Numerical analysis of linear buckling of wind turbine blade with different trailing bonding models

The work focus on the linear buckling analysis of wind turbine blade with different trailing bonding models. Based on finite element model, it has been demonstrated that there are some differences for buckling load factor between different models. Several different models are valid for buckling analysis.


Introduction
The rotor blade length has been continuously increased for improvement the capacity and efficiency of the turbine. Sandwich structure is chosen for part of the structure of the wind turbine blade because sandwich structure has many excellent characteristics, such as high stiffness to weight ratio, high strength to weight ratio, excellent fatigue properties etc. because of the thin composites shell cross section, stability analysis is vital criterion for wind turbine blade design. Some researchers (1) believe that the ultimate strength of the blade is governed by instability phenomena in the form of delamination and buckling. Many works (2,3,4) have discussed the buckling calculation, but the FE models of the blades are different. Less research pays attention to the trailing edge models. In this work, comparison of the models with different trailing bonding models has been conducted to evaluate the linear buckling results.

Panel buckling theory
ESDU standard 94007 has given the panel buckling theory, which is based on the elastic, thin plate, small deflection, and classical laminate theory. Many details also can be referred form the paper (2).Based on the classical laminate theory, the load-deformation relationships can be obtained: (3)

Figure 1. Panel buckling
where N is the forces, M is the moment , ε is the strain, κ is the curvatures. Boundary condition can be assumed as buckling modes with sinusoidal displacement of form, seen Figure 1. where u and v are in-the-plane displacements, and w is the out-of-plane displacements. λ and η are parameters associated with the number of buckled half-waves along x and y directions respectively. The critical buc-kling load in the longitudinal direction per unit width of plate (N) can be obtained from (3).

Modelling
The investigated blade consists of two spar caps and two spar webs (see Figure.2, 3). Based on the aero-dynamic considerations, the cross sections of the blade are different aerofoils. From the root to the tip, there is a taped shape. A brief summary of information of the blade is shown in

Load cases
In numerical analysis, two type load case are applied on the FE model.one is minimum edge-wise direction bending moments, another is minimum flap-wise bending moment. Both are the envelope of the entire extreme load case.

Boundary condition
The end nodes of the root are fixed all 6 degrees of freedom .the forces are applied on the main spar cap(see figure 5).

Result
Based on the FEM, numerical analyses have been conducted to evaluate the effect of the trailing model on the linear buckling. From Table 3, Model B and C have little deviations. Under the min edge-wise moments, load factor of the Model D is 2.9, while the Model A is 1.63.Generally speaking, in order to define the shell-solid coupling, the constraint require more fine mesh of the solid part, Model D maybe need to improve the mesh density. More work need to be done continuously.

Conclusion
There are some differences among the four models. Although more works need to be done extensively and continually, the result maybe alerts the designer pay attention to the different FE models. The