## 4 Structural Optimization Design
### Constructing the Optimal Model  
The essence of optimal design is the problem of finding extrema, establishing mathematical relationships between the design variables and optimization objectives, and generating mathematical models [18]. The three elements of the optimization model are the design variables, the constraints, and the objective function. Combined with the practical situation of optimization of the large-body structure, three elements can be defined: a total of five parameters, \(R_{1}\), \(R_{3}\sim R_{6}\), were chosen as the design variables based on the results of the orthogonal tests in Section 4.1; the constraints were the stiffness and strength of the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Test Number** & \(R_{1}\) & \(R_{2}\) & \(R_{3}\) & \(R_{4}\) & \(R_{5}\) & \(R_{6}\) \\ \hline
2 & 1 & 2 & 2 & 2 & 2 & 2 \\
3 & 1 & 3 & 3 & 3 & 3 & 3 \\
4 & 1 & 4 & 4 & 4 & 4 & 4 \\
6 & 2 & 1 & 2 & 3 & 4 & 5 \\
7 & 2 & 2 & 3 & 4 & 5 & 1 \\
8 & 2 & 3 & 4 & 5 & 1 & 2 \\
9 & 2 & 4 & 5 & 1 & 2 & 3 \\
10 & 2 & 5 & 1 & 2 & 3 & 4 \\! &! &! &! &! &! &! \\
25 & 5 & 5 & 4 & 3 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Orthogonal test table. large-body structure; and the quality of the bulk structure was an objective function. Having identified the three elements, we constructed the optimal design model, the objective function relation equation. This study used the optimal Latin square method to conduct experiments to obtain the data for constructing the relational equation of the objective function [19]. The optimized Latin square method has a better and more uniform filling of the sampling space, which can reflect the characteristics of the sample space while retaining the advantages of the original Latin square method in terms of efficiency and effectiveness. The ANSYS APDL software was used to obtain the mass, maximum stress, and deformation values for large structures under the most dangerous conditions for different design variables, and the resulting test results data were organized into test tables. Some of these are shown in Table 3.  
In order to obtain optimal values for each design variable, the bulk structure was then optimized to reduce the redundancy of the design. It was necessary to construct expressions for the five design variables as a function of the bulk structure's mass, maximum stress, and maximum deformation. The experimental data obtained from the optimized Latin square design was first processed using regression analysis. The EXCEL regression analysis tool is more convenient, simpler, and more efficient than other methods. Therefore, a regression analysis of the experimental data using the data processing tool EXCEL was selected from a variety of regression analysis methods. First, the specific influence coefficients of the five design variables on the objective function were analyzed, and a table of the regression analysis results for the expression of the large-body structure mass function is shown in Table 4.  
Collating the data in the table yields the following expression for the regression function of the mass \(M\) on the five design variables:  
\[M=1216390X_{1}+169125.3X_{2}+241171.9X_{3}+34127.85X_{4}+234725.8X_{5}+4595.752 \tag{1}\]  
The results of the regression analysis of the expression for the maximum stress function of the large-body structure subjected to the analysis can be seen in Table 5.  
Collating the data in the table yields the following expression for the regression function of the maximum stress \(S\) on the five design variables: