Trans RINA, Vol 153, Part A4, Intl J Maritime Eng, Oct-Dec 2011


It is considered as a linear elasto-dynamic problem, which means that the damping coefficient is proportional to the velocity of displacement and the recovering to the initial state force is a linear function.


The excitation amplitude of nominal stresses at the point of study is as a function of the axial load subjected to the structures due to the vertical induced bending moment. Vertical bending moment at a probability level of 10-8, representing 25 years lifespan with an operating time at sea is defined by direct calculations. The vertical bending moment acting for a life time of 0.85*25=21.25 years at sea close to a midship section is with an absolute value of 680 MNm.


The wave-induced stresses w t are considered as a


stationary, narrow-banded Gaussian process with a zero mean and variance,


 w waw os wt are described as:


    , (2) where


 tc w a w


Dc 


21 2 m


n 22 1 2 K Ln nc is the normal stress amplitude, w is the


natural frequency for the first elastic mode of vibration and w is the phase angle. For the case studied here w is assumed as 0.93 radian per second and w


is considered 0. The amplitude a w is a random variable,


which for a short sea-state condition may follow a Rayleigh distribution.


The car breaking load applied to the stiffener is treated as a transient process:


     c  cactexp where a c is the natural    kc ct sin ct (3) DD D 


is the excitation normal stress amplitude,  c frequency assumed as 3.64 radian per


second, ck =0.04 is damping factor and c is the phase angle.


The excitation amplitude, a c of the transient process, c t , is considered as a random variable that follows a


Rayleigh distribution which implies that the process can be treated as a narrow-band Gaussian process with time- dependent variance. The combination of


w t and c  t then becomes the sum of a stationary Gaussian


process and a transient one. The process is similar to that of the combination of two stationary processes, but has differences.


The car breaking loading induces stresses that result in additional damage to the wave induced load damage and this is modelled as a transient process. For simplification here, the phase angles are not taken into account.


Hot-spot 12 345 6


Car breaking 9.52E-04 5.71E-02 1.29E-03 8.28E-02 1.20E-05 5.96E-04 Wave Total


Figure 6– Fatigue damage of Hotspots 1 to 6


The fatigue analysis of the welded joint reveals six areas of high stress concentration. The fatigue damage for the spot-weld model as hotspot 1, 2 and 3 respectively and


1.51E-01 1.36E-01 2.09E-01 2.06E-01 7.23E-02 1.05E-01 1.52E-01 1.93E-01 2.10E-01 2.89E-01 7.23E-02 1.06E-01


0.E+00 5.E-02 1.E-01 2.E-01 2.E-01 3.E-01 3.E-01


 wc (8)       exp km 


oc m


  


  2


 m m , (5) 


where the material descriptors of the S-N curve are taken from [21] as K =1012.38, m=3 and ov =0.11 and  =1. The number of car breaking cases during a service life, considered in the example here, is 1622. The stress range,


 i is calculated as:  


 i a compressive   ii i ,n


i n


,,, SCF


 where i a tensile , , 


(6) (7)


SC iF is the stress concentration factor of the hotspot considered. Finally the total fatigue damage for any hotspot is calculated as:


The fatigue damage assessment is based on the Miner [18] summation


rule. The


basic assumption of the


method is that the structural damage per load cycle is constant at a given stress range. It is assumed that the stress range is distributed according to a two-parameter Weibull


induced load is calculated using the close form solution of Nolte and Hansford [19] as:


w D K Ln n


vT od o 


  1


m w


 m 


 


m (4)


and the fatigue damage for the transient process is calculated as proposed by Jiao and Moan [20] as:


distribution and fatigue damage for wave-


©2011: The Royal Institution of Naval Architects


A-235


Damage


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64