Reliability analysis of a crashed thin-walled s-rail accounting for random spot weld failures

Abstract

Possibly the most common application of spot welding is in the automobile manufacturing industry, where it is almost universally used to weld the sheet-metal car components. However, due to manufacturing inaccuracies and fatigue failures an important number of spot welds may be missing in an operational vehicle. It seems that to properly analyse the reliability of such structures, in particular crashworthiness reliability, the spot weld failures must be considered. Representing properties of each spot weld in a stochastic model by corresponding random variables is extremely inefficient. Therefore, in this article an approach is proposed for handling spot-weld defects in the reliability analysis by accounting for their averaged influence on a failure criterion. The approach consists of the appropriate treatment of a random noise component of the limit state function. The noise results from the strategy of deleting a certain number of randomly selected spot-weld elements from the finite element model each time the limit state function value is computed.

Dealing with noisy limit state functions in structural reliability analysis is a challenging task. The only method that seems to be insensitive to this phenomenon is Monte Carlo sampling, which for most of the applications of practical interest is prohibitively expensive. Having this in mind, a method based on the algorithm proposed by Zou et al. and published in the journal of Reliability Engineering and System Safety in 2002 is investigated in this article. The method combines the best features of the first-order reliability method, the response surface technique and the importance sampling method to achieve both accuracy and efficiency. A detailed study on the reliability of thin-walled s-rail subjected to crash is performed. Some suggestions concerning the modification of the original algorithm are proposed.

Keywords:

• crashworthiness reliability
• response surface approximation
• adaptive importance sampling
• spot-weld failures

Acknowledgements

The principal part of the presented work was realised under the framework of the EC-FP6 APROSYS-SP7 (Virtual Testing) Integrated Project. The partial support from the Polish Committee for Scientific Research grant No. N519 010 31/1601 is also gratefully acknowledged. The authors express their gratitude to the company Altair Development France for granting them the licence for the Radioss software. Prof. K. Dolinski from the Institute of Fundamental Technological Research of Polish Academy of Sciences is thanked for his helpful comments.