Blade materials, testing methods and structural design - Wind Power Generation and Wind Turbine Design - page 457

The difference between the linear and the non-linear results is, at least in part,
caused by the Brazier effect. The crushing pressure (that is the transverse stresses
due to curvature described in Section 7.1.2) is fl attening the cross section and
introduces compressive strains into the shear webs. This crushing pressure varies
with the square of the applied load as found by Brazier [49], resulting in the noted
deviation from linear responses. The fl attening of the cross section will probably
initiate buckling which accelerates the failure evolution. Other non-linear phe-
nomena, such as changes in geometry and loading confi guration (which follows
the geometry in the non-linear analysis), will also contribute to the observed non-
linearities. For further discussion of this see Jensen et al . [ 77 ].
In the study in Branner et al . [76], it was found that the corner stiffness greatly
infl uence the overall non-linear behavior of the box girder. The webs take a larger
part of the overall cross section deformation when the corners are stiff. It is seen
from the stiff corner models, that the core density have some infl uence on the ulti-
mate strength. In contrast, the soft corner models show that the core density has
almost no infl uence on the ultimate strength. The ultimate strength of a box girder
was also studied experimentally and numerically [78]. It was found that for the
shear webs, failure was initiated by shear failure of the core (see Fig. 27).
7.3.5 Testing of long sections of a main spar to determine buckling behavior
Kühlmeier [79] worked with buckling of wind turbine blades in his PhD thesis. In
Kühlmeier et al . [80], a 9 m long airfoil blade section, designed to fail in buckling,
was build and tested destructively in a four-point bending confi guration. Based on
numerical analysis, it was found that a linear buckling analysis will over-predict the
ultimate strength of the blade. How much the strength is over-predicted depends
on the size of the imperfections present in the blade and the sensitivity of the
structure with respect to the imperfections. It was suggested that a bifurcation
buckling analysis with a knockdown factor applied on the buckling load will give
a good estimate on the ultimate strength of the blade. The value of the knockdown
factor will depend on the size of the imperfections as well as the imperfection
sensitivity. For the 9 m blade section a factor of 1.25 was found to assess the
ultimate strength of the blade.
7.4 Full wind turbine blade models with damage
Overgaard and Lund [81] analyzed the full-scale blade collapse described in
Section 4 [2]. A geometrically non-linear and linear pre-buckling analysis was per-
formed for predicting the failure of the blade due to local buckling on the suction
side of the airfoil. The geometrical imperfection sensitivity of the blade was evalu-
ated by imposing the strain gauge measurement for the full-scale experiment as an
imperfection pattern. Figure 28 displays the response of the obtained imperfection
amplitude where the 23% amplitude model fi ts the best of the evaluated models.
It is seen that the imposed imperfection pattern is directly proportional with the
longitudinal strain measured in the strain gauges [82]. An important discovery is
that the buckling shape is unaffected by the presence of geometrical imperfections,