Fatigue damage calculation of ULCS due to quasi-static wave response and springing response

Transcription

1 Fatgue damage calculaton of ULCS due to quas-statc wave response and sprngng response V. Boutller 1), S. Maherault 1), M. Huther 1), J. Henry 1), G. Parmenter 1) 1) Bureau Vertas, Marne Dvson, 67/71 Boulevard du Château eully-sur-sene cedex - France Abstract Shp transport s growng up rapdl leadng to shp s sze ncrease, and partcularly for contaner shp, the last generaton s now called Ultra Large Contaner Shp (ULCS). Due to ther ncreasng szes, they are more flexble and ther structural natural frequences may fall nto the range of the encounter frequences of the waves. Therefore, waves may nduce sprngng vbraton of the whole hull grder, whch wll ncrease the fatgue damage. Ths phenomenon s dsregarded n the present classfcaton fatgue rules for shp desgn and constructon. On offshore structures, several methods of combnaton of low and hgh frequences loads are proposed for the determnaton of fatgue damage n the ISO/FDIS 1991 standard. But none of them are relevant for ULCS fatgue evaluaton. The purpose of the present paper s to propose a practcal method for fatgue damage calculaton applcable for classfcaton of ULCS. Ths methodology s called the Total stress RAO. Keywords Fatgue damage, ULCS, Total stress RAO, wave loads. Introducton sprngng, The sprngng shp structural response was reactualzed recentl n the context of the ULCS. Indeed, due to ther huge dmensons (length close to 4m) whch reduce the structural natural frequences and partcular ther operatng condtons (speed up to 27 knots) whch ncrease the exctaton frequences, a lnearly nduced sprngng becomes possble. Ths phenomenon s dsregarded n the present classfcaton fatgue rules for shp desgn and constructon due to the fact that sprngng has dsappeared wth the down-szng of shps snce the ULCC (Ultra Large Crude Carrers), 55,tdw tankers bult between 1976 and On offshore structures, ths phenomenon, contnuous forced frequences exctaton by waves, also exsts, and several methods of combnaton of low (quas-statc) and hgh (resonance) frequences loads are proposed for the determnaton of fatgue damage n the ISO/FDIS 1991 standard. But, among these methods, the smple damage summaton would be un-conservatve due to the nonlnear relaton of fatgue damage and stress. The combned spectrum and the combned spectrum wth dual narrow banded correcton factor would be unconservatves because the two effects (wave and sprngng) are dependent each other n our case. Then, none of those loads combnatons proposed n the standard are relevant n our case, except the tme doman cycle countng, whch s a very tme consumng method. In ths paper, a practcal method for fatgue damage calculaton applcable for classfcaton of ULCS s proposed. Ths methodolog called the Total stress RAO, has been verfed wth the consdered most accurate one, the Ranflow cycle countng method appled to the stress tme hstory. Frst, the two methods used for these calculatons of fatgue damage are descrbed. Secondl those methodologes are appled and compared on one crtcal detal of a ULCS. A set of sea states s selected n order to analyze the contrbuton of the sprngng response on the short term damage. A comparson between Total stress RAO method and other methods proposed by the ISO standard s done. Theores Some aspects of 3D lnear hydro-elastc models of sprngng Ths method s based on the full couplng of 3DFEM (Fnte Element Method) structural model and 3DBEM (Boundary Element Method) hydrodynamc model. Only lnear sprngng n frequency doman s consdered. The so called modal approach s used, whch means that the total structural response s presented as a seres of the dry structural modes precalculated by the 3DFEM structural code.

2 We wrte : H = ( x, z, t) = ξ ( t) h ( x, = 1 ξ = 1 [ k] ( t) h ( x, + h ( x, + h ( x, Where h ( x x y, denotes the general moton/deformaton mode whch can be ether rgd or elastc. The above decomposton leads to the addtonal radaton boundary value problems (BVP) for elastc modes, wth the followng change n the body boundary condton : ϕ R n = h n (2) z (1) After solvng the dfferent BVP-s the resultng pressure s calculated usng Bernoull s equaton and ntegrated over the wetted surface n order to obtan the correspondng forces, so that the followng coupled dynamc equaton can be wrtten : DI { ([ m ] + [ A] ) ω [ B] + [ k] + [ C] }{ ξ} = { F } ω 2 (3) e Where : [ m]: modal genune mass [ k]: modal structural stffness [ A]: hydrodynamc added mass [ B]: hydrodynamc dampng [ C]: hydrostatc stffness { ξ}: modal ampltudes DI { F }: modal exctaton e The dynamc modal equaton s solved, makng the strans and stresses RAO s avalable n any part of the shp structure. Ths means that, for example, we can wrte for the stress x, z, t : dstrbuton ( ) ( x, z, t) = ξ ( ω) σ ( x, = 1 Where : ( x, σ represents the spatal dstrbuton of the stresses correspondng to each mode of moton/deformaton and ξ ( ω) are the modal ampltudes.e. soluton of the moton equaton (3). The total structural response s decomposed nto quasstatc and dynamc part, n order to clearly evaluate the nfluence of sprngng on the overall shp structural response. The decomposton nto the quas-statc and dynamc part also allows supermposng the sprngng response to the exstng quas-statc fatgue calculaton methods and ensures the proper convergence of the RAOs results. More detals about decomposton nto quas-statc and dynamc part are gven by Malenca (28). Ths model has been valdated by Malenca (23) on a barge. Then, the Total Stress RAO corresponds to the sum of the RAO (Response Ampltude Operator) of the wave quas-statc stress response and the RAO of the dynamc sprngng stress response. RAO σ ( ω) = RAO statc ( ω) + RAOdynamc ( ω) Where: ω s the wave pulsaton. Thanks to these RAOs, fatgue damage assessment and comparsons can be done. Fatgue damage assessment In ths paper, fatgue damage s determned by means of two approaches: 1/ A spectral analyss n frequency doman approach usng software 2/ A tme doman cycle countng approach Stress tme hstory was generated from Hsto software. Fatgue damage s then calculated from the stress tme hstory by means of Ranflow software. All these software (, Hsto and Ranflow) has been developed at Bureau Vertas. Spectral fatgue analyss Spectral analyss allows to determne long term fatgue damage consderng a wave scatter dagram by means of the followng procedure: Spectral analyss s performed n order to obtan the moments of the short term stress response spectra The long term dstrbuton of the stress range s determned (2 classes are used) assumng a Raylegh dstrbuton for the stress range durng a sea state.e. a Gaussan narrow-band stress process The number of cycles s calculated for each class of the long term dstrbuton, takng nto account the contrbuton of each sea state The fatgue damage s cumulated from the long term dstrbuton accordng to Mner s Rule. The spectral densty of response n ampltude S R ( ω) can be defned as: S ( ) ( ) * 2 R ω = S w ω RAO ( ω) (4) where: S W (ω) : wave energy densty spectrum ω: wave pulsaton RAO (ω) : transfer functon of the stress Spectral moments m, m1, m2, m3 and m4 can then be calculated. From these moments, some statstcal parameters of the tme response can also be obtaned such as Root Mean Square (RMS), mean perod (T m ), peak perod (T p ) and mean zero up-crossng perod (T Z ). The stress range s calculated as 2 tmes the stress ampltude.

3 Long term stress dstrbuton The method conssts n countng, over all sea states observed durng a reference perod D REF, the expected number of exceedance of a response level X: SS n ( X ) = n p ( X ) (5) ex 1 SS SS Where: n ex (X) : the expected number of exceedance of a response level X, over a reference duraton (shp desgn lfe tme) D REF : the total number of sea states SS p SS (X) : the probablty of exceedance of a response level X, durng a sea state SS, assumng that the stress range process s narrow banded,.e., the probablty of stress range follows the Raylegh s law. n : the number of cycles of the response for a sea SS state SS s defned as : (α D REF )/T Z ) p(ss) wth p(ss) equals to the probablty of occurrence of the sea state n the total number of sea states n the wave scatter dagram (α.salng factor,.e., rato of tme n open sea) Fatgue damage calculaton Then, the fatgue damage s cumulated consderng all classes accordng to Mner s Rule by usng the defned S- curve descrbed by the parameters (K, m) n order to obtan the total fatgue damage durng the reference perod D REF. S m = K Stress tme hstory and Ranflow The fatgue damage was determned by means of a tme doman cycle countng approach whch s, f rgorously performed wth a suffcent number of tme smulatons, consdered as the most accurate method of calculatng fatgue damage accordng to ISO/FDIS (25). As the stress hstory s not drectly avalable, t s necessary to buld up realsatons of tme hstory from nformaton provded by the spectrum data. It requres two steps of calculaton: 1. Generaton of stress tme sgnal wth software Hsto from the RAO and sea state spectrum 2. Fatgue damage calculaton wth software Ranflow. Ths software allows to count the cycles of the stress tme sgnal calculated above from the cycle countng Ranflow method and then to calculate the fatgue damage by means of the Mner s rule. Stress Tme hstory generaton We supposed that the sea (rregular wave) s defned as the sum of a large number () of regular waves whch are assumed to be snusodal wth dfferent wave length, ampltude and phase. Furthermore, the regular waves are assumed totally ndependent from each other. Therefore, the contnuous short term wave spectrum s represented as a seres of rays (sne components) of frequences ω and ampltude A : 2 A 2 ω (6) = S w ( ) ω Where: A Ampltude of the th component of the wave ω Interval of wave pulsaton The stress sgnal g(t) s calculated from Hsto software by the followng formula: ( ω e + = ( ) t ϕ ) g( t) Re.5 S( ω ) ω RAO ( ω ) e = where: Re[] : Real component ω : Encountered pulsaton e ϕ : Phase of the th component of the rregular wave whch s taken random RAO( ω ) : Response Ampltude Operator (n complex format) of the studed effect (stress here) decomposed n a real component and an magnary component. : umber of regular wave components whch consttute the rregular wave. s taken equal to In the above formula, we consder the ndex n the range ; +, so we have to consder the half ampltude formula: A/2 =.5 S ( ω ) ω In order to obtan an accurate estmaton of fatgue damage due to a short term sea state (.e. assumng that a coeffcent of varaton less than 1% s acceptable), a suffcent number of tme smulatons has been performed. Generall the number of smulatons was equal to ten for the selected sea states. Cycles countng and fatgue damage calculaton The treatment of the sgnal by applcaton of Ranflow Method conssts, accordng to the AFOR A 3-46 methodolog to extract frst the extrema and then the ranges (peaks to troughs). The Ranflow countng method allows to break up the tme stress sgnal nto a set of ndvdual stress cycle defned by range magntude and mean value. Then those values are assgned nto defned levels of stress ranges.e. they are put nto classes. The nterval of classes whch has been consdered s equal to.1 MPa.

4 Fnall we obtaned the lst of all stress ranges whch were extracted. Fatgue damage s then determned by summng the damage due to each stress range by means of the Mner s law. Short term damage The comparatve analyss of fatgue damage s performed on a seres of selected sea states,.e. at short term. Spectral method () We consder the Total Stress RAO and the spectral approach ( software) s used. The steps of calculaton are: Stress response s determned from the Total Stress RAO for each sea state from the spectral analyss. Spectral moments (m, m2, m4) are then calculated and statstcal Raylegh parameters, mean zero upcrossng perod (T Z ) of the response are determned. The long term dstrbuton of the stress range s bult up. The value of reference duraton D REF s 4 taken equal to years and α =1 (correspondng to the duraton of a short term sea state of 3 hours). The wave scatter dagram s consttuted by one sea state, SS =1, descrbed by (Hs, Tp) wth an occurrence probablty p SS =1. The fatgue damage calculaton s performed. The short term fatgue damage relatve to the consdered sea state (Hs, Tp) s gven n the output fle. Ranflow countng method We consder the Total Stress RAO and the stress tme hstory. The steps of calculaton are: Generaton of stress tme hstory for each sea state wth software Hsto from the Total Stress RAO gven n complex format. We made a suffcent number of smulatons n order to take nto account the randomness of the phase of the rregular wave s components durng a sea state. Cycles countng and fatgue damage calculaton for each smulaton wth the software Ranflow. The short term fatgue damage s calculated wth the Mner s rule. Applcaton Fg. 4: Data for fatgue calculatons Mddle Shp Hatch Corner FEM of the mddle shp hatch corner The selected sea states among those of the World Wde Wave Scatter Dagram are the followng: Tz=3.5 s; Hs=2m Tz=4.5 s; Hs=3m Tz=6.5 s; Hs=5m Tz=1.5 s; Hs=5m They are selected n order to analyze the contrbuton of the sprngng response on the short term damage over the Tz range wth rsk of structural resonance. Consderng each selected wave perod, the sgnfcant wave heght whch was taken corresponds to the maxmum reported n the wave scatter dagram wth a lmted value of Hs equal to 5 m (due to the fact that above 5m t was assumed that the shp speed wll be reduced deletng the rsk of resonance). So, the selected sea states are the most contrbutng to fatgue damage for each consdered wave perod. The consdered wave headng s 12 (wth head sea comng from 18 degrees); 12 s the headng where the sprngng s lkely to be. The consdered speed s the maxmum one,.e knots. These RAOs are gven for a structural dampng of 1%. The consdered stress RAOs, are those n the hatch corner radus free edge (see Fg. 4). For fatgue assessment of the hatch corner at free edge, a rod element s used to obtan stress at free edge. The stress range s based on the axal stress n the rod element. The RAOs of stresses (n Mpa/m) are functon of wave pulsaton (n rad/s), as shown on Fg. 5. To compare both approaches, one hatch corner located at the mddle part of a ULCS was selected. Structural detals The structural detal s one hatch corner located at the mddle part of the shp and more precsely t s located at the upper deck level (see Fg. 4). Ths detal s submtted to torson and bendng at wave headng equal to 12.

5 total Quas-statc + dynamc (Total RAO) Quas- Fg. 5: RAOs of stresses On Fgure 5: Statc RAO corresponds to the quas-statc stress response due to wave Dynamc RAO corresponds to the dynamc stress response due to sprngng. Total RAO corresponds to Total Stress RAO whch s equal to the sum (n complex) of the statc RAO and the dynamc RAO. The sea energy spectrum s a PIERSO-MOSKOWITZ wave spectrum. Because the detal s unwelded, the B S Curve (IACS 26) correspondng to a parent materal and a machned detal, s used. Ths B S Curve s defned below: m S = K K 1 = , m 1 = 4 (for 1 7 or S S q ) K 2 = , m 2 = 7 (for > 1 7 or S < S q ) S q = 1.3 MPa (Stress range at change of slope at = 1 7 ) Results For each selected sea state, we determned the damage due to the total response from the Total Stress RAO by means of the two methods: Ranflow Method whch s consdered as the method of reference and Spectral method wth Ranflow method results Stress Tme hstory (software Hsto) Ten stress tme hstores (wth duraton of 3 hours) are generated for each selected sea state wth Hsto software. The Fg. 6 s a part of one of the obtaned stress tme hstory for the sea state: (Tz = 6.5s /Hs = 5m). Ths sea state has been selected because the stress process s composed by both dynamc stress (due to dynamc sprngng response) and quas-statc stress (due to quasstatc wave response) whch are of the same order of magntude. Fg. 6: Stress tme hstory for Tz = 6.5s Hs = 5m It was checked that stress tme hstory consderng the Total Stress RAO s equal to the summaton of stress tme hstory due to quas-statc wave response and the stress tme hstory due to sprngng response. Stress cycles countng and damage calculaton (Ranflow) We performed the cycles countng and calculated the damage for ten smulatons for each sea state. Then, the mean value of the damage obtaned for the 1 smulatons s calculated. The table 1 gves, for each sea state, the maxmum/mnmum ampltude (Smax/Smn), the hghest stress range ( Smax), the total number of cycles (t) and the mean damage n term of Mner sum. The gven values are those obtaned for the smulaton whose damage s closer to the mean damage value. Table 1: Results for the Ranflow countng method for the Total Stress RAO Tz = 3.5s Hs = 2 m Tz = 4.5s Hs = 3 m Tz = 6.5s Tz =1.5s Smax Smn Smax t Damage 3.246E E E E-4 Spectral method wth Stress Response Spectra As mentoned before, the frst step of spectral method s to determne the stress response spectrum for each sea state. The Fg. 7 represents the wave spectrum and the Total Stress RAO for the sea state (Tz=6.5s /Hs=5m). The Fg. 8 represents the stress response spectrum for ths sea state. For the sea state: (Tz=6.5s /Hs=5 m), we note that the response spectrum s composed manly by the sprngng response.

6 total Fg. 7: Tz = 6.5s Hs = 5m Wave spectrum & Total stress RAO Table 3: Total RAO wth Total RAO wth Ranflow Rato ( / Ranflow) Bandwdth Parameter (ε) Comparson between and Ranflow countng method Tz = 3.5s Hs = 2 m Tz = 4.5s Hs = 3 m Tz = 6.5s Tz=1.5s Hs =5 m 3.331E E E E E E E E % 1.28% 6.89% 11.46% total When the wave perod (T ncreases, we note, on the table 3, that the dfference of damage obtaned from and Ranflow method ncreases wth the bandwdth parameter (ε).e. when the stress response process becomes more and more broad-banded (ε= for a narrow-banded process, ε=1 for broad-banded process). Moreover, we note that damages obtaned from are always lghtly greater than damages obtaned from the Ranflow countng method. Fg. 8: results Tz = 6.5s Hs = 5m Total stress response spectrum The Table 2 gves, for each sea state, the spectral moments (m, m2, m4), the hghest stress range ( Smax), the total number of stress cycles ( t ) and the damage. The hghest stress range has been calculated from the Raylegh dstrbuton: S max = 8 m ln (prob of exceedance =1/ t ) t Where: t Total number of stress cycles n one sea state ( t =18/Tz for a 3 hours sea state where Tz s the mean zero up-crossng perod of the stress response) Table 2: Results for the Total Stress RAO wth Tz = 3.5s Hs = 2 m Tz = 4.5s Hs = 3 m Tz = 6.5s Tz =1.5s m m m Smax t Damage 3.331E E E E-4 Comparson between and Ranflow method The table 3 summarzes the damage obtaned, for the selected sea states, from Ranflow Method and Spectral approach () wth the Total stress RAO. To understand the orgn of the dfference of damage between and Ranflow method.e. to determne the stress range levels whch contrbute the more to the short term damage, two knds of graphcs can be drawn: The frst one shows the short term stress dstrbuton obtaned from the two approaches: Ranflow method and. assumes a Raylegh dstrbuton.e. a narrow-banded process. The second one shows the cumulatve damage dstrbuton obtaned from the two approaches. The use of the two graphcs smultaneously allows to lnk the cumulatve damage to the stress dstrbuton. Two graphcs are presented on Fg. 9 and Fg. 1 for the selected sea state (Tz = 3.5s /Hs=2m). Two graphcs are presented on Fg. 11 and Fg. 12 for the selected sea state (Tz = 6.5s /Hs=5m). The analyss of those graphcs allows to say that: For sea states (Tz = 3.5s /Hs = 2m) and (Tz = 4.5s /Hs = 3m), consdered almost as narrow-banded, the stress dstrbuton obtaned from Ranflow method s close to the Raylegh dstrbuton consdered n except for the hghest stress ranges part of the dstrbuton (Fg. 9). For hghest S, the dfference between the two methods s explaned by the resdue of the Ranflow Method. However, the contrbuton of hghest S to the short term damage s low (around 1%) due to the low number of cycles (less than 1 cycles).

7 Consequentl the short term damage (correspondng to cumulatve damage at =t) obtaned from the two methods s very close (around 2%) (Fg.1). Therefore, for those sea states, the assumpton that the stress s narrow-banded s acceptable. For sea states (Tz = 6.5s /Hs = 5m) and (Tz = 1.5s /Hs = 5m), whch have more broad-banded characterstcs, the stress dstrbuton obtaned from Ranflow method s close to the Raylegh dstrbuton consdered n except for the hghest and the smallest stress ranges parts of the dstrbuton (Fg. 11). For hghest S, the dfference between the two methods s due to the same reason as ths one gven below. The contrbuton of hghest S to the damage s low as shown on Fg. 12 due to the low number of cycles (less than 5 cycles). For smallest S, the number of cycles counted by Ranflow s greater than the number of cycles counted by. Ths s due to the fact that Ranflow counts small stress range cycles whch do not cross the zero stress level, contrary to whch does not count those types of stress cycles. The contrbuton of those smallest S to the total damage (cumulatve damage at =t) s low as shown on Fg. 12. However, overestmates lghtly the damage produced by cycle of mean level stress range. Consequentl the short term damage (correspondng to cumulatve damage at =t) obtaned from the two methods s close (around 9%). Therefore, for those two sea states, the assumpton that the stress s narrowbanded s more or less acceptable. cumulatve damage dstrbuton delta_s Fg. 1: (log scale) Ranflow FATA Tz = 3.5s Hs = 2m Cumulatve damage dstrbuton Fg. 11: (log scale) Ranflow FATA Tz = 6.5s Hs = 5m Short term dstrbuton We shall also note that the maxmum dfference between and Ranflow Mner sum corresponds to (Tz=1.5s /Hs=5m), sea state where the wave response s predomnant to the sprngng one, the closest to classcal wave wthout sprngng responses cumulatve damage dstrbuton Ranflow FATA delta s Fg. 9: (log scale) Ranflow FATA Tz = 3.5s Hs = 2m Short term stress dstrbuton Fg. 12: (log scale) Tz = 6.5s Hs = 5m Cumulatve damage dstrbuton The table 6 summarzes the comparson between the Total stress RAO method and other methods proposed by the ISO/FDIS 1991 standard (as smple summaton, combned spectrum and Ranflow method). The Ranflow method s consdered as the most accurate method of calculatng fatgue damage accordng to ISO/FDIS Results n thrd and fourth lnes are un-conservatve and results n frst lne are conservatve. For the smple summaton method, the wave and the sprngng response spectra and Mner sums are calculated separatel and then the Mner sums cumulated. For the combned Spectrum method, the wave and the sprngng response spectra are calculated separately then summed. From the resultng spectra, the Mner sum s

8 calculated as for the smple summaton. Table 6: Damage comparson wth other methods proposed by API Total RAO wth Ranflow method Smple Summaton Combned Spectrum Tz = 3.5s Hs = 2 m Tz = 4.5s Hs = 3 m Tz = 6.5s Tz = 1.5s 3.331E E E E E E-3 3.5E E E-4 1.4E E E E E E E-4 To conclude regardng the combnaton of hgh frequency and low frequency damage wth ther respectve applcaton: Ranflow countng method s the most accurate method of calculatng fatgue damage accordng to ISO/FDIS Smple summaton method s un-conservatve Combned spectrum methods provdes a conservatve estmate of the damage when responses spectra are ndependent (for example for the determnaton of damage due to swell and wnd seas usng a bmodal spectrum). evertheless, n our case of dependent stress responses (quas-statc wave response and sprngng response), ths method s unconservatve. Dual narrow band s used when frequences of the two spectra are very dstnct. Total RAO method has to be used n the case two responses are dependent.e. fatgue calculaton due to quas-statc wave response and sprngng response. In the case study of ths paper, ths method s conservatve versus the Ranflow countng method n a range of less than 1%. Concluson The present paper proposes and valdates a practcal method for fatgue damage calculaton applcable for classfcaton of ULCS submtted to the combnaton of dynamc sprngng response and quas-statc wave response. Ths method conssts to use the spectral approach usng the Total Stress RAO correspondng to the sum (n complex) of the RAO wave and the RAO sprngng. Those RAOs were determned usng HydroStar BV software. The valdaton of ths method was performed by calbraton wth respect to the Ranflow method whch s generally consdered to be the most accurate method for fatgue damage calculaton. Those two methods were appled for determnaton of fatgue damage of a crtcal detal: one hatch corner of an ULCS submtted to torson and bendng at wave headng equal to 12. A set of sea states correspondng to several wave perods (Tz=3.5s, Tz=4.5s, Tz=6.5s and Tz=1.5s) were selected for the determnaton of the short term damages. As sad above, the comparson of the damage results, obtaned from spectral method and Ranflow method shows that spectral damage s lghtly hgher than those gven by the Ranflow method n the range between 1% to 11%. Those results are gven for one partcular structural dampng; nevertheless, the change of ths structural dampng value wouldn t change the concluson of ths study. The dfference of damage between and Ranflow ncreases when the stress process becomes more and more broad-banded.e. when Tz ncreases. But the dfference remans acceptable versus the normal practce for classcal wave spectral response,.e., wthout sprngng response. References AFOR A 3-46, Fatgue sous sollctatons d ampltude varable: Méthode Ranflow de comptage des cycles, ovembre 1993 ISO/FDIS Petroleum and natural gas ndustres Specfc requrements for offshore structures Part 7: Staton keepng systems for floatng offshore structures and moble offshore unts, (25). DV/Bureau Vertas, Fatgue Desgn Recommendatons for FPSO, Report , October 24. User Manual, Bureau Vertas, March 28. IACS, Common Structural Rules for Bulk Carrers (26), January 26. IACS, Common Structural Rules for Ol Tankers (26), January 26. Malenca S., Tutman J.T., Bgot F., Sreta F.X. (28). "Some aspects of 3D lnear hydro elastc models of sprngng" Malenca S, Moln B., Remy F & Senanovc I. (23) ). "Hydro elastc response of a barge to mpulsve and non mpulsve wave loads. 3 rd Int. Conf on a Hydro elastct Oxford.