Extended IACS incremental-iterative method for calculation of hull girder ultimate strength in analysis and design

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1 Extndd IACS incrmntal-itrativ mthod for calculation of hull girdr ultimat strngth in analysis and dsign S. Kitarovic, J. Andric & V. Zanic Univrsity of Zagrb, Faculty of Mchanical Enginring and Naval Architctur, Zagrb, Croatia ABSTRACT: Thortical background and oprational aspcts ar givn for th proposd xtnsion of th IACS incrmntal-itrativ mthod. Mthod is usd for th assssmnt of th hull girdr ultimat bnding momnt as on of th dsign attributs within optimization basd dcision making procss and is implmntd in OCTOPUS dsign nvironmnt. Exampls of application ar givn and th gnral conclusion basd on th rsults obtaind is prsntd. 1 INTRODUCTION Sinc th ultimat strngth might b prcivd as th most maningful safty masur of th ship's hull girdr structur, prdiction of th ultimat bnding momnt bcoms ssntial and unavoidabl part of th ship structural concpt dsign procss. Mthods mployd should support multipl failur mods and thir intractions, whil giving prcis prdiction of collaps and post-collaps bhavior of th structural mmbrs involvd (particularly thos undr comprssion). On th othr hand, multipl xcutions within dsign loop dmand utilization of stabl, robust and sufficintly fast algorithms. Considration of th abov statd dmands rsultd in dvlopmnt of th improvd incrmntalitrativ mthod for longitudinal ultimat strngth assssmnt basd on IACS prscribd incrmntalitrativ mthod. Incorporatd mthod particularitis includ contmporary advancs which improv th accuracy during multi-dck ship application, as wll as th ability to considr vrtical shar forc influnc on th ultimat hull girdr strngth. Purpos of this papr is to giv an insight into thortical background and oprational aspcts of this mthod. It is to b usd for th assssmnt of th ultimat bnding momnt as on of th dsign attributs within optimization basd dcision making procss, as implmntd in OCTOPUS dsign nvironmnt (Zanic t al. 7). EXTENSION OF THE BASIC METHOD.1 Gnral rmarks Ultimat longitudinal strngth is dfind hrin as th valu of bnding momnt at which th flxural stiffnss of th hull girdr (i.. th slop of momnt to curvatur curv) assums th valu of zro, as illustratd by Figur 1. Figur 1. Qualitativ hull modul momnt to curvatur (M-Φ) rspons curv, obtaind by utilization of th Brnoulli-Eulr bam idalization of th hull girdr. Th gnral approach for assssmnt of th momnt to curvatur rlationship usd in IACS prscribd incrmntal-itrativ mthod is similar to th on originally proposd by wll known and widly sprad Smith's mthod (Smith 1977) and will not b furthr discussd hr. Modifications of th basic mthod ar introducd in ffort to nabl inclusion of th ffcts disrgardd by th basic mthod and thus improv th ovrall accuracy of th analysis. Influnc of th shar strss and dck fficincy is incorporatd into basic mthod as illustratd by th Figur, which rprsnts gnral flowchart of th proposd mthod.

2 Figur. Flowchart of th proposd mthod.. Inclusion of th shar strss influnc Longitudinal ultimat strngth is usually analyzd at th hull girdr cross-sction with maximum bnding momnt, whr th shar forc is ngligibl. Accounting for shar might b intrsting whn thr is a cross-sction along th hull girdr with lss thn maximum valu of bnding momnt, but with significant valu of th shar forc (cass of altrnat loading conditions). Sinc in this cas it is not so obvious whthr th hull girdr will collaps at th sction with th maximum valu of th vrtical bnding momnt or at th sctions with high vrtical bnding momnt and shar forc valus, both scnarios dsrv th du considration. Th ffct of th vrtical shar forc on th hull girdr ultimat strngth is considrd trough th influnc of th warping inducd shar strss distribution of th hull modul on th collaps (buckling, yild) of th principal structural mmbrs. For th structural valuation of primary rspons at th concpt dsign lvl th bam idalization is oftn usd. Sinc this valuation is basd on th xtndd bam thory which nds cross-sctional charactristics usually obtaind using analytical mthods, this can b vry complicatd for th ralistic combinations of intrconnctd opn and closd thin-walld (un)symmtric cross sctions. Application of th nrgy basd numrical mthods givs an opportunity for altrnativ approach basd on dcomposition of a cross sction into th lin finit lmnts btwn nods i and j (Figur 3) with coordinats (y i, z i ), (y j, z j ); lmnt thicknss t ; matrial charactristics (oung s modulus E, shar modulus G) and matrial fficincy RN and RS (du to hatchs, cutouts, lightning hols, tc.) with rspct to normal/shar strsss rspctivly. Th mthodology (Zanic & Prbg 5) is basd on application of th principl of minimum total potntial nrgy with rspct to th paramtrs which dfin th displacmnt filds of th structur. Figur 3. Cut-out from th longitudinal structural mmbr considrd as th transvrs strip (S 1 -S ) with xtrnal loading p and warping filds u. Primary displacmnt fild (following classical bam thory) is dfind by displacmnts and rota-

3 tions of th cross sction as a whol. Scondary displacmnt fild u (x,y,z) u(x,y,z) rprsnts warping (dplanation) of th cross sction. For picwislinar FEM idalization of th cross sction, dividd into n lmnts, with shap functions N in lmnt coordinat systm (x,s), th warping fild rads: u = T s s i u( s) x = = x N u 1 (1) l l u j Elmnt strain and strss filds ε and σ ar obtaind from strain-displacmnt and strss-strain rlations: u = = T 1 ui ε γ xs B u = 1 () s l l u j T σ xs = G γ xs = G B u (3) Total potntial nrgy of th x-long transvrs strip, or sgmnt, of th bam (with sction dividd into n lmnts): Π= = n = x V T σ ε dv 1 Β T 1 u ΒdV T S p( x, s) u( s) ds = V S K u F( s) u( s) ds = u T F (4) whr p(x,s) = xtrnal loading on two cross sctions (S 1 and S ) of th strip. Th minimization of total potntial nrgy lads to classical FEM matrix rlation K D u D = F D (shortnd to Ku = F). Th lmnt stiffnss matrix for th proposd linar displacmnt distribution along th lin lmnt is: G t RS 1 1 K = (5) l 1 1 Normal strss is varying with x and s. In th bam sgmnt of lngth x, at a crtain point of th cross sction, th rsultant strss is givn by: p(x,s) σ(x,s) = σ(x+ x,s) S σ(x,s) S1 = ξc(s) = Q(x) x= Q(x)F(x,s) x I(x) (6) whr ξ c (s) = distanc from th considrd point to th nutral axis. Vctor of th nodal loads for th lmnt of th unsymmtrical cross sction, in bnding about th Z axis, rads: z F ( x) = Q ( x) F ( x) = y E Q ( x) t RN = E I y ( I I ) Z z I yicl l + yicl l + sinα 6 I sinα 3 zicl l + zicl l + sinα 6 sinα 3 Z Z (7) For th cas of bnding about th Z axis th matrix rlations Ku = F with u= Q (x) u, can b convrtd into xprssions K u = F for th warping du to unit load F. For th nod warping u i (x), unit warping u(x) must b multiplid with Q(x). Embdmnt of th prsntd mthodology into th ovrall incrmntal-itrativ procdur for th ultimat strngth assssmnt rsts on th following rational assumption. Each cross sction of th hull girdr has particular ratio of th vrtical bnding momnt and th vrtical shar forc drivd from thir rspctiv distributions for th considrd loading condition. This ratio is approximatd as constant during th incrmntation of th hull girdr curvatur/momnt, nabling th calculation of th rspctiv shar forc within ach incrmnt. This, in a turn, implis that additional itrativ loop should b placd ovr th balancing loop for ach incrmntal stp, sinc th valu of th momnt usd for th calculation of th shar forc should b qual to th on obtaind by th summation of th contributions of th balancd hull modul principal structural mmbrs. Sinc th instantanous hull modul nutral axis vrtical position is changd during th itration and/or incrmntation, th rspctiv quivalnt hull modul momnt of inrtia, as wll as th instantanous load vctor for hull modul vrtical bnding should b updatd accordingly, in ordr to produc valid unitary warping distribution usd for th calculation of th hull modul shar strss distribution. For this purpos, 'fficincy' of th principal structural mmbrs is rprsntd by th ratio of thir oung's modulus and thir instantanous scant modulus, whr instantanous scant modulus is calculatd for ach principal structural mmbr as th ratio btwn th strss and strain corrsponding to th last valid quilibrium stat. Furthrmor, unitary warping distribution calculation mthodology assums highr rsolution discrtization of th cross sctional modl whn compard to th incrmntal-itrativ mthod usd for th ultimat strngth assssmnt. Thrfor, principal structural mmbrs ar assignd with thir rspctiv lin lmnts (with avragd nodal valus of th unitary warping displacmnts), and th valu of th unitary warping displacmnt is calculatd for ach of thm in th following mannr: Stiffnr-plat combinations ar assignd with th fiv lin lmnts in a cas of th T-profil stiffnr with th attachd plating. Two for th both parts of th flang, two for th both parts of th attachd plating and on for th wb. If th stiffnr cross sction is of angl or flat bar typ (bulbs ar rprsntd as quivalnt T-profils), th assignd numbr of lin lmnts is ithr four or thr rspctivly. Sinc th plating lin lmnts ar always charactrizd by th considrably gratr valu of th unitary warping dis-

4 placmnt than th stiffnr lin lmnts, th gratr valu among thos two is chosn as rprsntativ. Transvrsly stiffnd plats ar rprsntd by on lin lmnt, sinc only plating is longitudinally rlvant, and th avrag valu of that lin lmnt's nodal unitary warping displacmnts is accptd as th rprsntativ on. Knuckls ar assignd with two lin lmnts, whil multipl panl intrsctions ar assignd with th numbr of lin lmnts qual to th numbr of intrscting panls. Rprsntativ valu for ach of thos principal structural lmnts is calculatd as th avrag valu of th group. Whn distribution of th unitary warping displacmnts of th hull modul is known, th shar strss distribution can b calculatd using th following xprssion for th shar strss of th considrd principal structural mmbr: p u = Q MAX G (8) l whr = shar strss of considrd principal structural mmbr; Q = instantanous shar forc valu acting on th hull modul; dnots proprtis of th considrd lin lmnt; p dnots plating. In ffort to quantify th influnc of th calculatd shar strss on th strss obtaind by th mans of th valid strss-strain curvs for vry principal structural mmbr, th following lliptic intraction formula (ao t al. 5) is usd, both for comprssion and tnsion: σ M σ L + U = 1 (9) whr = calculatd shar strss of considrd principal structural mmbr; U = ultimat shar strngth of th plating in comprssion/tnsion; σ M = longitudinal strss modifid with th influnc of th shar strss; σ L = longitudinal strss drivd from valid strss-strain curvs. If th considrd principal structural mmbr is in comprssion, thn th ultimat dg shar strngth of th propritary plating is considrd according to th critria givn by (Paik 3): E U = E E E E for <.5 E for.5<. E for >. (1) whr = yild strss of th matrial undr pur shar loading according to von Miss critria: σ = (11) 3 whr σ = spcifid yild strss of th matrial; E = lastic shar buckling strss of th simply supportd plats: π E t E = k (1) 1(1 ν ) b whr k = buckling cofficint for th shar loading, dpndant on th aspct ratio of th considrd plat: k b a b a for for a 1 b a < 1 b σ M is calculatd using (9): (13) C σ M = σ L 1 = σ L K (14) U If th considrd principal structural mmbr is in tnsion, thn th ultimat dg shar strngth of th propritary plating is considrd according to th von Miss critria, which givs U =. In this cas σ M is calculatd according to th following xprssion: T σ M = σ L 1 3 = σ L K σ (15) K C and K T rprsnt shar influnc cofficints of th considrd principal structural mmbr in comprssion or tnsion, rspctivly. According to thir dfinition givn in quations (14) and (15) it can b sn that calculatd shar strss valu can not xcd th considrd valu of th ultimat shar strss, which is thrfor considrd as th limiting valu. In this boundary cas (whn calculatd shar strss is qual to th ultimat shar strngth in comprssion or yild strss in tnsion) th shar influnc cofficints will assum th valu of zro, which will ffctivly xclud th considrd principal structural mmbr from th balancing procdur and annihilat it's contribution to th sctional vrtical bnding momnt. It should also b notd that if th usd ratio of th hull modul vrtical bnding momnt and th shar forc is small (actual limit valu is dpndant of th structural modl layout), a larg valus of th shar forc will b imposd throughout th incrmntation squnc. This might caus a vry larg valus of th shar strss in a considrabl numbr of th hull modul principal structural mmbrs and th balancing procdur might fail to find th quilibrium stat

5 of th sction du to larg longitudinal strss rductions inducd by th influnc of th shar strss..3 Dck fficincy cofficints Important drawback of th basic mthod is that it assums linar strain distribution ovr th hull modul hight. This constrains th considration of th shar lag ffcts and limits th valuation of th hull girdr longitudinal strngth significantly, spcially in th cas of multi-dck ships with complx transvrs sctions, whr som discontinuous longitudinal hull girdr componnts ar imposd with rducd dformation. Hr, linar distribution assumd by th basic mthod, and givn by th quation (16), can not b considrd as accurat. ε =Φ y (16) HM whr ε = strain imposd on considrd principal structural lmnt by hull modul curvatur Φ HM ; y = distanc from th cntroid of th considrd principal structural lmnt to th hull modul ffctiv horizontal nutral axis. An approximat procdur using linar-lastic 3D FEM analysis is usd for prdiction of th fficincy of ach principal structural lmnt in ordr to obtain mor accurat avrag strain as input for th strss-strain curvs. Strss of ach principal structural lmnt can b obtaind from th rapid 3D FEM analysis of th gnric coars msh hull girdr modl (Zanic t al. 9). Th ratio of this strss and th strss calculatd by th mans of th Brnoulli-Eulr bam idalization can b intrprtd as structural fficincy cofficint (Biot t al. 6): k ( σ ) E ( ε ) ( ε FEM FEM FEM = = = (17) ( σ EB) E( ε EB) ( ε EB) ) whr (ε FEM ) = primary strain imposd on considrd principal structural lmnt obtaind by th mans of th 3D FEM analysis; (ε EB ) = strain imposd on considrd principal structural lmnt obtaind according to Brnoulli-Eulr bam quation; E = oung's modul of th considrd principal structural lmnt; (σ FEM ) = primary strss in considrd principal structural lmnt obtaind by th mans of th 3D FEM analysis; (σ EB ) = strss in considrd principal structural lmnt obtaind according to Brnoulli-Eulr bam quation. Strain du to instantanous hull modul curvatur is multiplid by th calculatd structural fficincy cofficint and this product is usd as input into rlvant strss-strain curvs. If contribution of th dcks to th hull girdr strngth is to b valuatd, an avrag structural fficincy or dck fficincy cofficint valid for vry principal structural lmnt of th particular dck can b dfind as an avrag valu of th structural fficincy cofficints of all dck componnts. Sinc th total dck axial forc is qual whthr calculatd as th sum of th forcs on th dck componnts considring thir individual structural fficincy cofficints, or by ovrall approach using th avrag structural fficincy cofficint, th dfinition of th dck fficincy cofficint is givn by: k N i= 1 D = N i= 1 ( A k σ ) ( Aσ ) i i (18) whr N = numbr of primary structural lmnts of th dck; A = ara of th cross sction of th considrd primary structural lmnts of th dck; σ = strss of th considrd structural lmnts of th dck. This is valid sinc strain imposd on ach principal structural lmnt is not contributd by th dirct intraction of th adjacnt lmnts. Du to th dcoupld natur of th principal structural lmnts, th imposd strain is dtrmind solly by th distanc of th considrd lmnt from th horizontal nutral axis. Sinc th sam valu of th k is usd throughout th curvatur incrmntation squnc, implmntation of this modification has som obvious limitations rgarding ovrall accuracy, but rlativly simpl and not so tim consuming natur of th procdur nabls bttr structural rspons assssmnt and rndrs this modification of th basic mthod as convnint for th application within th optimization basd concpt dsign loop. 3 EXAMPLES OF APPLICATION 3.1 Chmical tankr Th work on xampl of application prsntd hrin was originally prformd by th UZ-FMENA within th scop of th FP6 projct IMPROVE (Naar at al. 8), whr longitudinal ultimat strngth valuation was prformd for th hull girdr of th 4 DWT ocan-going chmical tankr (Figur 4) dsignd to carry larg varity of diffrnt cargos in thirty cargo tanks, as on of th thr spcific products considrd by th projct. Th main particulars of th vssl ar as follows (SSN 8): Lngth ovrall: m; Lngth btwn prpndiculars: m; Bam moldd: 3. m; Dpth to main dck: 15. m; Scantling Draught: 11.1 m; Cargo tanks capacity (total): 44 m 3 ; Capacity of Duplx cargo tanks: 6 8 m 3 ; Srvic spd: 15. Knots.

6 Figur 4. Chmical tankr dsignd by th SSN, Szczcin, Poland (SSN 8). Non-linar FEM analysis of th prismatic structural modl of th vssl was prformd (Naar t al. 8) for two xtrm loading scnarios (brifly dscribd in sction 3.1.) and th rsults obtaind wr usd in sction for comparison only. Span of th considrd on bay modl is 356 mm, whil th unsupportd lngths of th transvrsly stiffnd and cross stiffnd panls of th coffrdam ar: 89 mm (for th panls blow th hight of 51 mm) and 178 mm (for th panls abov th hight of 51 mm). On bay modl of longitudinally rlvant structur producd using MAESTRO modlr and usd as input for th longitudinal ultimat strngth assssmnt using OCTO- PUS softwar is givn by th Figur Structural modl Sinc th structur was considrd as prismatic, only th product's midship sction (on-bay) modl was producd and analyzd. Structural layout, main structural dimnsions, as wll as th stiffnr scantlings usd ar givn by th Figur 5. Figur 6. MAESTRO on bay structural modl of th analyzd midship sction. Structural modl of th chmical tankr midship sction discrticisd with th structural lmnts supportd by th IACS incrmntal-itrativ mthod (stiffnr - plat combinations, hard cornrs, transvrsly stiffnd plats) is givn by th Figur (mm) Figur 5. Midship sction drawing of th analyzd structur (Naar t al. 8). Two diffrnt matrials wr usd for structural lmnts, namly: high tnsil stl (AH36) and stainlss stl. Stainlss stl is usd only for th cargo tank plating (innr plating of th doubl sids and doubl bottom, coffrdam plating and strngth dck plating), whil high tnsil stl is usd for th rst of th structur. Rlvant matrial proprtis of th matrials usd ar spcifid by tabl 1. Tabl 1. Proprtis of th structural matrial. Matrial proprty High tnsil stl Stainlss stl oungs modulus (N/mm ) 1 1 Poisson ratio (-).3.3 ild strss (N/mm ) Z (mm) Stiffnr Plat Combinations Hard Cornrs Transvrsly Stiffnd Plats Figur 7. Longitudinal ultimat strngth modl of th analyzd midship sction Loading scnarios Two loading conditions of th vssl wr idntifid and considrd as xtrm ons (Naar t al. 8). In both cass th ralistic loading distributions wr dtrmind using hydrostatic analysis. First considrd loading scnario is th on giving th maximum hull girdr vrtical bnding (at corrsponding fram station), which constituts th usual approach for th longitudinal ultimat strngth assssmnt. Rlvant distributions for this loading scnario ar givn by Figur 8.

7 E+7 Momnt tonn.mx1^ Shar tx1^ Load t/m Buoyancy Wight Nt Load Shar Momnt Long. Pos. m Figur 8. Loading distributions for th first xtrm loading scnario (Naar t al. 8). Th scond xtrm loading scnario corrsponds to th loading condition with th larg valu of shar forc and th hull girdr sction whr th valu of th shar forc to vrtical bnding momnt ratio is rlativly high and might hav an impact on th collaps of th hull girdr. Rlvant distributions for this loading scnario ar givn by Figur 9. Vrtical bnding momnt in knm kkk 8.E+6 6.E+6 4.E+6 HOGG.E+6.E+ -6.E-4-4.E-4 -.E-4.E+.E-4 4.E-4 6.E-4 SAGG -.E+6-4.E+6-6.E+6-8.E+6 Curvatur in 1/m Momnt tonn.mx1^ Shar tx1^ Load t/m Buoyancy Wight Nt Load Shar Momnt Long. Pos. m Figur 9. Loading distributions for th scond xtrm loading scnario (Naar t al. 8) Rsults For th givn particular xampl of application considration of dck fficincy cofficints was disrgardd du to th structural configuration of th analyzd hull girdr (singl-dck structur) and only shar strss influnc was includd into analysis. Sinc th first loading scnario (LC1) is analyzd at th sction with maximum vrtical bnding momnt whr th shar forc is ngligibl, th momnt to curvatur rlationship for sagging and hogging of th hull girdr indicatd by th Figur 1 is obtaind by th mans of th original (unmodifid) IACS incrmntal-itrativ mthod. Th plot corrsponding to scond xtrm loading scnario (LC) is obtaind with includd shar strss influnc, and is also givn in Figur 1. Valus of th ultimat vrtical bnding momnts obtaind by xtndd IACS incrmntal-itrativ mthod (as implmntd in OCTOPUS softwar) for both loading scnarios in sagging and hogging ar givn by Tabl. SAGG - Maximum vrtical bnding momnt SAGG - Significant shar forc HOGG - Maximum vrtical bnding momnt HOGG - Significant shar forc Figur 1. Hull girdr vrtical bnding momnt to curvatur rlationships obtaind for LC1 and LC. Tabl. Rsults obtaind by th xtndd IACS incrmntalitrativ mthod for both loading scnarios (valus in knm). SAGG HOGG LC1 (max. M V ; Q V ) LC (max. Q V ; M V ) Nonlinar FEM analysis prformd showd that th analyzd hull girdr structur will collaps at th sction of th maximum vrtical bnding momnt for both loading scnarios considrd, rndring th comparison of th rsults obtaind by two mthods mployd not valid for th LC (sinc th structural collaps occurrd at th diffrnt hull girdr stations). Rsults obtaind by th NL FEM ar summarizd in th Tabl 3. Gnrally, basd on th rsults obtaind, it can b argud that nglcting of th shar inducd ffcts for hull girdr transvrs sctions with significant shar loading lads to ovrly optimistic and possibly unsaf stimat of th ultimat bnding capacity. Tabl 3. Rsults obtaind by th nonlinar FEM analysis for both loading scnarios considrd (valus in knm). SAGG HOGG LC1 (max. M V ; Q V ) LC (max. M V ; Q V )

8 3. Multi-dck structur Application of th procdur givn in th sction.3 is xmplifid by th analysis of th gnric structur of th simplifid passngr ship, namly th 'ISSC bnchmark' (ISSC 6). Spcification of th structural layout, dimnsions and loading usd by th various authors/contributors involvd in analysis of this rfrnc structur by various propritary mthods (including th nonlinar FEM analysis) is givn by th sam rfrnc. Hr, only rsults of th nonlinar FEM analysis will b usd for comparison purposs. Figur 11 dpicts th procdur of dtrmination of th dck fficincy cofficints for this particular xampl of application (Andric 7). Th rsults prsntd show xcllnt agrmnt with th rfrnc rsults of th nonlinar FEM for th sagging cas, whil for th hogging cas rfrnc rsults ar approachd from th saf sid. VERTICAL BENDING MOMENT (knm) kkkkkk 3.E+6.5E+6.E+6 1.5E+6 1.E+6 5.E+5.E+ -5.E+5-1.E+6-1.5E+6 -.E+6 -.5E+6 Unmodifid IACS mthod Extndd IACS mthod NL FEM HOGG NL FEM SAGG -3.E+6-3.5E-4-3.E-4 -.5E-4 -.E-4-1.5E-4-1.E-4-5.E-5.E+ 5.E-5 1.E-4 1.5E-4.E-4.5E-4 3.E-4 3.5E-4 CURVATURE (1/m) Figur 1. Rsulting momnt to curvatur plots obtaind by both unmodifid and xtndd IACS incrmntal-itrativ mthods suprimposd with th rsults of th nonlinar 3D FEM using th prismatic ISSC bnchmark modl. HEIGHT OF STRUCTURE (mm) k Dtrmination of primary strss distribution along th hight of 3D structur D FEM D Bam Dtrmination of th dck fficincy cofficints to b applid on D structur. Extnsiv validation of th implmntd mthodology for ultimat strngth valuation of multi-dck structurs trough comparison of rsults obtaind by nonlinar FEM and Coupld Bam (CB) mthod (Naar t al. 4) analysis was prformd. Multipl variants (structural opnings, dltion of dcks, rplacmnt of pillars with longitudinal bulkhads, tc.) of th rfrnc ISSC multi-dck structur wr analyzd within th scop of th FP6 projct IM- PROVE (Naar t al. 8). 3.E+6.5E+6 6 M ult =.39 1 knm HOGGING NORMAL STRESS (N/mm) Figur 11. Procdur for dtrmination of th dck fficincy cofficints using th prismatic ISSC bnchmark modl. Th rsults of th hull girdr ultimat strngth analyss prformd by all thr mthods availabl (original IACS incrmntal-itrativ, xtndd IACS incrmntal-itrativ and nonlinar FEM) ar prsntd suprimposd in Figur 1, and ar summarizd in trms of th obtaind ultimat vrtical bnding momnts in Tabl 4. Momnt [knm].e+6 1.5E+6 1.E+6 5.E+5.E CB FEM MS Dflction at midship [mm] FEM panl failur in shar FEM panl failur in comprssion CB panl failur in shar CB panl failur in comprssion MS panl failur in comprssion Tabl 4. Rsults obtaind by th thr mthods availabl for hogging and sagging loading scnarios (valus in knm). Unmodifid IACS Extndd IACS NL 3D FEM HOGG SAGG Figur 13. Momnt to dflction curvs at midship sction for prismatic multi-dck structur with dck opnings in hogging (Naar t al. 8). Vry good agrmnt of th rsults was accomplishd and rconfirmd (Figur 13).

9 Th valu M ult = knm is th ultimat momnt obtaind with NL FEM (Naar t al. 8). For modifid IACS mthod (dnotd MS), th momnt valu is M ult = knm. 4 APPLICATION IN DESIGN Incrmntal natur of th dscribd concpt for th ultimat strngth assssmnt nabls prdiction of th structural collaps dynamics and stablishmnt of th collaps squnc of th principal structural mmbrs of th hull modul. Th knowldg about that squnc of th substructurs (such as dcks) composing a hull girdr can giv a vry usful information rgarding th wakst or critical structural aras. Collaps squnc for th scond application cas is prsntd in th Figur 14 for sagging cas, as an xampl. Gnrally, it can b notd that th rsults obtaind by xtndd IACS incrmntal-itrativ mthod ar in bttr agrmnt with th rfrnc rsults of th nonlinar 3D FEM analysis whn compard to th rsults of th original IACS mthod, nabling safr stimat of th hull girdr ultimat bnding capacity. Furthr rsarch has to b prformd to fully undrstand th limitations of prsntd mthod and how it could b applid and improvd for application to multi-dck structurs. Dtaild invstigation will b prformd to idntify changs of th dck cofficints through dsign cycls and othr possibilitis of additional updats and improvmnts of th prsntd mthod. Ultimat strngth safty masur as a dsign objctiv could b vry usful in multi-critria dcision making sinc it drivs th dsign procss towards th most rational matrial distribution and safr ship dsigns. MOMENT (knm).e+ -5.E+5-1.E+6-1.5E+6 -.E+6 -.5E+6 D3 bottom D3 D4 Unmodifid IACS mthod Extndd IACS mthod D4 Mult=-1.8 E+6 -.5E-4 -.3E-4 -.1E-4-1.9E-4-1.7E-4-1.5E-4-1.3E-4-1.1E-4-9.E-5-7.E-5-5.E-5-3.E-5-1.E-5 D5 LBHD D4-D5 curvatur (1/m) D5 Mult=-1.95 E+6 D6 LBHD D5-D6 D6 D7 D7 LBHD D6-D7 Figur 14. Collaps squnc for th sagging cas. Furthrmor, idntifid collaps scnario can b hlpful in structural optimization with th ultimat vrtical bnding momnt as a dsign attribut. This nabls subsqunt rdsign of th critical componnts rsulting in a globally safr structur, spcially if th mthodology is mployd within th optimization basd concpt dsign loop. 5 CONCLUSIONS Considring th rsults of nonlinar FEM analysis for th first application cas it can b concludd that th structural collaps, of th particular tankr structur considrd, is not influncd by th vrtical shar forc inducd ffcts. This can b gnrally xplaind by sufficint hull girdr wbbing (doublsids) abl to ffctivly sustain imposd shar loading. Consquntly, th structural collaps of th singl-sidd hull girdr structur (i.. bulk carrir) might prov mor pron to shar ffcts considrd. Rsults of th hull girdr ultimat strngth analyss of th scond application cas (multi-dck) show vry good agrmnt with th rsults of th nonlinar FEM analysis, spcially for th sagging cas. ACKNOWLEDGMENTS Thanks ar du to th Croatian Ministry of Scinc, Education and Sport for long-trm support of th national projct Considrabl part of work prsntd in this papr was fundd by th Europan Commission through th EU FP6 STREP projct IMPROVE (Contract No. TST5-CT ). Spcial thanks ar du to Prof. H. Naar who ld MEC tam from Tallinn for xtnsiv propritary work on loading dtrmination, non-linar FEM modling/analysis and th plasant collaborativ work prformd on th IMPROVE projct. REFERENCES Andric, J. 7. Dcision support mthodology for concpt dsign of th ship structurs with hull-suprstructur intraction. PhD dissrtation (in Croatian), Univrsity of Zagrb, Croatia. Biot, M. t al. 6. Collaps Analysis of a Modrn Cruis Ship Hull Girdr. San Francisco: ISOPE 6. Hughs, O.F Ship Structural Dsign - A Rationally- Basd Computr-Aidd Optimization Approach. Jrsy City: Th Socity of Naval Architcts and Marin Enginrs. IACS 6. Common Structural Ruls for Doubl Hull Oil Tankrs. IACS 8. Common Structural Ruls for Bulk Carrirs. ISSC Tchnical Committ III.1 6. Ultimat Strngth. Procdings of th 16 th Intrnational Ship and Offshor Structurs Congrss Vol 1. Southampton. MAESTRO v8.7, Softwar documntation, DRS-C3 Advancd Tchnology Cntr, Stvnsvill, MD, USA. Naar, H. t al. 4. A thory of coupld bams for strngth assssmnt of passngr ships. Marin Structur, Vol 17, Issu 8 : Naar, H. t al. 8. Dlivrabl D3. - Rport on Assssmnt of ultimat strngth at th arly dsign stag. FP6 STREP Projct IMPROVE (Contract No. TST5-CT ).

10 Paik, J.K. 3. Ultimat Limit Stat Dsign of Stl-Platd Structurs. Chichstr: John Wily and Sons Ltd. Smith, C.S Influnc of Local Comprssiv Failur on Ultimat Longitudinal Strngth of a Ship's Hull. Tokyo: PRADS SSN 8. Information on Stability and Longitudinal Strngth: Chmical Tankr 4 DWT, Szczcin: IMPROVE/4-3, Vrsion 9/1/8. ao, T. t al. 4. Influnc of Warping du to Vrtical Shar Forc on Ultimat Hull Girdr Strngth. Lubck- Travmund: 9th Symposium on Practical Dsign of Ships and Othr Floating Structurs. Zanic, V. & Prbg, P. 5. Primary rspons assssmnt mthod for concpt dsign of monotonous thin-walld structurs. Acta Polytchnica Vol 45, No 4/5: Zanic, V. t al. 7. Dcision Support Problm Formulation for Structural Concpt Dsign of Ship Structurs. Procdings of MARSTRUCT 7: Zanic, V. t al. 9. Dsign Environmnt for Structural Dsign: Application to Modrn Multidck Ships. Procdings of IMchE, part M, Journal of Enginring for th Maritim Environmnt, Vol.3, No.M1: 15-1.