To further very the methodology, we performed the MC simulations with strainweighted selection scheme [8] without and with quality control of 20 spot welds for optimized design. 75 samples with 100 missing spot welds have been used for each simulation. Their scatter clouds are shown in fig 9 along with worst case variations obtained by our proposed procedure for missing of the same number of spot welds. 0 2 4 6 8 0 0.5 1 1.5 2 2.5 Relative Eigenfrequency Shift (%) − Mode 1 Relative Eigenfrequency Shift (%) − Mode 2 MC without QC MC with QC WC without QC WC with QC Fig. 9 Scatter clouds of MC simulations along with worst case variations Results confirm firstly, effectiveness of quality control methodology to guarantee the impact of failure in the remaining uncontrolled spot welds within acceptable level: spread of eigenfrequencies shifts are much smaller for quality controlled spot welds formulation, secondly, procedure proposed to obtain robustness curve is efficient as well as accurate: 10 analyses required to find the worst case variations while 75 analyses for MC simulations are unable to find the worst case variations of the same degree. Nevertheless, the important question lies in finding an acceptable compromise between robustness and the cost of controlling additional spot welds following assembly or the cost of reinforcing critical spot welds to avoid failure during the lifetime of the vehicle. To answer this question, the behavior of missing of uncontrolled spot welds on the eigenfrequency is analyzed as a function of the number of quality controlled spot welds for optimized design up to relative eigenfrequency shift of 1.0% for mode 1. Maximum 40 spot welds are considered for quality control. Curves in fig 10 show that the design is becoming less sensitive to missing spot welds as the number of quality controlled spot welds increases. These curves show that there is no gain in robustness in case of controlling 10 spot welds but the robustness increases rapidly above this number. Robust optimization and quality control in spot welded structures 307
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