duce manufacturing cost and spot welds represent a significant contribution to the overall cost of the vehicle. Therefore, it is a worthwhile task to reduce the number of RSWs on the vehicle without compromising the performances. Due to mass production, even a small reduction in their number could lead to substantial reduction in the cost. However, the number and spatial distribution of spot welds has a significant impact on the structural performance criteria that must be taken into account by an analyst including the static, dynamic, and crash behaviors. Currently, the numbers of spot welds and their locations are largely based on the designer’s technical know-how and experience. However, this proves to be a daunting task for even the most experienced designers and problem has not been fully addressed by the research community. Some authors have examined the issue of improving the performance criteria by optimally relocating a fixed number of spot welds in the structure [2, 4, 5, 12, 13]. However, attempting to solve the optimization problem based on a fixed number of spot welds, where one is interested in finding the best locations, can pose two problems. First, this number may be too small and the solution may not be feasible even for the best distribution. Secondly, a priori defined number of RSWs may be too large and the overall production cost will be high due to the presence of redundant spot welds. This suggests that not only the locations but also the number of RSWs should be included in the optimization procedure as a variable to be determined. Thus, the aim should be to minimize the number of RSWs and find the best distribution of the existing number of RSWs simultaneously, so as to ensure an acceptable level of performance as dealt in [6– 11]. Although simulation time for large and complex structures has been reduced over the years, the iterative nature of the discrete optimization problem still requires careful attention to calculation costs. Hence, in order to optimize the number of spot welds on the structures containing thousands of RSWs in a reasonable time, a simple decision making indicator is needed which can predict the contribution of the individual RSW towards the performance criteria. This indicator will not only be helpful to find the locations of the most influential RSWs but will also serve to indicate the redundant RSWs whose contributions towards the performance criteria are negligible. Bearing this in mind, we propose an optimization procedure which uses the elastic strain energy based indicator to remove the redundant spot welds and simultaneously, adds the new spot welds in the proximity of the most influential RSWs. Another aspect of this study concerns the impact of uncertainty in the form of missing or defective RSWs on the structural performances. Indeed, when a BIW leaves the assembly line it is not unusual to find a small percentage of spot welds missing. Moreover, fatigue effects through the lifetime of the vehicle can lead to the breakage of spot welds. The important question to address here is just how many RSWs can be defective without compromising the specified performance criteria. In [3, 8], authors have used Monte Carlo (MC) simulations to study this problem under the assumption that each spot weld has equal chance of being defective or missing. Q. I. Bhatti and M. Ouisse and S. Cogan 298
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