# Selection Criterion of Reanalysis Methods for Plane Truss Optimization
## 5 Numerical Examples
### Truss Design Calculation Based on User Preferences  
The STSA-P method [32] can convert the user's design preferences for structural appearance into design objectives, thus achieving the effect of guiding structural optimization based on user preferences. This method was applied to design a two-hinged arch truss structure with a span of 20 m. Figure 8 shows the initial structure and load conditions. The point load \(F\) was 150 kN, and the distributed load \(q\) was 100 N/cm. The members were solid and circular, with a material density of 7.85 g/cm\({}^{3}\) and an elastic modulus of 210 GPa. The maximum tensile and compressive stresses were both 31 kN/cm\({}^{2}\). The design objectives of this example included user preferences, structural mass, and maximum node displacement.  
Based on the above information, a user was invited to conduct the truss design using the STSA-P method, and the design results are presented in Figure 9 and Table 6.  
Figure 7: Selection process of reanalysis methods.  
The design results consisted of 12 nodes, 21 member elements, and 20 DOFs. The design objective values were all within the \"tolerable\" and \"desirable\" range, and the user was also satisfied with the design results. In terms of computational efficiency for structural analysis, the total optimization time, the time of using complete analysis (Cholesky factorization) for calculation, and the time of using the selection criterion for calculation were all recorded. Based on these data, the time proportion of complete analysis was calculated to show the time contribution of structural analysis to the entire optimization process. In addition, the efficiency improvement ratio was calculated to demonstrate the efficiency improvement of structural analysis by using the selection criterion. The results are summarized in Table 7.  
Based on the information presented in Table 7, it can be concluded that the total time spent on complete analysis in the design process of the STSA-P system was only 11.82%. This is due to the low structural DOFs, which resulted in shorter calculation times for structure analysis. Additionally, during the optimization process, tasks such as selecting grammar rules and calculating cost functions further decreased the proportion of time spent on structural calculation.  
After applying the selection criterion, the efficiency of structural calculation increased by approximately 4%. However, the improvement ratio was limited due to the low DOFs of the structure, which were less than 50. According to the selection criterion, the complete analysis is used for shape modifications and topology modifications that involve changes  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Design Objectives** & **User Preference** & **Structural Weight** & **Node Displacement** \\ \hline Value & 1.665 & 1974.152 kg & 1.424 cm \\ Range & “Tolerable” & “Tolerable\({}^{2}\) & “Desirable” \\ \hline \hline \end{tabular}
\end{table}
Table 6: Information on design objectives.  
Figure 8: Initial layout of the structure.  
Figure 9: Design results based on STSA-P.  
in structural DOFs. As a result, the difference between using complete analysis and the selection criterion is further minimized.  
In summary, the selection criterion has limited effectiveness in improving efficiency when the number of structural DOFs is low.