Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

2.3.3 Design Variables
The choice of design parameters for performance tailoring varies from application to
application. In general, it is desirable to choose variables that have a significant effect
on the performance metric and can be controlled to high accuracy during manufac-
turing. For example, geometric properties, such as the cross-sectional diameter of the
truss elements affect the performance metric and can be specified to a relatively high
precision in practice. In contrast, the material properties of the truss elements also
affect the performance metric, but are not good choices for tailoring parameters be-
cause it is difficult and costly to manufacture a material with a very specific Young’s
Modulus.
The design variables used in the SCI development model are the cross-sectional
diameters of the truss segments and lumped masses placed at pre-determined locations
along the truss. The truss diameters are constrained to be symmetric about the center
of the array so that there are only four tailoring parameters as listed in Table 2.3 and
shown in the accompanying figure.
Table 2.3: Tailoring parameters for SCI sample problem.
Name Description x0
∂¯σz
∂x
d1 cross-sectional diameter of truss 1 & 4 0.10 [m] -11.81
d2 cross-sectional diameter of truss 2 & 3 0.10 [m] -31.15
m1 lumped mass on -x truss 0 [kg] 9.31
m2 lumped mass on +x truss 0 [kg] 9.31
00 11
00 11
00 11
00 11
00 11
d 1
1
m 1
Y
d2 000 111
000 111
000 111
000 111
d 2
m 2
d 1
2 3 4
000 111
000 111
000 111
000 111
The third column of the table gives the nominal value for the parameters, x0,
and the fourth column lists the normalized sensitivity, ¯ dσz
dx
X
of the performance metric
with respect to the tailoring parameter. The normalized sensitivity is defined as the
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