## 3 Stiffness Matrix Calculation of Composite Blade Section  
The cross-sectional structure of the wind turbine blade is shown in Figure 2. It is mainly composed of the blade leading edge, main beam, trailing edge, and web. Each part of the blade section is laid with different composite laminates. Using the idea of discretization and equivalent stiffness superposition [30; 31], the blade section is discretized into several regional segments along the wind turbine airfoil profile direction. Then, combined with the theory of composite laminates, the effective engineering constants of each layer of the segment in the region are calculated. After that, the equivalent characteristics of the regional segments are obtained by the weighting method. Finally, the blade cross-sectional structure characteristics of each segment are obtained by summation. Therefore, the stiffness characteristics of the blade cross-section are obtained. The flow chart of the model is shown in Figure 3.  
The aerodynamic shape of the wind turbine airfoils and the blade structural parameters are particularly important in the flow chart. The aerodynamic performance of the blade is determined directly by the wind turbine airfoil's geometry. The stiffness characteristics of the blade are directly determined by the internal plying parameters (such as the layer thickness, layer angle, layer sequence and so on). After the blade cross-section is discretized, each segment is laid by several laminates. The effective engineering constants of the ply can be obtained by Equations (3) and (4), when the layer angle of the unidirectional ply is \(\alpha\). \[E_{x}^{ply}=\frac{1}{\frac{1}{E_{1}}\cos^{4}\alpha+\left(\frac{1}{G_{12}}- \frac{2v_{12}}{E_{1}}\right)\sin^{2}\alpha\cos^{2}\alpha+\frac{1}{E_{2}}\sin ^{4}\alpha} \tag{3}\]  
\[G_{xy}^{ply}=\frac{1}{\left[\frac{4}{E_{2}}+\frac{4+8v_{12}}{E_{1}}-\frac{2}{ G_{12}}\right]\sin^{2}\alpha\cos^{2}\alpha+\frac{\sin^{4}\alpha+\cos^{4}\alpha}{G_{12}}} \tag{4}\]  
where \(E_{x}^{ply}\) and \(G_{xy}^{ply}\) are the effective Young's modulus and shear modulus with a layer angle, respectively; E\({}_{1}\) and E\({}_{2}\) are the elastic modulus of materials; \(G_{12}\) is shear modulus of materials; and \(v_{12}\) is Poisson's ratio. Figure 2: Schematic diagrams of the blade cross-sectional parameters. As is shown in Figure 4, the equivalent Young's modulus \(E_{equiv}\), shear modulus, thickness \(t_{equiv}\), and \(A_{equiv}\) area can be expressed as:  
\[E_{equiv}=\frac{\sum_{i=1}^{m}E_{x,i}^{ply}t_{i}^{ply}}{\sum_{i=1}^{m}t_{i}^{ply}} \tag{5}\]  
\[G_{equiv}=\frac{\sum_{i=1}^{m}G_{xy,i}^{ply}t_{i}^{ply}}{\sum_{i=1}^{m}t_{i}^{ply}} \tag{6}\]  
\[t_{equiv}=\sum_{i=1}^{m}t_{i}^{ply} \tag{7}\]  
\[A_{equiv}=\sum_{i=1}^{m}A_{i}^{ply}=\sum_{i=1}^{m}t_{i}^{ply}w_{seg} \tag{8}\]  
where \(i\) is the _ith_ply in a segment; \(m\) indicates the number of plies in an segment; \(E_{x,i}^{ply}\) is the effective Young's modulus of the _ith_ply; \(t_{i}^{ply}\) and \(A_{i}^{ply}\) are the thickness and area of the _ith_ply, respectively; and \(w_{seg}\) is the width of an segment. Figure 3: Flow chart of the mathematical model. The elastic center of the blade cross-section can also be calculated using the weighting method:  
Figure 3.0  
Figure 3.1  
where, \(I\) is the \(I\)th segment; \(N\) is the number of a segment; \(E_{equ,l}\) and \(A_{equ,l}\) are the equivalent Young's modulus and area of the \(I\) segment, respectively; and \(\overline{x}_{c,l}\) and \(\overline{y}_{c,l}\) are the mass center coordinates of the \(I\)th segment. The moments of inertia for each segment can be calculated using an integral formula:  
Figure 3.2  
Figure 3.3  
Figure 3.4  
where, \(I_{xx}\) and \(I_{yy}\) are the moment of inertia with respect to \(x\) axis and \(y\) axis (Figure 4), respectively; and \(I_{xy}\) is the product of inertia. Careful treatment should be given to the above moments of inertia which are calculated relative to the local axes and centroid of each segment.