## 2 Numerical Modeling and Analysis
### Analysis Results
The analysis with the smallest thickness was the one with t = 2 mm, for which the maximum displacement was 16.32 mm in the \(X\)-axis, 27.64 mm in the \(Y\)-axis, and 20.35 mm in the \(Z\)-axis. Accordingly, it can be concluded that for a thickness increase of 3 mm a reduction in displacements equal to 16.36% in the \(X\)-axis, 6.62% for the \(Y\)-axis and 27.56% for the \(Z\)-axis was achieved. Therefore, the increase in thickness under the specific loading scenario conditions resulted in higher reduction in displacements in the \(Z\)-axis than in the \(X\)- and \(Y\)-axes. Furthermore, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Modulus of Elasticity, E**} & \multicolumn{3}{c}{**Displacements**} \\ \cline{2-4}  & **X-Axis** & **Y-Axis** & **Z-Axis** \\ \hline E = 2340 Mpa & 14.13 mm & 25.00 mm & 15.40 mm \\ E = 1520 Mpa & 14.21 mm & 25.83 mm & 15.82 mm \\ E = 1000 Mpa & 14.28 mm & 26.53 mm & 16.21 mm \\ E = 320 Mpa & 14.44 mm & 28.25 mm & 17.23 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Max displacements in the three axes for various values of the modulus of elasticity of the brace material. Figure 10: Von Mises stress results (MPa) for material with modulus of elasticity: (**a**) E = 2340 MPa, (**b**) E = 1520 MPa, (**c**) E = 1000 MPa, and (**d**) E = 320 MPa. according to the diagram shown in Figure 11, the largest displacement values are observed in the \(Y\)-axis, but the largest overall change is found in the \(Z\)-axis. Moreover, the smallest displacements are observed on the \(X\)-axis, leading to the conclusion that the brace is stiffer in the horizontal direction, specifically in the \(X\)-axis direction. The analysis results for different values of the elasticity modulus are illustrated in Table 3, showing that as the modulus of elasticity of the material decreases, the maximum developed stress decreases as well. The observation regarding local vs. global change in developing stresses holds here also, as in the case of increasing thickness. Namely, for E = 2340 MPa the maximum stress is 40.36 MPa, for E = 1520 MPa it is 26.91 MPa, for E = 1000 MPa it is 18.15 MPa, and for E = 320 MPa it is 6.17 MPa. Regarding the observed displacements, they decrease in all three axes as the modulus of elasticity of the brace material increases. In particular, from Table 4 and Figure 12 it is confirmed that the smallest change in displacements is observed in the \(X\)-axis, followed by the \(Z\)-axis, while the largest change is observed in the \(Y\)-axis. In more detail, for an increase in elastic modulus of 2020 MPa, a reduction in 2.14% was achieved in the \(X\)-axis, 11.5% for the \(Y\)-axis, and 10.62% for the \(Z\)-axis. According to Table 4, the highest displacement values are observed on the \(Y\)-axis, while the displacements on the \(X\)- and \(Z\)-axes are quite close, with the \(X\)-axis plot being almost a straight line, which reveals the fairly small change in displacements on this axis. Figure 11: Section thickness—Displacements chart describing the change in deformation with increasing the thickness of the section of the brace. Figure 12: Modulus of elasticity–displacements chart describing the change in deformation with increasing modulus of elasticity.