# Size and Shape Optimization of a Guyed Mast Structure under Wind, Ice and Seismic Loading
## 6 Results and Discussion
In the post-processing phase, in fact, the optimized section chosen by the list of the FE software was manually edited since the structural constraint violation or the maximum performance ratio was not reached during to the optimization process. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No Parameters** & **PR Initial** & **PR Optimized** & **PR Design** \\ \hline  & [\%] & [\%] & [\%] \\ \hline
1 & & 45.7 & 40.5 \\
2 & & 39.5 & 43.1 \\
3 & & 50.5 & 50.6 \\
4 & 28.0 & 54.4 & 58 \\
5 & & 65.8 & 60.2 \\
8 & & 68 & 66 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Averaged performance ratios obtained in each optimization scenario. \begin{table}
\begin{tabular}{c c c} \hline \hline
**No Parameters** & **Initial Mass [kg]** & **Optimized Mass [kg]** & **Design Mass [kg]** \\ \hline
1 & & 1003 & 1176 \\
2 & & 1051 & 1111 \\
3 & & 803 & 818 \\
4 & & 574 & 588 \\
5 & & 403 & 453 \\
8 & & 385 & 408 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Mass values before/after optimization and after proper approximation (design) using commercial steel profiles. Moreover, in Table 9, the optimized design section for different independent iterations and the proposed industrial solutions according to product list, provided by the software, are listed. As expected, the mass reduction achieved during the optimization process results higher than the design solution due to the approximation issue. For the proposed scenario, the iteration (\(N_{trial}\)) that guarantees the best objective function is the second. In Appendix A, the graphical (through histogram charts) and numerical representation (through tables) of the optimization result for each scenario are provided. In order to provide an overview of the objective function trend, the performance ratios and mass reduction for each scenario were collected into Figures 12 and 13. The mentioned values were obtained for each scenario, making an average of the results, before and after optimization, independently, for each steel profile composing the central pole. Figure 12 highlights an almost monotone increment of the performance ratios to the number of design variables. Interestingly, for a number of variables n \(\geq\) 5, no significant improvements are achieved. Figure 13 emphasizes an important reduction of structural mass as the design variables increase. Once again, n = 5 represents trade-off. If the number of variables exceed 5, no significant improvements are observed. Figures 12 and 13 show a comparison between each scenario in terms of the average performance ratio and mass reduction, respectively. Figure 12 highlights the difference with the initial state, which has an average performance ratio \(PR_{0}\) = 25.6%. An evident improvement is achieved for scenarios that include the thickness t as the design variable. Figure 11: Scenario G.—PRs trend. In blue—the performance ratios of each pole before optimization are illustrated, otherwise orange for the optimized solution. In green—PRs at a design configuration according to the product list. Figure 12: In blue, orange, and green, the average PRs, respectively, at the initial condition, after optimization, and design solution. Figure 13: Increasing the number of design variables, the final mass becomes gradually smaller, until 385 kg (scenario H). In particular, from Scenarios D, E, F, G, H, the average performance ratios exceed 50%, resulting in a more than 40% difference compared to the initial state. Figure 12 shows that the commercial profiles are sufficient to accommodate the optimized solution.