Fatigue life assessment in non-Gaussian random loadings D. Benasciutti * , R. Tovo Department of Engineering, University of Ferrara, via Saragat 1, 44100 Ferrara, Italy Received 30 January 2005; received in revised form 28 July 2005; accepted 23 September 2005 Available online 18 November 2005 Abstract This paper treats the theoretical fatigue analysis of non-Gaussian random loadings. It first reviews a method recently developed by the Authors, which is capable to account for the effect of load bandwidth and non-normality. Fatigue lives from simulated Gaussian and non-Gaussian loadings, as well as data from experiments taken from the literature, are compared with theoretical estimations. The non-Gaussian loading was modelled as a transformed Gaussian process. The results show how the load non-normality has a great effect on both the cycle distribution and the fatigue damage; the proposed method seems able to account for this effect correctly. Furthermore, the theoretical predictions are shown to be substantially comparable (with some exceptions) with the experimental data. q 2006 Elsevier Ltd. All rights reserved. Keywords: Non-Gaussian random loading; Transformed Gaussian process; Fatigue life; Rainflow count; Spectral density 1. Introduction In the time-domain analysis of structures subjected to random loadings (as those generated by wind and/or waves, or those produced on vehicles by the irregularity of the road profile), an appropriate cycle counting technique and a damage accumulation hypothesis are used to estimate the fatigue service life. Among all counting procedures, the rainflow algorithm is widely regarded as the best counting method, while the Palmgren–Miner linear damage rule is adopted for its simplicity. In order to assure reliable statistical estimations, this approach usually requires many loading records, resulting from costly or simply lengthy experimental data acquisitions. For this reason, the theory of random processes is often an easier and quicker alternative approach; a power spectral density (PSD) is used to characterise the random loading response and to estimate both the distribution of rainflow cycles and the fatigue service life [1]. The theory usually assumes that the load is Gaussian, since this is a simplifying hypothesis, which allows simulating representative time histories from the load PSD, as well as finding explicit formulae for both the cycle distribution and the fatigue damage. Without doubt, a well-known example is the narrow-band approximation, which, however, in wide-band loadings gives too conservative damage estimations; hence, the effect of load bandwidth is normally evaluated by a proper damage correction factor [2,3]. Otherwise, approximate methods, resulting from either simple theoretical consider- ations or best fitting techniques, are available [4–7]. However, in many realistic applications the Gaussian hypothesis could be not correct, since observed structural responses are non-Gaussian, due to either non-Gaussian external excitations (e.g. wave or wind loads), or the structural non-linearities, or both. Under certain circumstances, the load non-normality may be responsible of an increase of the rate of fatigue damage accumulation [8–11]; consequently, all the spectral methods valid for Gaussian loadings may provide non-conservative estimations of the service life if applied to non-Gaussian loads. The need to develop proper methodologies accounting for load non-normality is then clear. The narrow-band approximation can be easily updated to the non-Gaussian case, but, in wide- band loadings, the effect of load bandwidth still remains undetermined [8,9,11]. An attempt to evaluate the effect of both the load bandwidth and non-normality on fatigue damage through appropriate correction coefficients was proposed in Ref. [12]. Nevertheless, the present Authors, by means of more theoretical considerations, provided general relations about the distribution of rainflow cycles in non-normal loads, which were the basis of a new method, able to account for both the bandwidth and the non-normality of a random load. The analysis of non-Gaussian loads measured on a Mountain Bike International Journal of Fatigue 28 (2006) 733–746 www.elsevier.com/locate/ijfatigue 0142-1123/$ - see front matter q 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2005.09.006 * Corresponding author. Tel.: C39 532 97 4911; fax: C39 532 97 4870. E-mail address: dbenasciutti@ing.unife.it (D. Benasciutti).