## 4 Numerical Results
### Topology Design and Structural Analysis  
Four new models were created based on the previously optimised control arm design, aiming to translate such findings into practical geometries suitable for manufacturing. These models incorporated key features from the optimisation results and considered common design practices for control arms (Figure 7). Thus, Model 1 is a reinforced version of the solutions presented in Table 2. Model 2 is a commonly used design for the control arm. Model 3 is a reinforced version of the solutions shown in Table 4, and Model 4 is a variation of Model 3 with a modified boundary contour. This modification involves a 50% increase (1.5 times) in the boundary contour thickness compared with the baseline model. The localised increased thickness is achieved by a 6 mm outward offset from the original boundary contour, which was set to 1.5 times the nominal value of the remaining part. With the respective design modelling completed, the essential and natural boundary conditions used in the optimisation process were imposed, and static linear analyses were performed with each model shown in Figure 7 and also with a completely solid model. Table 5 presents the displacement and von Mises stress fields obtained for the solid model using both FEM and RPIM. The comparison revealed minimal discrepancies between the methods. Tables 6 and 7 show the obtained von Mises stress field and displacement field of each studied model for the FEM and RPIM analyses, respectively. Then, Table 8 summarises the structural values (obtained with the linear static analyses) and volume fractions of the designed models. Notice that \(K\) represents the directional stiffness of the component regarding the applied load. It is calculated with the following expression:  
\[K=\frac{1}{n}\cdot\sum_{i=1}^{n}\frac{f_{i}}{d_{i}}, \tag{32}\]  
being \(n\) the number of nodes along the natural neighbour, \(f_{i}\) the force applied at node \(n_{i}\) of the natural boundary, along direction \(Ox\), and \(d_{i}\) is the displacement obtained at the same node \(n_{i}\), along the same direction \(Ox\). Based on the presented results, the following conclusions can be drawn:  
Figure 7: Optimised models of the control arm for the elasto-static analysis. (**A**) Model 1, (**B**) Model 2, (**C**) Model 3, and (**D**) Model 4. * Comparing with the other proposed models, Model 2 shows the lower von Mises stress and higher stiffness. Additionally, its specific stiffness is close to the solid arm. Therefore, it appears that Model 2 shows the best mechanical performance. These results align with initial expectations, as the circular material removal promotes a more uniform stress distribution throughout the structure. Consequently, stress does not concentrate at specific points, leading to a reduction in the risk of failure and an overall increase in the model's stiffness. * Models 1 and 3 adopted similar design approaches, both employing a triangular material removal strategy, resulting in identical performance values. However, Model 1 allows for lower stress values. The thickness of the bar seems to be less important than its orientation. Therefore, the reason behind the best performance seems to be a multifactorial problem, depending on the bars' orientation, thickness, and distribution. * Model 4, a variation of Model 3 with a thicker outer contour (known as coating), displayed higher stiffness and lower maximum von Mises stress as anticipated (when directly compared with Model 3). However, due to the increased volume fraction associated with this reinforcement, the specific stiffness remained unchanged compared with Model 3. It was verified that both formulations are capable of producing very similar results. With Tables 6 and 7, it is possible to understand that FEM consistently predicts slightly lower stresses than RPIM formulation. This can be explained by the higher bending stiffness of the constant strain triangular element, well documented in the literature [33].