## 4 Numerical Results
### Control Arm Optimization  
This subsection applies a BESO-like algorithm, inspired by bone remodelling applications in which the output is not a binary density structure, to optimise the stiffness of a suspension control arm by making use of the FEM and the NNRIPM as solvers. The optimisation parameters were chosen based on values previously documented in the literature [32]. Penalisation ratios (PRs) of 5% and 10% are applied, and the reward ratio (RR) will be kept at all moments to 1%. The effective von [PERSON] stress criterion is used exclusively. The process began by finding a 3D CAD model of a relatively functional control arm. The geometry was then simplified to a 2D format using Solidworks(r) Student Edition 2023 SP2.1 (Figure 3). The created 2D sketch was subsequently exported to FEMAP 2021.2 MP1 (student version licence) for mesh generation before being imported into the software developed by the research team written in Octave/Matlab (2023b). Four different meshes were built, corresponding to four distinct case studies that will be further analysed: a mesh D1 with the arm's characteristic perforation (Figure 4A), a mesh D2 without the perforation (Figure 4B), a mesh D3 with perforation and material non-remodelling zones (Figure 4C), and a mesh D4 without perforation and with material non-remodelling zones (Figure 4D). The material non-remodelling zones, at the essential  
Figure 2: Schematic representation of the optimization algorithm flowchart. and natural boundary conditions, are necessary to ensure that these zones do not reduce its material density. By maintaining a homogeneous and continuous material distribution at the essential and natural boundary conditions, strain/stress concentrations are avoided in these sections, expectedly allowing for a smoother material remodelling. The material properties considered were purely academic and do not represent a specific material. Thus, the following mechanical properties were assumed: [PERSON]'s modulus \(E=1\) MPa and Poisson's ratio \(\
u=0.3\). Respecting the control arm function, the essential and natural boundary conditions shown in Figure 5 were considered. At the circular surface, a distributed load of \(f=1\) N/mm was applied. These boundary conditions replicate bending (flexion) of the component, a common mechanical behaviour experienced during the structure's operation. Figure 4: Nodal discretizations of the control arm. (**A**) Discretization of the model with central perforation—D1. (**B**) Discretization of the solid model (without perforation)—D2. (**C**) Discretization of the model with central perforation and remodelling domain constraints—D3. (**D**) Discretization of the solid model with remodelling domain constraints—D4. Figure 5: Essential and natural boundary conditions of the suspension control arm. Figure 3: Adopted suspension control arm. (**A**) 3D geometric model and (**B**) 2D sketch for the construction of the 2D models. Tables 1-4 present the obtained topologies for the different meshes and control arm arrangements considered. Analysing the design solutions allows us to understand that the perforation in the control arm is situated in the null stress location. Thus, this indicated that this perforation serves solely to reduce the component's overall mass. Examining real-world suspension assemblies further strengthens this observation, as the perforation often appears without hindering the component's functionality. The optimisation results suggest the possibility of even more substantial material removal compared with the original design. The obtained density fields consistently displayed highly binary structures (clear distinctions between solid and practically void regions) across all cases. Notably, a penalisation ratio (PR) of 5% yielded the most promising solutions. These solutions exhibited a clear improvement and better connectivity between generated sections, particularly evident when comparing the initial and final iterations of both methods.