Biomedical Engineering Reference
In-Depth Information
Constraint 3
Objective
function
Constraint 1
Constraint 2
Design space
Constraint 4
Target
Figure 7.3
Illustration of optimization.
CASE STUDY 7.1
The diameter of a hollow cylinder with closed ends may not exceed 100 mm and its length may
not exceed 200 mm but must not be shorter than 50 mm. The thickness of the material is fixed
at 5 mm. The target volume is 0.995-1.005 liter and the mass of the cylinder is to be minimized.
Determine the values of cylinder diameter and length that satisfy these criteria. Our optimization
problem is written as follows:
Objective function:
cylinder mass
2
D
π
fDL
o
(,)
1
DLt
2
t
π
ρ
4
(where r = density of steel at 7850 kg/m
3
)
Constraints:
cylinder volume
D
2
π
fDL
o
(,)
2
L
4
t
000
.
5m
D1m
.
0
0
00
.
5L 2m
0
.
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