However, large number of analyses required for a meaningful MC simulation renders its use impractical. Hence, we propose a simple and less costly approach based on the impact of the most influential spot welds on the modal behavior. The objective is to plot a robustness curve showing the evolution of eigenfrequencies when progressively more influential spot welds are defective or missing. This robustness curve also serves as a useful decision making tool for deciding both how many spot welds should be inspected following assembly as well as pointing to a small number of critical spot welds that should be reinforced. This presentation is organized as follows. In next section, optimization procedure is presented along with a brief description of decision making indicator for modal behavior. FE models are presented followed by optimization results. In sec 3 the issues related to robustness and quality control of a small percentage of influential spot welds are presented and finally, the conclusions of the study are drawn in the last section. 2 Spot weld optimization 2.1 Description of optimization procedure A flowchart of the proposed optimization procedure is shown in the fig 1. The procedure will remove the redundant spot welds from the structure and simultaneously, will add the spot welds at the sensitive locations to the proximity of the most influential RSWs. This implies that either software has capability to create new spot welds when and where needed, or that a pool of candidate spot welds is already available in the numerical model which can be activated when needed. A decision making indicator presented later on will be used to rank the existing spot welds signifying their contribution to the performance criteria of interest. 2.2 Decision making indicator The decision making indicators are the tools implemented in the spot welding optimization procedure to select the spot welds which are redundant and should be removed or those which are critical and should be reinforced. The indicators are used to correlate the contribution of individual spot welds to the target behavior and ideally should be easily calculated and lead to unambiguous choices. Two categories of indicators can be envisaged, namelya priori anda posteriori. The former are indicators which forecast in advance the influence of spot welds without removing them from the structure while the latter require the explicit removal of the spot welds from the structure. In practice, a posteriori indicators are very costly to evaluRobust optimization and quality control in spot welded structures 299
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