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376 Finite Element Modeling and Simulation with ANSYS Workbench

45
40
35
Response
30
25
20
15
10
9 2
8 1.8
7 1.4 1.6
Design variable 2 6 1.2
5 1 Design variable 1

FIGURE 11.4
A 3-D response surface representation.

collection for such an array even for a fairly small value of n. As Table 11.1 shows, 16 experi-
mental runs are needed already for four input variables (x , x , x , and x ) at two levels (0
3
4
1
2
and 1). The number of simulation runs will be overwhelmingly large for multiple inputs
at many different levels.
A grid of data points of minimum density over the multivariable design space is often
used instead. Especially, central composite design (CCD) is a popular design, due to its
efficiency in providing much information in a minimum number of required numerical

TABLE 11.1
Design of Experiments: 16 Experimental Runs
for 4 Inputs at 2 Levels
Inputs
Experimental runs x 1 x 2 x 3 x 4
1 0 0 0 0
2 0 0 0 1
3 0 0 1 0
4 0 0 1 1
5 0 1 0 0
6 0 1 0 1
7 0 1 1 0
8 0 1 1 1
9 1 0 0 0
10 1 0 0 1
11 1 0 1 0
12 1 0 1 1
13 1 1 0 0
14 1 1 0 1
15 1 1 1 0
16 1 1 1 1