Keywords: composite beam, Brazier effect, windturbine blades.

Windturbine blades are often designed as a composite structure. The load bearing element is a composite beam, that carries the load from the tip to the root, which is connected to the rotor. The dimensions of the beam will normally vary along the beam. The primary loads on the beam is the wind load which is perpendicular to the axis giving bending and shear with centrifugal loadings giving axial tension. The wind pressure acts on the wing shell and is transferred to the composite beam acting as a load perpendicular to the the beam axis.

A linear stress analysis of the beam will give axial stresses in the longitudinal direction and some shear stresses due to the shear load. The most significant will normally be the axial stresses. The composite beam is constructed from a number of layers which have different strength and stiffness parameters. In order to optimize the design the main strength and stiffness is therefore assigned to the longitudinal direction. The axial strength and stiffness perpendicular to the beam axis could therefore often be an order of magnitude less and the same is true for the shear stiffness or strength.

The windturbine wings are subjected to large wind pressures and often the maximum displacements will be relatively large. A non-linear analysis taking into account large displacements will often be necessary. The primary effect of the large displacement analysis is a kind of ovalization of the cross-section known as the Brazier effect. This effect has previously been studied in [1], and a so-called crushing pressure was identified. The crushing pressure results in a axial compression in the webs perpendicular to the beam axis. This phenomenon has to be taken into account in the design and would set a limit on the minimum pressure capacity of the web.

In the present analysis a more detailed study of the Brazier effect has been made. The so-called crushing pressure is still important but more important is the identification of bending of the web causing much larger stresses at the surface. The flange is also subjected to the Brazier effect and it corresponds to both bending and shear perpendicular to the beam axis. The shear stresses can sspecially explain some failure modes at the connection between web and flange.

The Brazier effect is analysed both numerically using Finite Elements and by a simple model only taking into account the cross-sectional deformations in its own plane. The simplified model could be used in optimizing the material layout of the beam instead of performing relatively costly full geometrically non-linear calculations.

1

F.M. Jensen, B.G. Falzon, J. Ankersen, H. Stang, "Structural testing and numerical simulation of a 34 m composite wind turbine blade", Composite Structures, 76, 52-61, 2006. doi:10.1016/j.compstruct.2006.06.008

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