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Structural Design and Response in Collision and Grounding

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Force (N)8.00E+087.00E+086.00E+085.00E+084.00E+083.00E+082.00E+081.00E+08Intersection ModelConventional Model0.00E+000 5 10 15 20 25 30Penetration (m)Figure 33 - 150kdwt Bulk Carrier Strik<strong>in</strong>g Rigid Wall[30]7.2 DAMAGE Bow ModelDAMAGE 5.0 <strong>in</strong>cludes a deformable bow. The <strong>in</strong>itialbow geometry is the same as <strong>in</strong> Damage 4.0, illustrated <strong>in</strong>Figure 16. Bow crush<strong>in</strong>g is modeled us<strong>in</strong>g L-, T- <strong>and</strong> X-form super-elements <strong>in</strong> an ‘<strong>in</strong>tersect<strong>in</strong>g unit method’ [37].Bow <strong>and</strong> side force-deformation calculations arecompleted separately (uncoupled). These calculations areperformed assum<strong>in</strong>g that the bow strikes a rigid wall <strong>and</strong>that the side is struck by a rigid bow. The results are thencompared <strong>in</strong>crementally with deformation applied to theweakest component (bow or side) at each <strong>in</strong>crement.This results <strong>in</strong> deformation <strong>and</strong> energy absorption <strong>in</strong> bothcomponents.7.3 DTU Bow Model [38]Strik<strong>in</strong>g VesselDeformation of the Strik<strong>in</strong>g VesselA’’ A’comparison of the crush<strong>in</strong>g forces for respectively thebow <strong>and</strong> the side, it can be determ<strong>in</strong>ed which vesseldeforms dur<strong>in</strong>g the considered step.Before calculation of the deformation of the twovessels the follow<strong>in</strong>g calculations are carried out:1. The Force-Penetration curve F struck (δ A ) for the struckvessel is calculated, where the strik<strong>in</strong>g vessel is rigid.2. The Force-Penetration curve F strik<strong>in</strong>g (δ B ) for thestrik<strong>in</strong>g vessel is calculated, where the struck vesselis assumed rigid.If the strik<strong>in</strong>g vessel has a bulbous bow, the analysis ofthe crush<strong>in</strong>g forces is separated <strong>in</strong>to a bulb analysis <strong>and</strong>an analysis of the top of bow above the bulb.The force-deformation curve for the struck vessel isdeterm<strong>in</strong>ed by the procedure described <strong>in</strong> Section 5.2.4<strong>and</strong> for the strik<strong>in</strong>g vessel by the procedure described <strong>in</strong>Pedersen et. al [34].A commonly used procedure for tak<strong>in</strong>g <strong>in</strong>to accountthe deformation of the bow is to compare the two forcepenetrationcurves, F struck (δ A ) <strong>and</strong> F strik<strong>in</strong>g (δ B ), at each step.This approach, however, only <strong>in</strong>cludes a very limitedlevel of <strong>in</strong>teraction. In reality, the force-penetration curvefor the side of the struck vessel is a function of thedeformation of the bow, <strong>and</strong> vice versa. This stronger<strong>in</strong>teraction is taken <strong>in</strong>to account by compar<strong>in</strong>g the forcesF A <strong>and</strong> F B , which is determ<strong>in</strong>ed as:A'Struck vessel: FA= FStruck( δ A )(1)A''F = δ + δ(2)Strik<strong>in</strong>g vessel: ( )B F Strik<strong>in</strong>gwhereF A force to crush the struck vessel;F B force to crush the strik<strong>in</strong>g vessel;F struck force from the force-penetration curve for struckvessel, where the strik<strong>in</strong>g vessel is rigid;F strik<strong>in</strong>g force from the force-penetration curve forstrik<strong>in</strong>g vessel, where the struck vessel is rigid;δ A penetration <strong>in</strong>to the struck vessel;δ B deformation of the strik<strong>in</strong>g vessel;A’ cross-sectional area of the strik<strong>in</strong>g vessel takenat a distance of δ A +δ B from bow or bulb tip;A’’ cross-sectional area of the strik<strong>in</strong>g vessel takenat a distance of δ A from bow or bulb tip;See also Figure 34.ABδ Aδ BStruck VesselFigure 34 - Deformation of vessels dur<strong>in</strong>g collision. TheA’s relate to areas not lengthsA more recent DTU model also predicts damage tostruck <strong>and</strong> strik<strong>in</strong>g vessels <strong>in</strong> a collision event [38]. Theanalysis is carried out <strong>in</strong> penetration steps. Only one ofthe <strong>in</strong>volved vessels can be deformed <strong>in</strong> each step. By aThe forces at the struck <strong>and</strong> the strik<strong>in</strong>g vessel F A <strong>and</strong> F Bare compared• If F A > F BDeformation of strik<strong>in</strong>g vessel, δ B is <strong>in</strong>creased• If F B > F ADeformation of struck vessel, δ A is <strong>in</strong>creasedThe reason for correct<strong>in</strong>g the resistance of the struckvessel is that if the bow is deformed, the resistance isapproximately equal to the force at the side times the ratiobetween the areas. For a s<strong>in</strong>gle hull vessel the correction18

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