2.4 Illustration In this study, the objective is to minimize the number of spot welds while keeping the eigenfrequencies of the first torsion and bending modes higher than to those of the nominal design. The first torsion and bending modes of the nominal design are shown in fig 3. MSC.Nastran is used to perform the modal analysis up to 65 Hz and takes almost 20 minutes on a Windows XP professional based computer having processor speed of 3.0 GHz with 2.0 GB RAM. (a) (b) Fig. 3 Modes shapes (a) torsion mode. (a) bending mode Figure 4 shows the evolution of both eigenfrequencies during the optimization process. The procedure efficiently removed more than 14% of the total RSWs in only 6 iterations while both eigenfrequencies of the final design are better than those of the nominal design: 0.61% higher for mode 1 and 0.1% higher for mode 2. Note that the eigenfrequencies continue to improve despite of the fact that the total number of RSWs is decreasing. This is due to the addition of RSWs at the critical interfaces having higher influence. The final distribution of RSWs is shown in fig 5. The proposed procedure is also designed to improve the robustness of the structure against defective or missing spot welds. This objective is achieved implicitly by sharing the loads of critical spot welds by adding the new spot welds at sensitive locations to their proximity. As a result, their indicator values will decrease, reflecting that if missing will produce less variations in the eigenfrequencies. To visualize this for the current illustration, we plotted the indicator values of first 270 spot welds of highest values for the nominal as well as the optimized designs in fig 6. Decreases in the indicator values of individual spot welds as well as in the mean values can clearly be observed. This means that optimized design is certainly now more robust against missing of spot welds and we will verify this fact in a posteriori robustness analysis in the next section. Q. I. Bhatti and M. Ouisse and S. Cogan 302
RkJQdWJsaXNoZXIy MTMzNzEzMQ==