On Fatigue Damage Computation in Random Loadings with Threshold Level and Mean Value Influence

The probability density functions used to characterize the distribution of fatigue cycles in random loads are usually defined over an infinite domain. This means that they give a non-zero probability to count cycles with an infinitely large peak or valley, which however seems of less physical sense. Moreover, practically all the methods existing in the literature completely neglect the negative effect on fatigue strength produced by fatigue cycles with positive mean values. With theses premises, this work tries to further extending the probabilistic theory used by the frequency-domain methods by addressing to distinct problems. First, it tries to include on cycle distributions the effect of a threshold level (representing a limit state of a system or simply an ultimate static strength). Secondly, it uses the Goodman mean value correction to include the effect of mean values of counted cycles in the fatigue analysis of random loads by frequency-domain methods. The fatigue load is modeled as a stationary random process with constant mean value ; two approaches of increasing complexity are presented: in the first one, only the effect of is considered, while in the second one also the effect of the random mean value calculated with respect to , is added. The proposed theoretical formulae are applied to two frequency-domain methods, namely the narrow-band approximation and the TB method. Finally, a comparison of the proposed formulae with the results from preliminary numerical simulations is show