## 4 Composite Optimization
### Structural Performance in Pure Torsion  
In addition to low mass, a critical requirement in the design and manufacture of racing automobile chassis structures is high stiffness. This necessity arises because lateral loads are transmitted from the front to the rear of the vehicle in proportion to the roll stiffness of the suspension assemblies. Therefore, a sufficiently robust platform must be provided to support their mounting, as vehicle dynamic performance and handling critically depend on this parameter. As a general principle, the target stiffness of a structure is determined by comparing the deformation with the deflections of the suspension springs and tires. However, the inherent adjustability of race car suspension systems to varying conditions complicates this comparison. Consequently, defining the optimal rigidity of a race car chassis remains challenging. Conversely, some scholars argue that chassis stiffness should be increased only until the overall mass of the structure remains within acceptable limits [28]. Moreover, it is important to note that in this study, chassis stiffness is determined by the applied boundary conditions and, consequently, by the output of the genetic algorithm. Therefore, its load behavior must be assessed based on specific performance criteria. The analysis of chassis torsional behavior under complex loading is challenging due to the complexity of the resulting stress field. Consequently, to circumvent the precise specification of local stress tensor as boundary condition--which may compromise accuracy--a simplified scenario involving the application of a pure moment was utilized. In this scenario, the torsional load was applied at the nodes located on the plane bisecting the centers of the front wheels. This approach eliminated vertical surface loads on the monocque, thereby simplifying the stress distribution within the structure. Additionally, it facilitated comparisons between the numerical results and an analytical beam torsion model to support conclusive data evaluation [29]. The chassis torsional response was evaluated analytically by partitioning it into two segments, simulating the monocque cockpit, modeled as springs in series with the first segment represented as a U-shaped tube and the second as an orthogonally shaped tube under torsion, as in Figure 18. Additionally, the model's movement was constrained at the rear of the U-shaped section and a moment was applied at the front. The resulting torsional stiffness or twist angles from both analytical and finite element models were then compared. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Normal Stress (\(\sigma_{\text{x}}\)) (MPa)** & **Normal Stress (\(\sigma_{\text{y}}\)) (MPa)** & **Normal Stress (\(\sigma_{\text{z}}\)) (MPa)** & **Element Size (mm)** \\ \hline
178.92 (MPa) & 62.86 (MPa) & 6.38 (MPa) & 27.5 \\
152.41 (MPa) & 78.47 (MPa) & 4.75 (MPa) & 22.5 \\
144.01 (MPa) & 81.78 (MPa) & 5.08 (MPa) & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Impact of the element size on the maximum absolute normal stress values. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Shear Stress (\(\tau_{\text{xy}}\)) (MPa)** & **Shear Stress (\(\tau_{\text{yz}}\)) (MPa)** & **Shear Stress (\(\tau_{\text{xz}}\)) (MPa)** & **Element Size (mm)** \\ \hline
41.00 (MPa) & 13.10 (MPa) & 20.15 (MPa) & 27.5 \\
59.41 (MPa) & 12.96 (MPa) & 20.19 (MPa) & 22.5 \\
53.21 (MPa) & 12.66 (MPa) & 31.68 (MPa) & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Impact of the element size on the maximum absolute shear stress values. For the U-shaped section, the initial hypothesis posits that the applied torque induces torsional deformation by twisting the section about its central top-bottom point of geometry. Consequently, this action transforms the section's exploded view into a horizontally oriented lozenge-shaped parallelogram or rhombus, analogous to the deformation observed under shear force in classical mechanics [24].