Computational Methods for Debonding in Composites

12 On Buckling Optimization of a Wind Turbine Blade 253
Fig. 12.4 Thedesignarea(the
trailing edge sandwich panel)
is divided into 14 patches.
Results of the topology optimization
will be presented for
the zoomed area
Zoomedarea
Patch14
Patch13
Patch12
Patch11
Patch10
Patch 9
Patch 8
Patch 7
Patch 6
Patch 5
Patch 4
Patch 3
Patch 2
Patch 1
The whole trailing edge panel is allowed to change in the design optimization
(including the part close to the trailing edge marked with the color red in Fig. 12.2),
and it is divided into 14 patches as illustrated in Fig. 12.4. Each patch has 12 layers
of equal thickness 0.5 mm, i.e., the total thickness is 6 mm everywhere in the design
area. The buckling modes of the lowest eigenvalues are local modes of the trailing
edge panel (see also Fig. 12.1B).
First the candidate materials are GFRP unidirectional material oriented at 0 ◦ ,
+45 ◦ , −45 ◦ , and 90 ◦ for the two outer layers whereas the foam material also can
be selected together with the four GFRP candidate materials for the 10 inner layers.
The mass constraint M is set to 24.9 kg which corresponds to 2/3 of the design
domain being filled with foam material.
When solving the optimization problem given by Eq. (12.12) the three lowest
eigenvalues are taken into account in all design iterations. The penalization power p
used in the weight functions in Eq. (12.2) is initially set to 1 and increased by 1 for
every 10 design iterations until p equals 3. The move limit used on all DMO design
variables is 5%, i.e. each design variable may change up to 5% in every design
iteration.
The result of the optimization can be seen in Fig. 12.5. If the GFRP material
has been selected, then the material orientation is shown for each finite element,
whereas white means that the foam material has been selected. The results of the
optimization are shown for the zoomed area defined in Fig. 12.4.
The DMO convergence measure, see Eq. (12.6), is h95 = 0.89 and h99.5 = 0.84.
Thus, in 5/6 of the domain a distinct choice of material is obtained. The convergence
of the lowest eigenvalue is monotonic and is increased from λ1 = 1.05 for the initial
design where all weight factors on the candidate materials have equal values to
λ1 = 2.23 for the optimized design where the mass constraint is active.
It is seen that the GFRP material at the left part of the trailing edge part (at the
transition to the spar cap) should be oriented at 0 ◦ , and the overall distribution of
foam material through the thickness seems reasonable. However, the GFRP material