Comparison of Shell and Solid Finite Element Models for the Static Certiﬁcation Tests of a 43 m Wind Turbine Blade

: A commercial 43 m wind turbine blade was tested under static loads. During these tests, loads, displacements, and local strains were recorded. In this work, the blade was modeled using the ﬁnite element method. Both a segment of the spar structure and the full-scale blade were modeled. In both cases, conventional outer mold layer shell and layered solid models were created by means of an in-house developed software tool. First, the boundary conditions and settings for modeling the tests were explored. Next, the behavior of a spar segment under different modeling methods was investigated. Finally, the full-scale blade tests were conducted. The resulting displacements and longitudinal and transverse strains were investigated. It was found that for the considered load case, the differences between the shell and solid models are limited. Thus, it is concluded that the shell representation is sufﬁciently accurate.


Introduction
m and turbines of over 6 MW are currently available on the market [1]. The upscaling is motivated 26 by an expected reduction in cost of energy (COE) for larger turbines [2]. However, this leads to rapid 27 increases in rotor mass and the resulting loads [3,4]. Furthermore, blades are designed with relatively 28 high total safety factors (often as high as 3). Nevertheless blade damages are frequent [5,6]. While 29 most of these damages result from manufacturing defects [7], there is also a need to improve the 30 understanding of the structural behavior of the blades. To limit the complexity, in a first step, a 10 m long portion of the blade's spar structure is modelled.

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This can be seen in Figure 3. The layup of the girders is simplified in this model to consist of only uni-121 directional (UD) GFRP material. At the inboard end of the model, a multi-point-constraint of the type 122 "beam" is applied, which rigidly connects the surface to a reference node. Similarly, at the outboard 123 end, a master node is connected to the surface, but by means of a "continuum distributing coupling", 124 which distributes the loads. Three different load cases are considered: pure-flap-wise load, combined 125 flap-wise and edge-wise load and torsion. An overview of the load cases can be seen in Table 1.

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The tool works by first calculating the OML shape. On this shape functions can be defined to 141 accurately calculate the positions of ply edges, shear webs and adhesive bonds. These are then used 142 to partition the blade shape, obtaining a topology onto which the layup and pre-defined blocks can 143 be assigned. In this way, a wide variety of models including those using solid elements can be created.

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(a) Longitudinal stress S11 for the flap-wise load case. (b) Shear stress S13 for the flap-wise load case.

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(c) Longitudinal stress S11 for the combined flap and edge-wise load case. (d) Shear stress S13 for the 228 combined load case. (e) Longitudinal stress S11 for the torsion load case. (f) Shear stress S13 for the If we compare the displacements and rotations of the tip end master node, we notice that the absolute 231 differences are very limited. This means that the overall stiffness of the structure is accurately 232 modelled using the OML shell approach. However, some differences appear when we compare the 233 stress values along a path on the side of the spar at the half-length position, shown in Figure 3. In the 234 resulting graphs, plotted in Figure 8, the presence of the adhesive bond and girders becomes apparent 235 in the solid models, while the side wall of the OML shell model does not contain these features.

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The reason why the OML shell model results in accurate results despite not modelling the web joint 237 accurately could be that the shear stiffness resulting from the girder, adhesive and flange included in 238 the solid model but not in the OML shell model is compensated by the shear stiffness resulting from 239 the excessive size of the shear webs in the OML shell model.

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To investigate this more accurately, the girder is also modelled using an OML shell approach with 241 the adhesive bonds represented by solid elements in contact with the outer shape. The resulting 242 model was found to have a lower stiffness, resulting in a larger tip deflection, which differs from both 243 the pure shell and solid models. It can therefore be concluded that this naive approach which is 244 employed in several works should not be used.

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Next, the applied loads are validated. As mentioned, the magnitude of the applied connector loads 253 is based on measured loadcell values during the actual experimental tests. The resulting root bending 254 moment is therefore compared to the measured values, as can be seen in Figure 9. This shows good 255 similarity for each of the different load cases.