May 2015
Intermediate to advanced
466 pages
10h 33m
English
Content preview from Optimization
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179Constrained Optimization
F f r
g
k
i
m
i
( ) ( )
( )
x x
x
= −
=
∑
1
1
(6.10)
See Figure 6.5, where we observe that modied function remains feasible
for different values of r
k
.
Example 6.2
A welded beam (Ragsdell and Philips 1976) has to be designed at mini-
mum cost whose constraints are shear stress in weld (τ), bending stress
in the beam (σ), buckling load on the bar (P), and deection of the beam (δ).
The design variables (see Figure 6.6) are
x
x
x
x
h
l
t
b
1
2
3
4
=
The optimization problem is
Minimize
f x x x x x( ) . . ( )x = + +1 10471 0 04811 14
1
2
2 3 4 2
0 0.5 1 1.5 2 2.5 3 3.5 4
0
20
40
60
80
100
120
x
F(x)
f
r
k
= 0.1
r
k
= 0.2
r
k
= 1
Feasible ...
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