Fatigue life analysis for non gaussian processes

Abstract

In this thesis the effect of non-Gaussian loadings on fatigue is investigated. Fatigue causes catastrophic failure of structures due to repeated stress loadings which are individually not strong enough to harm the structure. The cumulative effect of many cycles results in damage and eventual failure. Here fatigue damage due to highly non-Gaussian stress loadings is investigated in the frequency domain. In the first work, using synthetic data two popular Gaussian transformation methods in literature were compared for a wide selection of kurtosis and skewness parameters. Secondly, a formula giving the correction factor for lognormal distributed stress using one of these transformations was developed. In the third work nine different non-Gaussian to Gaussian transforms, including eight from the literature and one newly developed here, are compared using extremely non-Gaussian stress loading, calculated from real observed wind speed data. First, the U transform of Johnson and Winterstein's Hermite polynomial based transformation are compared. A synthetic Gaussian random data was created and transformed with both methods to a non-Gaussian form, which was then converted back to Gaussian form. The fatigue lifetimes of the initial unchanged load and the final Gaussian load we obtained by the Dirlik method and compared. The non-Gaussian to Gaussian transform was performed using the parameters obtained by following the procedure given by Winterstein for his transform and parameters obtained by the Slifker - Shapiro approximation for the Johnson U transform. The process was repeated scanning a wide distortion rate space, varying both skewness and kurtosis. The results showed that neither method was able to get back to exact Gaussian form with 0.0 skewness and 3.0 kurtosis. Johnson method consistently gave close to 0.0 skewness but its kurtosis values were around 2.8. Winterstein's method resulted in a greater variation, where after small distortions, the results displayed high accuracy, but as distortions increased, the accuracy decreased. As a consequence, the predicted fatigue lives were also off by about 15% for the Johnson method and Winterstein's method showed a greater variability. Next, a correction factor for the Johnson L-transform was calculated. For this part Gaussian data was distorted using the inverse of the Johnson L-transform into lognormal form. Fatigue lifetimes of the original Gaussian and distorted lognormal were calculated in the time domain by the Rainflow cycle counting and Palmgren-Miner summation rule and the results were compared. The ratio of the fatigue lifetimes was calculated as the correction factor. Procedure was repeated with different shape parameters. The logarithm of the correction factor was fitted to a cubic polynomial of the shape parameter, the fit was excellent. Finally, stress obtained by effect of real wind speed data on a hypothetical traffic sign panel was investigated. The aerodynamic force on the panel and finite element method was used to find the maximum principal stress which occurs at the base of the poles. The stress loading turned out to be extremely non-Gaussian with skewness 2.8 and kurtosis 16,8. The non-Gaussian stress loading was converted to Gaussian form using eight different non-Gaussian to Gaussian transformations from literature. In addition, a new algorithm, combining the Johnson's B transform with the Nelder-Mead's Downhill Simplex optimization was developed. The optimization searched for the best fit parameters in the Johnson distortion parameter space. All nine transforms were compared in terms of how close the skewness and kurtosis values of the transformed data were to the Gaussian values of 0.0 and 3.0. It was seen that only the new method using optimization could give the exact Gaussian values. Fatigue lifetimes were calculated in the frequency domain using their output and corrected for the non-Gaussian nature of the data. Corrections were performed using Winterstein's 2nd order correction formula. The nine transforms were also compared in how close the corrected fatigue lifetimes calculated by each were to the time domain calculation using rainflow cycle counting. The new algorithm had the closest predicted lifetime. Overall, this thesis presents a detailed study on non-Gaussian to Gaussian transformations. Multiple comparisons and improvements have been presented in this work, which contribute to essential literature in this field. I hope that the results presented here will be of value to future work and researchers engaged in related inquiries.