Study on the application of spectral fatigue analysis

Journal of Marine Science and Application, Vol. 5 ,No.2 , June 2006 ,pp.42 -46Study on the application of spectral fatigue analysisLIU Xiang-chun, FENG Guo-qing, and REN Hui-longCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaAbstract: Fatigue failure has long been an important issue for ships and ofshore structures. Among thenumerous methods for predicting fatigue life, the spectral method is accepted as the most reliable. AI-though the theory behind spectal analyis is straight foward, the analysis itself is complicated andtime-consuming because it is closely related to crtical technical detils such as the application of fatigueloading ( wave pressures and the inertial forces due to cargoes), the extraction of the stress, and thecalculation of stress RAO. Here , four key technical details-loading application, displacement boundarycondition, the calculation of stress RAO, and the extraction of the fatigue stress -are discussed thorough-ly. For each aspect, a resolution is presented based on the finite element pre-and post-processing sof-ware MSC/PATRAN or FE solver MSC/NASTRAN. The resolutions are efetive and eficient, whichcan help engineers perform spectral fatigue analysis accurately and faster.Keywords: spectral fatigue analysis; load aplication; BC; stress RAO; stress extractionCLC number: U661.43 Document code: A Article ID:1671 - 9433(2006)02 -0042 -05 .1 Introduction2 Theory of spectral fatigue analysisFatigue failure has long been an important issue forThe main idea of behind spectral fatigue analysis canships and offshore structures. To ensure sufficient febe generalized as follows 1 :tigue strength during the service life , a fatigue strength1) The ship motion response and load responseassessment needs to be done at the design stage. Gen-are calculated by linear method.erally, methods for assessing fatigue strength can be2) The stress response is obtained by finite ele-classified into two groups : the cumulative fatigue dam-ment analysis.age method, which is based on S-N curves; and the3) The long- term ditribution of the stress range isfracture mechanics method, which is based on crackobtained from the summary of the short-term distribu-propagation. For the cumulative fatigue damage meth-tion of the stress range, which is assumed as a Ray-od, simplified procedures related to classification soci-leigh distribution. Each short-term distribution of theety and spectral fatigue analysis were considered. Astress range corresponds to a voyage case. Here themong the several methods for estimating fatigue life ,voyage case is defined as a ship voyage under some seathe spectral method is regarded as the most reliable.state with a certain loading condition, heading andAlthough the theory behind spectral analysis is straight-speed, where sea state is specified by a wave scatterforward, the analysis itself is complicated and time-diagram.consuming because it is closely related to critical tech-4) The fatigue damage in the design life is sum-nical details such as the application of fatigue loadingmarized by the. fatigue damage from each short-term( wave pressures and the inertial forces due to car-distr中国煤化工goes)，the definition of the displacement boundaryYHCN M H Gtigue analysis is out-condition, the extraction of the stress ，and the calcula-lined in Fig. 1tion of stress RAO.Received data :2005 - 10 -09.LU Xiang-chun ,e al :Study on the Aplicain of Specral Fatigue Analysis.43.Ship motion3D linear wavewheref(β) is the spreading function and normally a-and wave loadsload calculationdopled asf(βB) =2cos(β) .computationprogramFE modelStress RAOAssuming the probability distribution of the stress is aRayleigh distibution, then the probability distributionWave spectrumStress responseof the stress is represented asand scatterspectrum anddiagramstress distributionf。(σ) = °exp(-ano2mowhere m。is the zero order moment of the stress re-Miner rule andCumulativeS-N curvefatigue damagesponse process.Fig. 1 Spectral fatigue analysis flow chart2.3 Cumulative fatigue damage2.1 Wave spectrumWhen the long-term stress range distribution is definedThe parametric Pierson-Moskowitz spectrum is recom-through a short-term Rayleigh distribution within eachshort-term period, the fatigue criterion reads,mended as wave spectrum and expressed asG m(w) =()."(-台(等)一)D=r(1+四)SP. . P.p0.12./2mogp)",where T, is average zero-crossing period, H, is signifi-where D is the cumulative fatigue damage, T。is thecant wave height, and w is wave frequency.design life in seconds, a and m are S-N curve parame-ters, F() is the Camma function, Nna is the totalThe wave spectrum should be modified by ship speednumber of load conditions considered, Pn is fraction ofU, wave frequency w, and heading angle 0. The rela-design life in load condition n, n, is the total number oftion between the encounter frequency w。and the wavesea states, nn is the total number of headings, P: is thefrequencywis Gm(w.) =-G. ,(w)probability of occurrence of sea state i, P; is the proba-2wUcosθBbility of occurrence of headingj, Vim is the zero-Cross-ing frequency of stress cycles in short-term condition i,2.2 Short term distribution of the stress rangej combined with load condition n, mojn is the zero spec-By linear superposition, the stress spectrum is obtainedtral moment of stress response process in short-termas follows,conditioni , and j is combined with load condition n.CGx(w,) = |H。(a,)| ” ●C(w.) ,where H。(w.) is the stress transfer function.3 Implementation of spectral fatigueanalysisThe spectral moments of order n of the stress responseprocess for a given heading may be described as3.1 The load applicationm. = {w" . Cx(o,)dw。In fatigue analysis, only fluctuating loads contribute to .fatigue damage. Static water pressure and gravities ofThe spectral moments may include wave spreading asthe ship and cargoes do not lead to fatigue damage.m。= w。.Gx(w,)dw, =They中国煤化工erefore, when per-formirCNMHG_an entire ship, the/2:CHloads acung on une snup only Incluae the inertial load offw"，」f(β) . Gx(w,)dβdw.,the ship and cargoes induced by ship motion and theextermnal sea pressures. However, the inertial cargopressure induced by ship motion and the external sea●44.Journal of Marine Science and Application, Vol.5 ,No.2, June 2006pressure vary with different locations, i. e.，the loadis not constrained and is capable of motion of six de-acting on the finite element model ( FEM) varies withgrees of freedom. In this method, it is important to re-different elements. At the same time, the number ofstrain the relevant degree of freedom of the structure tothe finite element is very large with an entire FEM ap-make it impossible to move as a rigid body to ensureplied. Consequently, it is not feasible to apply the loadthe structural stiffness matrix is not singular. Constraintto the finite element model by hand. Then a problemforce at the constraint point also needs to be small e-presents itself regarding how to apply the large numbersnough to ensure a valid result. In fact, the applicationof the discrete pressure values to the finite elementof the boundary condition is still difficult and manymodel.FEA conductors are obsessed with it. The inertia reliefmethod in MSC/Nastran can perform the quasi -staticTo solve the problem, an automatic loading approachFEA without any constraint and solve the difficulty offor pressures'21 was developed. The main points of thisthe application of boundary conditions.approach are outlined as follows: the automatice loadingapproach for pressures is based on Patran Command3.3 The calculation of stress RAOLanguage of the noted MSC/PATRAN pre/ post pro-The strictest method may be quasi-static FEA in timecessing software. The element with wave pressure acteddomain. Stress analysis is conducted applying instanta-on is divided into two groups: one under the waterlineneous loads or pressure at several diferent instancesand the other across the waterline. For the first group，during one wave encounter cycle. The obtained stressesthe element pressure is applied directly. For the sec-are calculated. This method generally requires a signif-nd group, the influence of pressure partially acted onicant number of calculations to obtain the stress transferthe element is accounted for and the nodal force is de-function [5].rived by means of transforming the quadrilateral ele-ment into triangle element. Transforming the quadrilat-On the other hand，assuming the linearity of structuraleral element into a triangle element can be accom-response, a linear superposition method is available toplished by Patran Command Language fem_ .mod. _quad_calculate the stress transfer function. Dividing the sur-split( ). The inertial cargo pressures induced by shipface of ships hull into a number of panels and applyingmotion are directly applied to the elements on whicha unit load on each panel one by one, the load-stressinertial force acted. The approach turmns out to be ainfluence matrix, or the stress coeffcient can be calcu-useful tool for pressure application because it greatlylated by FE analysis. Pressure distribution on the hullenhances work efficiency.can be decomposed into discrete loads corresponding tothe above mentioned unit load ，and superposing theThe inertial load of ship was simulated by applying theload-stress influence matrix according to the pressureopposite acceleration to the finite element model. So,distribution pattern, the stress can be obtained. Calcu-the mass distribution of the FE model must comply withlating the stress in this way from the instantaneousthe mass distribution of real ship. But unfortunately,pressure distribution, the stress amplitude can be ob-the mass distribution of FE model is usually not in ac-tained by interpolating the instantaneous stress as a si-cordance with the mass distribution of the real ship.nusoidal function in time. This method is named theThe correction of the mass distribution of the FE modeldiscrete analysis method ( DISAM). This method ismust be carried out to make it equal to the mass distri-more useful than that of the quasi-static FE analysis inbution of a real ship.time domain if the number of panels on which unit load3.2 Boundary conditionis中国煤化工CH.CNMHGWhen performing finite element analysis, some dis-In caseswnere Te IUau in wiucn the linearity can beplacement boundary conditions must be specified to e-assumed, such as the internal pressure due to liquidliminate the rigid boy movement. The quasi-staticcargo or ballast water, stress armplitude can be calcu-method is usually used for the FEA of a structure thatlated by applying the real and imaginary parts of theLIU Xiang chun ,et al:Study on the plicaion of Specral Faigue Analysis●45●load. As for the extermal sea pressure, if only the hullimaginary part of the complex stress response. The re-surface below or at the sill-water plane is loaded withsultant stress can be described asextemal pressure, this method can be applied. Sinceσ =σc+iσ,,the dynamic pressure is calculated in the frequency do-and the amplitude of the resultant stress ismain, each loaded element will experience a sinusoidalσ=√σ: +σξ.loading around a mean level of zero. Each element istherefore loaded with a unique pressure amplitude and3.4 Stress extractionphase, which can be expressed by a real and imaginaryWhen performning a fatigue analysis ，among the struc-part using complex numbers. The results from the realtural details, the intersection between longitudinals andand imaginary load case will then be the real and imag-the web frames or transverse bulkheads is most ofteninary deflections and stresses ，which can again be usedthe position that needs to be checked. In the finite ele-to calculate the stress amplitude in any structural partment model of a ship, a beam element is usually usedof the vessel. The real and imaginary part method canto represent the longitudinals. For a beam element ,be explained as follows:there are four points, as shown in Fig. 2, at which thestresses can be output or extracted in MSC/NAS-The motion equation can be written asTRAN;Mi(I) = F(t) = Feld,(1)n(t) =- w.2ne'"d,(2)FCwhere η is a column vector consisting of amplitude ofmotion components , in complex number,; F is columnvector consist of amplitude of force components, incomplex number ;M is mass matrix ;w。is encounter fre-quency of wave.DThe external force can be expressed as the integrationFig.2 Transverse section of a longitudinalof pressures along the pressure action region. FrorEq.(1) and Eq. (2), the fllowing equation can bethere are also four kinds of stresses which can be out-put or extracted: axial stress, bending stress, maxi-derived :mum combined stress and minimum combined stress.-w?Mη=F= j[P(x,y,z)nds，(3)Some researchers confuse the stress output points andwhere the left part is the inertial force of the ship, thestress types, so it is important that the right point andstress type are used in the fatigue assessment. For theright part is the integration of the pressures.above mentioned structural details, the stress at pointRewrite the motion component η and pressure p(x, y,E should be extracted and the axial stress and bendingz) in complex numberstress should be extracted respectively. The maximumη=ηc+iηs.(4)combined stress is not applicable for fatigue analysis.p(x, y,z) = Pc(x, y,z) +ips(x, y,z) . (5)The reason the axial stress and the bending stress atSubstituting Eq. (4) and (5) into Eq. (3), the fol-point E should be extracted respectively is that there arelowing two equations can be obtained:different stress concentration factors for the axial stress- o;Mnc =fr(.oy,znds，ss (6)and the bending stress. For autoratic stress extraction,the corresponding PCL function can be adopted.中国煤化工- w?Mns =fe