modeling of the bolts without threads [28] and makes the multi-bolt structure act on the bearing surface by applying a preload [29]. The load-bearing structure is two thin nickel steel plates, both of which are elastoplastic flat plates. The two fast nickel steel flat plates were superimposed to simulate the connecting action of complex equipment, as shown in Figure 4. The nickel steel plate is meshed using a hexahedral structured mesh with a cell type of C3D8R cells. In order to make the simulation easier to converge and more precise, the area around the bolt holes and nut of the nickel steel plate is divided to obtain a more precise mesh, as shown in Figure 5 below.  
In this paper, a high quality mesh with 45,430 meshes is divided and partitioned at different locations to ensure the accuracy of the calculation results. At the same time, the  
Figure 4: Bolted connection model.  
Figure 5: Stress of multiple bolts.  
finite element analysis method has been widely used in the simulation analysis of the model, and the reliability of its analysis results can be effectively guaranteed under the condition of ensuring high quality meshes.  
In the solution stage, this paper sets four analysis steps, the first and second steps in the bolt's middle surface, gradually add the bolt load, that is, the preload. In the third and fourth steps, the current length is fixed in order to meet the actual engineering requirements, so that the bolt load changes with the deformation of the structure.  
The contact properties are set to finite slip and the junction-surface discretization method is used. For contact, the harder nickel steel plate is used as the master surface and the bolt surface as the slave surface, defaulting to contact when the distance between the two is less than 0.03. The tangential contact is set with a friction coefficient of 0.3, and the normal contact is a hard contact to prevent penetration.  
If a force of 15 KN is applied in the X and Y directions, the bolt will be severely deformed, thus affecting the simulation results, and the simulation mainly compares the stresses on the nickel steel plate and bolt before and after optimization, independent of the force direction of the plate. Therefore, in Step 3, the tension and pressure are applied to the upper nickel plate in the positive X-axis and negative Z-axis directions. The leftmost side of the lower nickel steel board applies a fixed restraint.