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This paper investigates the fatigue damage behaviour of random service loading histories and suggests a criterion to determine fatigue damaging cycles by using probability values. The rainflow strain range distribution is often used in fatigue damage prediction. The existence of very small amplitude of cycles that do not significantly contribute to damage makes the prediction process unnecessarily complex. Therefore, a criterion to determine the size of damaging cycles that contribute significantly to total damage values is desired. In this study, two datasets were compared, i.e. the standard SAE road profile for the suspension system and an experimental data recorded using a strain gauge installed on a vehicle component. Fatigue damage was determined using the Coffin-Manson, Morrow and Smith-Watson-Topper models. The distribution of strain ranges was identified by distribution fitting process. The relation between strain range magnitude and RMS values was explored using the probability of damage occurrence values. The results show that both sets of strain histories data fit well to a mixed Weibull distribution with n subpopulations. The probability of damage occurrence values obtained were very high, i.e. 0.9362 and 0.9987, indicating very high chances of damage incurred by these damaging cycles. Therefore, 2 RMS values is suggested as a criterion for damaging cycles determination.

Finite element analysis and optimization design carry out for the quasi static responses of foam-filled double circular tube is presented in this paper. In the investigation of the crashworthiness capability, some aspects were considered for variations in geometry parameters of tubes and the loading condition to investigate the crashworthiness capability. Empty, foam-filled, and full foam-filled doublé tubes of thin walled structures were observed subjected to oblique impact (0˚ -40˚). The numerical solution was used to determine the crashworthiness parameters. In addition, NSGA II and Radial Basis Function were used to optimize the crashworthiness capability of tubes. In conclution, the crash performaces of foam-filled double tube is better than the other structures in this work. The outcome that expected is the new design information of various kinds of cylindrical tubes for energy absorber application.