## 3 Method Implementation and Application
### Topology Optimization and Structural Analysis  
The next step is the TO of each promising shape to define a geometry that is structurally efficient and respectful of the constraints imposed by the requirements. The main substeps are:  
* The definition of the design space. * The definition of load conditions. * The first weight reduction and the analysis of results. * The final weight reduction and the analysis of results. * The structure embodiment into a feasible layout. The expected results are efficient structural models that have to resemble the starting shapes and respect the regulatory requirements. This phase corresponds to the embodiment design. Before performing a TO of the 3D CAD models of the representative shapes, we had to define the material, constraints, and loads as in the following list:  
* Material: SAE 304 stainless steel, which is the most common stainless steel used in analyzed applications. * Constraints: applied to the supports at the base of the pylon, which are fixed. * Loads: see the reference standard, integrated in the law 1341/1964 and D.P.R. 1062/1968. In particular, the pylons need to be verified in the following four Load Conditions (LC):  
1. LC#1: All conductors and guard ropes have to be intact at \(-5\)\({}^{\circ}\)C, with the wind blowing at 130 km/h perpendicular to the electricity line. 2. LC#2: Under the conditions of temperature and load of LC #1, for the structures considered here, one conductor or one guard string is broken. 3. LC#3: All conductors and guard ropes are intact at \(-20\)\({}^{\circ}\)C and under load due to the presence of ice sleeves on conductors or guard ropes, with the wind blowing at 65 km/h perpendicular to the line. 4. LC#4: Under the conditions of temperature and load of LC #3, one conductor or one guard string is broken. Figure 10: Preliminary set up of the 3D CAD model for the 380-kV line. (**a**) Capestrano Warrior statue; (**b**) Eagle; (**c**) Sail. According to the related standard and legislative specifications, the LC on the pylon are calculated by considering the following assumptions:  
* The weight of the equipment is evaluated considering the chain of insulators, the terminal tower clamps, and any additional clamps. * The wind thrust on the equipment is assumed to be equal to 10% of the brunt of the wind on the conductors. * The wind thrust on the support is approximated as if two adjacent faces of the support were exposed perpendicularly to the wind, cautiously neglecting the voids due to the reticular structure; the determined load is applied at different points so as to give the same resultant force. The calculations were carried out assigning:  
* Span length = 350 m;
* Diameter of guard ropes = 0.0115 m;
* Type of connection = ditching clamps;
* Conductor diameter = 0.0315 m;
* 20 hood and pin insulators made of tempered glass for each pylon. A TO was performed considering the most unfavorable LC to the model. With regard to Figure 11a, the worst conditions occur when the angle between the two adjacent spans (in green) is 120\({}^{\circ}\) and one of the conductors (in red) is broken. This causes bending in the same wind direction. Between the two LC of the standard that prescribe the breaking of a conductor (LC#2 and LC#4), LC#2 is applied. Compared to LC#4, it prescribes a higher wind speed and the absence of ice. This choice does not limit the result of the topological analysis; this analysis is expected to identify the optimal paths for the lines of force that cross the structure. The next engineering phase (see next subsection) will design in detail a structure that verifies all four LCs. The application of an asymmetrical load produces a model optimized only for unbalanced loads on one side. To solve this problem, in the optimization software the constraint of symmetry is imposed with respect to a user-defined plane. The TO was performed by using the Altair [EMAIL_ADDRESS] software. In Figure 11b, the model, the constraints, and the loads for LC#2 are summarized.