## 6 Results and Discussion  
### Optimised Topologies Using Non-Penalisation SEMDOT  
A parametric study on the filter radii was performed for the same evolution rate (\(ER\) = 0.50). It has been shown that decreasing the radius had the expected beneficial effect on reducing the computation time by reducing the number of iterations (from 175 to 155, 120 and 101) without losing quality for the solution until \(r_{min}\) = 2 (Figure 5). On the other hand, for \(r_{min}\) = 1, which is not a usual value for TO, the solution's quality was impacted (with 68 iterations). Firstly, the smoothness of its edges and its manufacturability was compromised. Compared with the baseline scenario (\(ER\) = 0.50 and 101 iterations), the solution with \(ER\) = 0.25 yielded 201 iterations, and \(ER\) = 0.75 decreased this number to 68. However, while the results for \(ER\) = 0.50 and \(ER\) = 0.25 were practically indistinguishable, the optimisation for \(ER\) = 0.75 was clearly different from the former, exhibiting rougher edges. It can be concluded that the trend attains improved solutions for smaller \(ER\), but values under \(ER\) = 0.50 do not change the solution significantly. Two solutions were taken for assessment purposes here. The first was defined by \(r_{min}\) = 2, while the second was the \(r_{min}\) = 4 solution. The goal was to assess the nonlinear behaviour of the solutions bounding the \(r_{min}\) acceptable range with large and small radii. Both cases were expected to have similar behaviour, given their topological similarity. The assessment showed that \(ER\) values including and under 0.50 (until 0.25) performed similarly. Hence, the following results were limited to \(ER\) = 0.50 and \(ER\) = 0.25 case. These results show adequate behaviour until the plate's ultimate state, including large and global displacements, dispersion of plasticity in four out of five bolt holes, and absence of local plasticity in the additional internal voids created by the TO process. The ultimate stress was achieved mainly within the non-optimisable domain with a mostly symmetric pattern. Hence, not only was the ultimate behaviour balanced (in the sense that it distributed yielding and plasticity almost uniformly), but the optimisation procedure was also proven to subtract material where it was not needed, even considering the ultimate nonlinear behaviour to which the plate was not optimised. The second solution (\(ER=0.50\) and \(r_{min}=4\)) nonlinear behaviour is depicted in Figure 12 (ultimate displacement shape), Figure 13 (longitudinal displacement map), Figure 14 (von Mises stress map), Figure 15 (stress map for areas exceeding the yield threshold), and Figure 16 (stress map for areas exceeding the ultimate threshold). Figure 11: Map of areas above ultimate stress of 450 MPa. Figure 9: [PERSON] stress map [MPa]. Figure 14: [PERSON] stress map [MPa]. Figure 12: Ultimate displacement shape (x2), with the undeformed shape (in grey) for comparison. Figure 15: Map of areas above yield stress of 345 MPa. This second batch of results depicts a slightly different scenario, with extensive plastic damage in the first four bolt holes and less prominent damage near the second hole, but with a much more widespread plasticisation by the first hole. The main difference between the first case and this second one lies in the latter's ability to keep the straightness of the large displacements in the fourth hole. Hence, despite a noticeable asymmetry in this hole, nearby plastic phenomenon, similarly to what happened for the first case, the in-plane transverse displacement was better controlled, avoiding this first likely local collapse and providing the conditions to develop the ultimate plastic phenomenon in the first hole, where there was more material, and therefore a longer ultimate displacement. The previously depicted differences in the two batches of results did not significantly impact the ultimate resistance, but fostered a non-negligible difference in the ultimate displacement.