## 3 Method Implementation and Application
### Topology Optimization and Structural Analysis
In the case of very large shapes, the TO continues to be applicable, but to obtain a better result it is better to proceed incrementally. The first step consists of considering the complete design volume (Figure 12, top row) and performing a TO for an initial reduction of material mass (Figure 12, bottom row, which shows TO  
Figure 11: (a) The most unfavorable Load Condition (LC#2), with two adjacent spans (in green) that form an angle of 120\({}^{\circ}\), and a broken conductor; (b) boundary, constraints, and load conditions (common to all the three shapes). models with only high-energy density elements, i.e., the elements that take part in carrying the loads). Table 9 collects the weight reduction after the first TO. Depending on the initial shape, this reduction is more than 50% for the stockier models (e.g., the Capestrano Warrior and the eagle models). For surface models (or thin thickness models), the reduction of material mass is much more limited, because the starting mass is consistently lower when compared to solid models. This is the case of the sail-shaped model, which consists of a mast (basically not reduced during the TO) and a sail, which is a thin thickness element: even if the percentage of mass reduction appears modest from Table 9, the model has been greatly lightened (Figure 12c). Figure 12a highlights a criticality in the Capestrano Warrior model: after the first weight reduction, the similarity with the starting form is lost. This criticality emerges because the Capestrano Warrior presents a series of identification elements of small dimensions with respect to the macroscopic dimensions of the structure. As the TO process removes these small elements, the resemblance to the starting shape is no longer recognizable. Therefore, in order to maintain the resemblance to the starting shape, a lot of small details should be preserved and shaped by means of several lattice structures in the detail phase. This is not acceptable because these additional structures would increase excessively the final weight of the pylon, mitigating the optimization result. Therefore, we did not consider it more convenient to continue further with the design of this pylon. Regarding the eagle and the sail-shaped models, the outputs of the previous phase (first weight reduction) suggest to apply further mass removal: therefore, each of them were modified and new project space was reconstructed (shown on the left side of Figure 13a,b). With particular respect to the eagle-shaped model, the first weight reduction suggests reducing the wings mass while the vertical support is not affected by any change. Therefore, with the aim to allow a further weight reduction during the second TO for enabling and exploring new designs of the vertical support, its upper diameter was slightly increased. Conversely, the mast in the sail-shaped model was not further modified since it was not the main design element to focus on; moreover, it is partially hidden by the sail, to which we addressed in our design efforts. The results of the second TO are shown on the right side of Figure 13a,b, which show TO models with both high- and low-energy density elements, i.e., the elements that have, respectively, a primary and a secondary role in carrying the loads. The models resulting from the TO provide an indication of the path of the lines of force. In order to make the structure as light and less impactful as possible, the results of TO were approximated, manually, by a reticular structure (Figure 14). This phase requires expertise in structural design; however, the following phase driven by structural analysis allows further modification of the geometry, limiting the influence of errors due to this manual phase. In each model, the main vertical support was discretized into a triangular reticular structure with a vertical axis, while the wings and the sail were delimited by reticular structures. Reinforcement elements were provided for the connection between the sail and the structure of the mast in the lower area.