WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

TOPOLOGY OPTIMIZATION WITH PADÉ APPROXIMANTS 1623
Figure 9. Optimized material distribution (25% reinforcement material) for minimized response of the
entire body for two different frequency intervals: (a) = 0.9–1.1 and (b) = 0.7–1.3.
Response, ln(uu - )
9.5
9
8.5
8
7.5
7
6.5
6
5.5
5
4.5
Fig. 9b
initial
4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency, Ω
Fig. 9a
Figure 10. Total response for the body for the two different optimized structures in Figure 9
and for the initial structure with 25% material uniformly distributed in the domain. Dashed
lines indicate the optimization interval.
4.2. Structural optimization of a tip-loaded cantilever
The tip-loaded cantilever shown in Figure 11 is a classical benchmark problem in structural
topology optimization with static loads [19]. A few works have considered similar optimization
problems for harmonic loads [20, 22] but only for single frequencies. Here, the proposed method is
used to optimize the distribution of solid and void in the cantilever so that the dynamic compliance
in the lower frequency range is minimized.
The problem is defined as a standard structural topology optimization problem in which a limited
amount of material (50%) with material parameters:
E = 1, = 1, = 0.3
Copyright q 2007 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2007; 72:1605–1630
DOI: 10.1002/nme