WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

TOPOLOGY OPTIMIZATION WITH PADÉ APPROXIMANTS 1625
Figure 12. Optimized distribution of 50% solid (black) for four different frequency intervals:
(a) = 0–0.02; (b) = 0–0.04; (c) = 0–0.06; and (d) = 0–0.08.
Response, ln(u tip u - tip )
13
12
11
10
9
8
7
6
5
initial
Fig. 12a
Fig. 12d
Fig. 12b
4
0 0.02 0.04 0.06 0.08 0.1
Frequency, Ω
Fig. 12c
Figure 13. Tip response of the four different optimized structures in Figure 12 and for the
initial structure with 50% material uniformly distributed in the domain. Dashed lines indicate
optimization frequency intervals.
Additionally, it appears that many local optima exists for this optimization problem especially
for larger optimization intervals. Different optima are obtained with variations in the optimization
procedure, e.g. the small differences due the choice of N and number of PA expansions (see
paragraph above) and also the choice of initial design. However, the designs differ only in structural
Copyright q 2007 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2007; 72:1605–1630
DOI: 10.1002/nme