## 2 Structural Analysis and Design of the Blade
### Blade's Material and Lay-Up Sequence  
The blades of a small wind turbine are manufactured from several materials; among the most common typical materials are E-glass/epoxy, S-glass/epoxy, carbon/epoxy, braided composite, aluminum, etc. Because of the diversity of materials used to manufacture the wind turbine blade, it was selected in this study the most typical materials to optimize the blade structure. Also, it will optimize the wind blade to reach high stiffness with minimum weight. It will certainly minimize the cost of the wind turbine and improve its performance. Table 2 shows the properties of the three selected materials used to optimize the wind turbine blade [24; 25].  
Figure 4: Schematic of blade sections.  
Figure 3: The variation of Lift (_Cl_) and drag (_Cd_) coefficients with the angle of attack.  
The blade of a small wind turbine consists of four basic parts: the root, the neck, the shell, and the shear web. Each part of the blade has a different layer thickness and fiber orientation. Determining proper fiber orientation and laminate thickness is significant in decreasing the difficulties of manufacturing and increasing the structural stiffness. The lay-up sequence, orientation, and laminate thickness are optimized for the selected composite materials. Table 3 presents the layers sequence of the blade, and Figure 5 shows the 3D model of wind turbine blade materials. Where each section is marked with diffident color. These colors reflect the difference in the thickness and fiber orientation of the composite material (Table 3).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **E-Glass/Epoxy** & **Carbon/Epoxy** & **Braided Composite** \\  & [24] & [24] & [24,25] \\ \hline \(E_{1}\) (GPa) & 48.7 & 136.7 & 62.8 \\ \(E_{2}\) (GPa) & 16.8 & 8.2 & 62.8 \\ \(G_{12}\) (GPa) & 5.83 & 4.45 & 9.68 \\ \(G_{23}\) (GPa) & 6 & 2.91 & 7.97 \\ \(v_{12}\) & 0.28 & 0.29 & 0.33 \\ \(v_{23}\) & 0.20 & 0.42 & 0.40 \\ \(X_{\rm T}\) (MPa) & 1170 & 1604 & 460 \\ \(X_{\rm C}\) (MPa) & 977 & 1305 & 420.4 \\ \(Y_{\rm T}\) (MPa) & 30.5 & 40.5 & 526.2 \\ \(Y_{\rm C}\) (MPa) & 114 & 239.7 & 420.4 \\ \(\rho\)(kg/m\({}^{3}\)) & 2000 & 1518 & 1800 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material properties of wind turbine blade.  
Figure 5: 3D model of the composite blade with 10 sections.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Section Name** & **Location (m)** & **Shell Layup** & **Thickness (m)** & **Shear Web Lay-Up** & **Thickness (m)** \\ \hline
1 & 0.200–0.400 & [(\(\pm 45\))3/08/(\(\pm 45\))]s & 0.0064 & [(\(\pm 45\))3/09/(\(\pm 45\))]s & 0.0070 \\
2 & 0.400–0.600 & [(\(\pm 45\))3/07/(\(\pm 45\))]s & 0.0058 & [(\(\pm 45\))3/08/(\(\pm 45\))]s & 0.0064 \\
3 & 0.600–0.811 & [(\(\pm 45\))3/06/(\(\pm 45\))]s & 0.0052 & [(\(\pm 45\))3/07/(\(\pm 45\))]s & 0.0058 \\
4 & 0.811–1.022 & [(\(\pm 45\))2/06/(\(\pm 45\))]s & 0.0048 & [(\(\pm 45\))3/06/(\(\pm 45\))]s & 0.0052 \\
5 & 1.022–1.233 & [(\(\pm 45\))2/05/(\(\pm 45\))]s & 0.0042 & [(\(\pm 45\))2/06/(\(\pm 45\))]s & 0.0048 \\
6 & 1.233–1.444 & [(\(\pm 45\))2/04/(\(\pm 45\))]s & 0.0036 & [(\(\pm 45\))2/05/(\(\pm 45\))]s & 0.0042 \\
7 & 1.444–1.655 & [(\(\pm 45\))2/03/(\(\pm 45\))]s & 0.0030 & [(\(\pm 45\))2/04/(\(\pm 45\))]s & 0.0036 \\
8 & 1.655–1.866 & [(\(\pm 45\))2/02/(\(\pm 45\))]s & 0.0024 & [(\(\pm 45\))2/03/(\(\pm 45\))]s & 0.0030 \\
9 & 1.866–2.077 & [(\(\pm 45\))/02/(\(\pm 45\))]s & 0.0020 & [(\(\pm 45\))2/02/(\(\pm 45\))]s & 0.0024 \\
10 & 2.077–2.288 & [(\(\pm 45\))/01/(\(\pm 45\))]s & 0.0014 & [(\(\pm 45\))2/02/(\(\pm 45\))]s & 0.0020 \\
11 & 2.288–2.500 & [(\(\pm 45\))/01/(\(\pm 45\))] & 0.0007 & [(\(\pm 45\))/01/(\(\pm 45\))]s & 0.0014 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The lay-up sequence of 2.5 m small wind turbine.