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Fig. 5. Geodesic dome
5.1 Optimum Geometry Design Problem
The optimum geometry design of a geodesic dome requires the selection of steel sec-
tions such as circular hollow sections or other types for its members from a standard
steel sections table and the height of the dome. This selection should be carried out
such a way that the dome obtained satisfies the serviceability and strength require-
ments specified by the code of practice while the economy is observed in the overall
or material cost of the structure.
The discrete optimum geometry design problem of geodesic dome where the
minimum weight is taken as the objective and the optimization constraints mentioned
above are implemented from BS 5950 [22], has the following form:
Find a vector of integer values I (Eq. 19) representing the sequence numbers for
total of nv design variables that consist of the discrete values given in the set arranged
for the height of dome and sequence number of circular hollow section given in
BS5950 that are to be assigned to ng member groups
[
]
T
I
=
I
, 2
I
,...,
I
(19)
1
nv
to minimize the weight ( W ) of the geodesic dome.
ng
t
r
Minimize ∑∑
=
W
=
m
l
(20)
r
s
r
1
s
=
1
subject to
δ
≤ δ
,
i
=
1
2
,......,
nd
(21)
i
iu
M
F
M
yk
ck
xk
(22)
+
+
1
k
=
1
2
,
nm
Ag
P
M
M
k
cxk
cyk
 
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