D. Benasciutti a, R. Tovo b

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1 «A COMPREHENSIVE APPROACH TO FATIGUE UNDER RANDOM LOADING: non-gaussian and non-stationary loading investigations» D. Benasciutti a, R. Tovo b a DIEGM, Dipartimento di Ingegneria Elettrica Gestionale Meccanica, Università di Udine, via delle Scienze208, Udine (Italy) b ENDIF, Engineering Department In Ferrara, Università di Ferrara, via Saragat 1, Ferrara (Italy) In most engineering applications structural members usually experience complex service random loadings. The main difficulties in fatigue life assessment are often related to the non-stationary and non-gaussian statistical properties of actual service loadings, since under such conditions structural integrity assessment and fatigue damage estimation can be hardly carried out. In the literature these structural loadings are often investigated by defining a direct link between power spectral density properties of service loadings and cumulated fatigue damage. Differently, the present authors proposed an apparently more complex approach capable to asses fatigue damage through the estimation of the whole marginal statistical distribution of counted cycles, as a function of both amplitude and mean value. One of the advantages of such an approach is the possibility of easily assessing the dependence of fatigue damage on mean values of counted cycles. Furthermore, it has been later demonstrated that the main gain is the possibility of taking advantage of the whole distribution knowledge to also assess the non-gaussian and non-stationary loading damage, under the same theoretical framework. This contribution aims to supply an overall survey of the proposed approach in order to summarise the applicability of achieved results to actual complex loading conditions experienced by structural components. «EFFECT OF WHIPPING AND SPRINGING ON FATIGUE (with Gaussian VS Non-Gaussian Modeling)» Wengang Mao, Igor Rychlik Chalmers University of Technology, Gothenburg, Sweden Wave-induced vibrations, also known as whipping and springing, are defined as high frequency response of ship structures, leading to the multi-peaked spectrum. In this presentation, the fatigue damage caused by whipping and springing is presented by investigating the amidships section of a 2800 TEU container ship that operates in the North Atlantic Ocean. We demonstrate that a simplified fatigue model based on the Gaussian load can be used to include the damage contribution from wave-induced vibrations. In this model, the significant response range h s and the mean stress up-crossing frequency f z are simplified using only the wave-induced loading and encountered wave frequency, respectively. The capacity and accuracy of the model is illustrated by application on the measurements of the 2800 TEU container ship for different voyages during However, the extreme prediction is largely influenced by the non-gaussian whipping responses. It is found that a more complicated non-gaussian model is required to include the contribution from whipping for 100-year stress prediction. A standard approach, employing a mixture of Gaussian loads, largely underestimates the 100-year stress.

2 «SOME ASPECTS OF RISK-BASED INSPECTION PLANNING» Jan Mathisen Principal Engineer DNV Energy/Risers, Moorings & Umbilicals This would include a brief introduction to quantitative RBI, the use of both Miner- Palmgren and fracture mechanics models for fatigue, probabilistic modelling and some requirements to the analysis of stochastic stress processes. I would also like to include brief mention of a few other current activities in DNV on fatigue analysis of offshore structures. «VALIDATION OF SPECTRAL FATIGUE ANALYSIS OF JACKET STRUCTURES IN BOMBAY HIGH FIELD» S. Nallayarasu 1, S. Goswami 2, J.S. Manral 2 and R.M. Kotresh 3 [Presenter: S.K. Bhattacharyya 1 ] 1 Department of Ocean Engineering, IIT Madras, India 2 Chief Engineer (C&M), Oil and Natural Gas Corporation, India 3 Deputy General Manager (Civil), Oil and Natural Gas Corporation, India. Fatigue analysis of offshore structures is an integral part of design of offshore structures and is carried out with suitable method of discretising the sea states. Historically, for most of the fixed offshore structures, deterministic fatigue analysis had been found to predict the fatigue damage reasonably well and this approach has been in use for several decades. Fixed structures with small topsides, mostly exhibit a static response characteristics and their natural periods may be in the order of less than 2 seconds. Offshore platforms with larger production capacity and somewhat deeper water depths may require specialized treatment of sea states due to their dynamic characteristics and are more vulnerable for fatigue damage. In this work, spectral fatigue analyses have been performed for two different platforms in Bombay high field, a 4-leg wellhead platform and a 8-leg process platform, and comparisons are made with deterministic analysis. The spectral fatigue analysis indicates that the predicted fatigue life of tubular joints are generally lower than those predicted by the deterministic analysis since the dynamic amplification of wave loads are treated approximately in the latter. For a few tubulars near the free surface, however, opposite may be true, probably due to the fact that local wave load dominates the response rather than the dynamic amplification. The importance of adopting the spectral method and its consequences on design are brought out in these two case studies «FAST SPECTRAL RAINFLOW FATIGUE DAMAGE ASSESSMENT UNDER WIDEBAND MULTIPEAK LOADING» M. Olagnon & Z. Guédé IFREMER Brest, France

3 The partition (i.e. identification and separation) of wave energies spectra into swell and wind sea is of great importance in offshore design applications since it provides a more realistic description of the sea states. However, the conventional procedure that recombines the identified wave systems for fatigue analysis leads to a very large set of sea states and to unpractical computations, especially when it is required for fatigue damage assessment to simulate the structural response to the resulting multi-peaked sea states spectra. For faster estimation of the fatigue damage in this case, one can make use of the so-called Iterative Component Addition (ICA), which was set up by the authors for the estimation in a conservative manner of the fatigue damage induced by a multipeaked spectrum in terms of the damages of each of its components taken independently. This formula was shown to meet the main expectations of engineering design, e.g. simple fatigue damage calculation with low computation time and reasonable conservatism (Olagnon & Guédé, 2008). Moreover, those formulas can be iteratively applied when more than two components need to be combined, as is the case in practice. Additional formulas allow to take into account two-slope S-N curves. This contribution intend to present that formula and to show some results of its application to fatigue damage assessment of an FPSO in West Africa area. In addition, some perspectives of this work will be outlined, including some guesses on how to treat non-linear responses from the identification of response systems. «DAMAGE RATES FOR STRUCTURES WITH UNCERTAIN PARAMETERS» Igor Rychlik Chalmers University of Technology, Gothenburg, Sweden For stationary Gaussian loads stresses are estimated by solving system of linear or non-linear differential equations. Variability of stresses, relevant for the fatigue accumulation process, are described by means of rainflow cycles. For ergodic stresses the damage rate can be evaluated (estimated) given the diff. equations and the load spectrum. However the computed damage can be erroneous due to uncertainties in the system properties, e.g. the exact values of mass, stiffness matrices or some load spectrum parameters are uncertain. Hermite polynomials expansions are employed to describe the degree of uncertainties in the estimated damage rates. The method is compared with more commonly used Gauss (error propagation) formulas. Examples taken from vehicle, offshore engineering and wind turbines blades are used as illustrations. «FAILURES IN APPLYING MINER S HYPOTHESIS TO BI-MODAL AND TRI- MODAL LOADINGS» Franck Sherratt, presenter francksherratt@hotmail.com The presentation will report re-analysis of existing fatigue test data on small steel specimens. Loading histories were bi-modal and tri-modal Power Spectral Densities, and emphasis will be placed on failures in the Palmgren-Miner Hypothesis. Rainflow counting is now the accepted way of identifying damaging

4 cycles, but even if rainflow counting is used the damage caused by cycles of low amplitude may be greater than that predicted by the hypothesis. This is usually explained by pointing out that cracks started by high amplitude cycles may be propagated by low amplitude ones, and models have been developed to allow for this. The paper will report tests which show that even if crack propagation does not make up a large fraction of life the low amplitude cycles may still do more damage than the hypothesis assumes. In one investigation the specimens were un-notched and initiation would take up most of the life, and in another nondestructive testing was used to detect the onset of very short cracks in mildlynotched specimens. In both cases low amplitude rainflow cycles sometimes caused more damage than expected. Empirical rules are proposed, but no physical explanation is put forward. «TWO COMPUTATIONS CONCERNING FATIGUE DAMAGE AND THE POWER SPECTRAL DENSITY.» Franck Sherratt, presenter francksherratt@hotmail.com When using frequency domain fatigue analysis fast empirical formulae like the Dirlik expression for the distribution of rainflow ranges may be used to provide estimates of other parameters which are equally empirical but which may be useful in testing or in design. Two of these are:- (a) Computation of a non-stationary time history made up of short periods of narrow-band signal whose variance is changed from time to time to generate a specified rainflow distribution. The target could be to match the rainflow distribution of a given stationary wide-band history. The technique could be used in testing, and would allow low energy resonant machines to be used in place of high consumption servo-hydraulic ones. A similar technique was once used in the aircraft industry. (b) Computation of the density distribution of damage within the frequency range of a PSD. This could be useful, for instance, to a designer using Finite Element Analysis to compute changes in dynamic response caused by dimensional changes, if the objective is long fatigue endurance. The presentation will concentrate on computational practicalities. «FATIGUE OF OFFSHORE STRUCTURES: APPLICATIONS AND RESEARCH ISSUES» Steve Winterstein, presenter SteveWinterstein@alum.mit.edu Web Page: This talk will survey various research issues arising from fatigue analysis of offshore structures and ships. Both bandwidth and non-gaussian effects will be discussed. Applications will include the tether fatigue of a tension-leg platform (including springing effects), and the combined low- and high-cycle fatigue analysis of an FPSO (floating production, storage, and offloading) vessel.

5 «FREQUENCY-DOMAIN MULTI-MODAL FORMULATION FOR FATIGUE ANALYSIS OF GAUSSIAN AND NON6GAUSSIAN WIDE-BAND PROCESSES» Zhen Gao, Torgeir Moan Centre for Ships and Ocean Structures, Norwegian University of Science and Technology Otto Nielsens v 10, N-7491, Trondheim, Norway A method for fatigue analysis of a general wide-band Gaussian process is developed in the frequency domain using a multi-modal spectral formulation (see Gao and Moan, 2008), based on a generalization of the principle proposed by Jiao and Moan (1990) for bimodal fatigue analysis. It approximates the rainflow cycles with large amplitudes as the sum of the envelopes of the process components. The method is derived and verified for ideal trimodal Gaussian processes. It is also applied to more general wide-band Gaussian processes. The accuracy of this method, as well as other methods by Dirlik (1985) and by Benasciutti and Tovo (2005), are demonstrated by extensive time-domain simulations. The proposed method is also capable of dealing with non-gaussian multi-modal processes. This is illustrated by the example of mooring line tension, comprising of both non-gaussian wave- and low-frequency components (see Gao and Moan, 2007). The accuracy of the method has been verified by the timedomain simulations and is considered to be practically acceptable. References: Benasciutti, D. & Tovo, R. (2005) Spectral methods for lifetime prediction under wide-band stationary random processes. International Journal of Fatigue; Vol. 27, pp Dirlik, T. (1985) Application of computers in fatigue. Ph.D. Thesis, University of Warwick. Gao, Z. & Moan, T. (2007) Fatigue damage induced by nongaussian bimodal wave loading in mooring lines. Applied Ocean Research; Vol. 29, pp Gao, Z. & Moan, T. (2008) Frequency-domain fatigue analysis of wide-band stationary Gaussian processes using a trimodal spectral formulation. International Journal of Fatigue; Vol. 30, pp Jiao, G. & Moan, T. (1990) Probabilistic analysis of fatigue due to Gaussian load processes. Probabilistic Engineering Mechanics; Vol. 5, No. 2, pp