ABSTRACT

For fatigue analysis under wave loading, the long-term probability distribution of stress range needs to be known The work described In this paper shows that, for any given sea-state, the short-term distribution of stress range can be closely approximated by a hear combination of two Weibull distributions A semi-theoretical technique has been devised to derive the parameters of these distribution and functions of the spectral irregularity factor The probability density function so obtained is shown to provide a close f it to the histograms of stress range obtained by simulation and rainflow counting In addition, the equivalent stress ranges obtained from this model compare very favourably with those obtained by slrnulation, In comparison with other empirical models, thus providing an accurate method for the prediction of fatigue damage under random loading, with minimal computational effort

INTRODUCTION

The characteristics of the fluctuating random stress in a structural component, especially In regions of stress concentration, for example the hot spot stresses In a tubular joint, are likely to be the dominant factors In determining the component's fatigue life and In influencing the overall performance and reliability of the structural system containing it The traditional approach to fatigue analysis under random loading is to adopt the Rayleigh approximation (see, e g Miles (1954)), In which it is assumed that the damage caused by any stochastic process, X(t). is the same as the damage caused by a very narrow band Gaussian stress process with the same standard deviation ax and mean level crossing rate vo as the original process The peaks from such a narrow band process are Rayleigh distributed and the cyclic range is twice the value of the peak This approach has been shown to overestimate fatigue damage under wide-band loading spectra to a considerable extent

Following theoretical developments for random loading under wave action, the entire wave loading history can be treated as being due to a series of different statlonary Gaussian sea states, e g Pierson-Moskowtz (P-M) or JONSWAP Depending on whether the response is inertia or drag dominated, the transfer function between sea surface elevation and stress can be either approximately Linear, or non-hear

By assuming a linear transfer function and allowing for the first mode resonant response of the structure, a series of double peak response spectra have been proposed by Wirsching (1976) These range from relatively narrow band to wide band depending on the dominant frequency of the seastate Taking a particular form of response spectrum, typical stress time-history can be generated by simulation (see Appendix B) and from these the sample distribution of stress ranges may be determined

There are a number of different cycle counting methods which can be used to determine the number of stress range cycles from any given stress time-history Of these the rainflow method has been demonstrated to have the closest f it with experimental results - see, for example, Dowling (1972) However, the rainflow cycle counting algorithm, requires an elaborate procedure involving first the simulation of the loading history and then the identification of the hysteresis loops

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