Environmental Engineering Reference
In-Depth Information
Fig. 10.4 Detailed FEA of
the base of the tower in
Fig.
10.1
. Image provided by
Sturt Wilson
ignored. Consider first the artificial case when T
max
= 0. Then (
10.24
) is imme-
diately an equation for td, which is proportional to the tower mass, and the
diameter and thickness can be chosen to avoid buckling. Thus td is minimised
when the maximum possible t/d is used to maximise the allowable stress.
Including the tower thrust turns (
10.24
) into a cubic equation for d if d/t is
assumed. Fortunately the cubic has only one real root, at least for the single case
considered here, and is easily solvable. This is done in the program
str_oct_to-
wer.m
which is available from the online materials but is not listed. Figure
10.5
shows the variation in mass with d/t for the same T
max
, m
tt
, h, and U as in
Table
10.2
. Two immediate results are apparent: first, a straight tower is signifi-
cantly heavier than the non-optimal tapered tower, and second, the minimum mass
occurs where F
max
deviates from F
y
.
The optimisation of tapered towers with different section thicknesses is not
possible analytically, but can be tackled by the evolutionary strategy described in
Chap. 6
for blade design. A suite of Matlab programs based on the work of Clifton-
Smith and Wood [
11
] is available from the online materials. Previously, Yoshida
[
16
] described the optimization of a large tower using a genetic algorithm. For the
present case, the tower genes are d
0
, d
h
, and the thickness of each of the N
s
sections,
with example constraints listed in Table
10.4
. All important tower information is
stored in data structure
data
created by running
tower_opt_setup.m
. Then, the
main program
tower_deopt.m
invokes the script
t_creator.m
to initialise the
population. To avoid creating towers with extreme values of CF, this script ref-
erences
tapered_oct_tower_opt.m
, a straightforward modification to the program
listed and discussed earlier in this chapter. Referencing is iterative and continues
until all the members of the initial population have a maximum CF within rea-
sonable limits. The main modification to
tapered_oct_tower.m
was to set CF = 0
and m
t
artificially high whenever CF
max
was exceeded, usually in determining the
susceptibility to buckling.
The optimisation can combine minimising tower mass, maximising the maxi-
mum capacity factor provided it remains below the safe limit, and maximising the
tower and turbine natural frequency as estimated by Method B from the last
section. The fitness function is modified from Eq.
7.2
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