## 3 Results and Discussions
Figure 12 shows the variations of blade deflections and Von-Mises stresses along the blade length, respectively. Figure 13 illustrates the distributions of mass along the blade length and the stiffness distribution using the three different materials under the same working condition. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**E-Glass/Epoxy**} & \multicolumn{3}{c}{**Braided Composite**} & \multicolumn{3}{c}{**Carbon/Epoxy**} \\ \cline{2-9}  & **QBlade** & **ANSYS** & **Difference \%** & **QBlade** & **ANSYS** & **Difference \%** & **QBlade** & **ANSYS** & **Difference \%** \\ \hline Von mises stress [MPa] & 38.51 & 39.68 & 2.94 & 39.20 & 39.75 & 1.38 & 39.96 & 40.37 & 1.015 \\ \hline Tip deflection [mm] & 43.20 & 46.46 & 7.016 & 29.32 & 33.54 & 6.61 & 16.86 & 18.29 & 7.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The tip deflections and von mises stress using different materials. Figure 11: Tip deflections of (**a**) carbon/epoxy, (**b**) E-glass/epoxy, and (**c**) Braided composite. Figure 12: Variations of (**a**) Von mises stress and (**b**) tip deflection along the blade. Figure 13: Distributions of (**a**) the density, (**b**) longitudinal stiffness, (**c**) Flapwise Stiffness, and (**d**) Edgewise Stiffness along the blade. Based on the results of Figure 12, it can be seen that the largest value of the stresses occurred at \(r/R=0.5\), i.e., in the middle of the blade. This is accrued because the thickness distribution of the shell at the root is appropriate. This causes the stress concentration in the middle of the blade, i.e., in the area of least damage and risk. While results of Figure 12b showed that the largest deflection occurred for E-glass material, followed by braided composite material, and then carbon epoxy material. Figure 13 shows the wind turbine blade's distributions of mass and stiffness. It is clear that this distribution was linear, thicker on the root side and less thick on the tip side. This makes it a suitable distribution for the composite materials layers along the length of the blade. The main objective of studying the dynamic problem of the wind blade is to determine the compatibility of the aerodynamic shape design with the structure of the blade or the status of mass distribution/stiffness that is appropriate along the length of the blade. The optimal mesh was selected depending on the mesh of the steady-state analysis, as shown in Figure 7. Figure 14 presents the natural frequencies and the displacements of the wind turbine blade for the first 6 th mode shapes using the selected materials, respectively. Figures 15-17 show the first 6 th mode shapes of the wind turbine blade using the selected materials. It A comparison was made between the results of Ansys software and QBlade to find the frequencies for different materials, as shown in Table 7.  
The wind turbine blade's structural stiffness depends on the materials' properties, especially Young's modulus (\(E\)) and the density (\(\rho\)). Therefore, the natural frequencies of the wind turbine structure depend basically on the ratio (\(\sqrt{E/\rho}\)). According to the results of the modal analysis of the wind turbine blade in Figure 14a, it's observed that the frequencies of the E-glass fiber material were less than those of braided composite and carbon epoxy materials, which made it less resistant to vibrations. Despite this, the braided composite and E-glass material results are not considered far away due to the convergence of their ratio (\(\sqrt{E/\rho}\)). While the carbon/epoxy material has the highest natural frequencies compared with the other materials because it has the highest ratio of (\(\sqrt{E/\rho}\)). Figure 14b shows the displacements of the blade tip at the selected modes shape of the three proposed materials. It can be seen that the carbon/epoxy material had the least displacement, due to the high stiffness of the material, followed by the braided composite material and then the E-glass/epoxy material.