Environmental Engineering Reference
In-Depth Information
and material anisotropy are much more recent and theories describing these fea-
tures are not yet fully developed.
An important non-linear large-defl ection effect is called the
Brazier effect
[ 49 ].
The Brazier effect is a non-linear effect resulting from curvature when bending a
beam or a slender structure. Because of the curvature the longitudinal compressive
and tensile stresses result in transverse stresses towards the neutral plane of the
beam. This causes fl attening of a hollow cylinder or suck-in deformation or a
hollow box. This then result in reduction of the bending stiffness of the section.
A fully consistent representation including the three centers has been given
e.g. by Krenk and co-workers [50-52]. This theory incorporates the effect of pre-
twist in the form a geometric coupling of extension and twist [52]. A numerical
procedure was developed for the parameters of a moderately thin-walled cell cross
section often used for wind turbine blades [53]. A further development of these
principles has been carried out later under the name of Variational Asymptotical
Beam Section Analysis (VABS) by Hodges [54]. In this method, a beam with arbitrary
cross sections consisting of different materials can be analyzed by a one-dimensional
beam theory. The method provides a simply way to characterize strain in an initial
curved and twisted beam and all components of cross sectional strain and stress can be
accurately recovered from the one-dimensional beam analysis.
7.1.3 FE models
In FE analysis a structure is modeled with a fi nite number of discrete elements
represented by some element nodes in which the elements are connected. Because
of the blade size, and lack of symmetry, most published research on wind turbine
blade design using FE analysis is done using relatively coarse meshes.
A comparison between a geometrically non-linear FE analysis and full-scale
blade testing has been investigated by Jensen
et al
. [8]. In their experiments, a 34 m
glass fi ber PMC blade was statically loaded to catastrophic failure. Strong non-
linearities in various blade responses were found. The Brazier effect was found to
dominate in the inner part of the blade. The relative defl ection of the box girder cap
was measured during the experiments and compared with linear and non-linear FE
analysis (see Fig. 15). The linear analysis was not capable of predicting these relative
cap defl ections, in particular at high loads. The non-linear analysis provided reason-
able agreement with experimental measurements. It is clear from this that non-linear
FE analysis is required for certain aspects of blade design.
The most common types of FE models used for the structural design of wind
turbine blades are:
Outer surface shell model - using shell element offset
Mid-thickness shell model
Combined shell/solid model
The application of these various models is described below.
The outer surface model
of a blade is a shell model based on shell elements that are
located on the physical outer surface of the aerodynamic shell. This approach is conve-
nient since the outer surface is often specifi ed from aerodynamical purposes. The
material is then offset inwards in order to locate it at the correct physical position,
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