第4卷第6期船舶力学V ol.4N o.6 2000年12月Journal of Shi p M echanics Dec.2000Finite Element Calculation of Three Dimensional H oldSection Stren g th of30000DWT Multi p ur p ose Shi pCHEN Qin g-q ian g,J IANG Nan,ZHU Shen g-chan g(China Shi p S cientific Research Center,Shan g hai200011,China)HU Jin-tao,WU Bin(Shan g hai Shi p Desi g n&Research Institute,Shan g hai200032,China)Abstract:In this p a p er,w e calculate and anal y ze the stren g th of the hold fram e of a30000DWT multi p ur2 p ose shi p b y3D F.E.M.Accordin g to direct calculation of G L Rules,the influence of lon g itudinal bendin g m om ents must be taken into account to g ether w ith the local loads of hull sections such as h y drod y nam ic p res2 sure,car g o load and g ravit y load.T he hull structure stresses and distortions are calculated under ballast,full and derrick o p eratin g load conditions.T he calculations indicate that the shi p stren g th can be ensured suffi2 cientl y accordin g to direct calculation of G L Rules.K e y w ords:finite element;hold section;srten g th;multi p ur p ose shi p;G L R ules1I ntroduction30000DWT multi p ur p ose shi p belon g s to a shi p for which there is an extensive dem and in the international m arket.T his t y p e of shi p either servers as a bulk carrier or as a containershi p.In com p arison w ith other t y p es of shi p,the hull structure of this shi p has its own features,such as lar g e deck o p enin g s,central lon g itudinal bulkhead at m id shi p.F or the structure features of this multi2 p ur p ose shi p,three hold sections are selected from N o.3to N o.5holds and anal y sis of three-dim ension hold section stren g th in the t y p ical o p eratin g m odes is carried out.B y usin g structural finite elem ent calculation and anal y sis of three-dim ensional hold section,the stress level and the stress distribution m a y be obtained and the hold section stren g th m a y be evaluated for the m ain hull of30000DWT multi p ur p ose shi p,so that the desi g ners m a y distribute the m aterials m ore reasonabl y and take necessar y m easures a g ainst the hi g h stress p ositions to av oid dam a g es to the hull structure in navi g ation.H old section anal y sis is an effective w a y in the direct calculation of the hull structure.T w o t y p ical load conditions,this is,full y-loaded de p arture and ballast arrival are selected to check the stren g th of three-dim ensional hold section in the hull structure.T he stren g th calculation and anal y sis are p erform ed for the calculated hold sections in the o p eratin g m odes when these hold sections are sub j ected to local load onl y and the concurrent action of the g irder bendin g m om ent and local load.2Princi p al p articulars of the hull and featuresT he30000DWT multi p ur p ose shi p is of double-bottom and double-shell structure and con-Received:2000-06-15tains five car g o holds for the containers.E ach hold m a y be divided into left and ri g ht half hold and either bulk car g oes or containers u p to six store y s m a y be loaded in the car g o hold.As for finite elem ent stren g th calculation of three hold sections ,three hold sections betw een N o.41and N o.145hold sections are selected to p erform calculation and anal y sis.T he p rinci p al p articulars of this shi p hull is g iven below:Overall len g th L =192.90mLen g th betw een p er p endicularsL p p =182.0m M olded breadthB =27.8m M olded de p thD =15.5m Calculated draftT =11.2m S p eedV =20.2kn Dis p lacem entΔ=42233.9t Block coefficient C b=0.723O p eratin g modes for anal y sis3.1Load conditionsExternal loads de p end on the fact that the hull is sub j ected to m ore heavil y t y p ical load condi 2tions.Basicall y ,this shi p is sub j ected to tw o load conditions ,i.e.full draft de p arture condition ,ballast de p arture condition.In the full draft de p arture condition ,three m iddle holds are loaded w ith car g oes ,fore and aft holds are em p t y holds ,ballast com p artm ent is in li g ht condition and the shi p is in sa gg in g condition ;in the ballast de p arture condition ,the shi p is loaded w ith no car g o ,ballast com p artm ent is full y loaded w ith ballast w ater and the shi p is in ho gg in g condition.T herefore ,these tw o load conditions are selected to be the load o p eratin g m odes ,servin g as the o p eratin g m odes for calculation under the action of the sa gg in g (ho gg in g )w ave bendin g m om ent to check the hold sec 2tion stren g th of the hull under the concurrent action of the g irder bendin g m om ent and the local load.In accordance w ith G L rules and Re g ulations ,it is necessar y to check the stren g th of hold section of the hull in tw o o p eratin g m odes in which the hold section is sub j ected to the load onl y w ithout reference to the action of the g irder bendin g m om ent.Because the shi p is re q uired w ith derricks at tw o transverse bulkheads ,the force and the bendin g m om ent p roduced b y them are g reater and w ill exert som e influence on the local p ositions in the hull ,hence ,in the loadin g o p er 2atin g m ode ,hold section stren g th of the hull is calculated a g ain to take into account the influence of the derricks.3.2O p eratin g modes for anal y sis(1)T he first o p eratin g m ode :full y -loaded de p arture and concurrent action of sa gg in g bendin g m om ent and hold section load.(2)T he second o p eratin g m ode :full y -loaded de p arture and the action of hold section load.(3)T he third o p eratin g m ode :full y -loaded de p arture and the action of hold section load and derrick load.52船舶力学第4卷第6期第6期Chen Q in gq ian g et al:F inite E lem ent Calculation (53)(4)T he fourth o p eratin g m ode:ballast de p arture and concurrent action of ho gg in g bendin g m om ent and hold section load.(5)T he fifth o p eratin g m ode:ballast de p arture and the action of hold section load.4Three dimensional finite element structure model4.1Determination of coordinate s y stemT he coordinate s y stem determ ined in this com p utational m odel is selected on the central lon g i2 tudinal section,the ori g in of coordinates is taken at the intersection p oint of the aft p er p endicular and the base line and on the basis of the ri g ht-handed coordinate s y stem law,X ax is(lon g itudinal) is in the bow direction,Yax is(transverse)is in the p ort direction of the shi p and Z ax is(vertical) is in the u p w ard direction to the deck.4.2Finite element model and boundar y constraintOn the hold sections of30000DWT multi p ur p ose shi p,all structures such as decks,bulkheads, bottoms and sides are m odeled and the finite elem ent m odel m ainl y consists of p late elem ents and beam elem ents.T hree inte g ral holds in N o.41to N o.145car g o hold area are selected in the cal2 culation of the finite elem ent m odel and the ri g id bulkheads are set at tw o ends of the transverse bulkhead for the boundar y constraints.In the calculation of local stren g th,the constraints are set at the bottoms and on the sides of N o.69and N o.sections and the sim p l y su pp orted ends are set at the ri g id bulkheads of tw o ends of the m odel.In the calculation of takin g into account the action of the g irder bendin g m om ent,the ri g id constraint is m ade at the ri g id bulkhead of the ri g ht end(at the p lace where X value is g reater) of the m odel and the bendin g m om ent and the shearin g force m a y be exerted on the ri g id bulkhead of the left end(at the p lace where X value is less)of the m odel and a certain node at the left to the central p lace of the cross-section of the hull beam.T he ri g id bulkhead consists of p late elem ents and beam elem ents and bendin g and torsion m om ent of inertia of the beam elem ent in tw o directions m a y take the sam e order of m a g nitude as that of the m om ent of inertia of the hull beam.T w o m odel ends and ri g id bulkheads onl y act as the boundar y conditions and no stren g th evaluation is m ade in the calculation.F i g.1shows the discrete dia g ram of three-dim ensional finite elem ent m odel for three-hold section structure of the hull.4.3T yp es of finite element model4.3.1Quadrilateral and trian g le p late elem entsT hese elem ents are g enerall y used in deck(p latform)p late,inner bottom p late,outer bottom shell p late,side p late,bulkhead p late,etc of the discrete hull.In addition,the discretization of bot2 tom keel and the w ebs of structural com p onents such as floor p late,side fram e m a y be realized in the form of the p late elem ent.4.3.2Beam elem entsT hese elem ents are norm all y used in the transverse beams on the sides,the strin g ers and the fram es for su pp ortin g the containers,etc.F i g .1T hree -dim ensional finite elem ent m odel for three -hold section structure of the hull4.3.3Bar elem entsT hese elem ents are used to set the boundar y constraint conditions in p erform in g the local stren g th calculation.4.4Sizes of finite element modelT here are m ore than 16000m odel nodes for calculatin g the three -dim ensional finite elem ent structure of the whole shi p hull.T he elem ents are divided into 22batches totalin g 31993elem ents and am on g them there are 14batches of p late elem ents am ountin g to 17745which are the p rim ar y elem ents for the m odel calculation ,7batches of beam elem ents am ountin g to 14240,a batch of bar elem ents am ountin g to 8.T he e q uations used to calculate the finite elem ent m odel of the structure total 65952(F i g .2shows the finite elem ent m odel of t y p ical cross -section structure of the m ain hull ).F i g .2T he finite elem ent m odel of t y p ical cross -section structure of the m ain hull4.5Boundar y force calculation in hold section anal y sisIn accordance w ith the direct calculation of G L Rules and Re g ulations ,the calculation and anal y sis m ethod for three -dim ensional finite elem ent of the hold section are re q uired to check the stren g th of hull hold section under the su p er p osition influence of the g eneral hull stren g th.It w ill be54船舶力学第4卷第6期necessar y to take into account the bendin g m om ent and the shearin g force for the g eneral hull stren g th,that is,in the direct calculation and anal y sis of finite elem ent m odel of three hold sections, the central p art of the m iddle hold is re q uired to have the stated bendin g m om ent value for the g eneral hull stren g th and the bulkhead p lace is re q uired to re g ulate the calculation of the hull boundar y force to determ ine the shearin g force value and the bendin g m om ent value new l y exerted on the boundar y.All actin g forces on the three-dim ensional finite elem ent m odel of the hold section, includin g the load force of the container car g oes,static w ave p ressure,d y nam ic p ressure,etc are g iven in the form of the concentrated nodal forces.T he si g n of the nodal forces is the sam e as the g lobal coordinate s y stem OXY Z.T he balance relation of all forces and m om ents actin g on the hold section m a y be ado p ted to determ ine the shearin g force and the bendin g m om ent added to the left end of the ri g id bulkhead.5Calculation of hull stren g th5.1Checkin g standardT he stresses obtained from the calculation are g enerall y resolved into the norm al stresses in X and Ydirections and the shearin g stress in XYdirection.T he stresses described in this re p ort refer to the nom inal stresses unless other noted and the nom inal stress is derived b y the follow in g ex p res2 sion:σ0=σ2x+σ2y-σxσy+3τ2x ywhereσ0:the resultant stress in the elem ent p lace;σx:the nom inal stress in the elem ent p lace and in X direction;σy:the nom inal stress in the elem ent p lace and in Y direction;τx y:the shearin g stress in the elem ent p lace and in XY direction.Stress discrim ination is usuall y m ade b y takin g the stress center of the q uadrilateral elem ent or trian g le elem ent as the standard,therefore,the stresses listed in the dia g rams are the stresses actin g on the elem ent center.Accordin g to the direct calculation of G L Rules and Re g ulations,(a)In consideration of the cou p lin g action of hull g irder bendin g m om ent,the stress in each structure com p onent of the hull hold section should not be g reater than the follow in g value:σ0= 230/k MPa.where k is a coefficient for comm on steel k=1.0,σ0=230MPa and for hi g h stren g th steel AH36 and DH36k=0.72.(b)T he stress in each structural com p onent of the hull hold section onl y sub j ected to the local load of the hull hold section should not be g reater than the follow in g value:σ1,σq=150/k MPaτ=100/k MPawhereσ1is the lon g itudinal bendin g stress of each structural com p onent sub j ected to the local load,第6期Chen Q in gq ian g et al:F inite E lem ent Calculation (55)σq is the transverse bendin g stress of each structural com p onent sub j ected to the local load andτisthe shearin g stress of each structural com p onent sub j ected to the local load.F or comm on steelσ1,σq=150MPa,τ=100MPa,and for hi g h stren g th steel AH36and Dh36σ1,σq=208.3/k MPa,τ=138.8/k MPa.(c)Checkin g u p should be based on the p erm issible stress(a)for anal y zin g the first and the fourth o p eratin g m ode and checkin g u p should be based on the p erm issible stress(b)for anal y zin g the second and the fifth o p eratin g m ode.5.2The first o p eratin g mode:full y-loaded de p arture and concurrent action of sa gg in gbendin g moment and hold section loadT his o p eratin g m ode is the o p eratin g m ode for shi p o p eration and a t y p ical o p eratin g m ode.Because the resultant bendin g m om ent is a g reater value,the g eneral stress level is g reater.It is reco g nized b y calculatin g that the stress distribution is less influenced b y the car g o w ei g ht load and the h y drod y nam ic p ressure of the hull,but influenced p rinci p all y b y the g irder bendin g m om ent.In this o p eratin g m ode,the deck stress is m ore uniform l y distributed and the stress distribution is less influenced b y the car g o w ei g ht load and h y drod y nam ic p ressure of the hull,but p rinci p all y in2 fluenced b y the g irder bendin g m om ent.Because of the g reater value of the sa gg in g bendin g m o2 m ent,the deck stress value is g reater at m idshi p,that is,near N o.119section and decreases g rad2 uall y in the direction of the stern p osition.S ince the m ain deck is far from the neutral ax is,its stress value is g reater.T he m ain deck of N o.3hold shows the m ax imum stress value due to bein g close to the m idshi p p osition and its stress value ran g es from206.52MPa to258.21MPa.T he stress value of the m ain deck of N o.4hold is relativel y less and its stress ran g es from137.68MPa to206.52MPa, whereas the stress value of the m ain deck of N o.5hold is much less.T he second deck falls a bit,and the stress at the p latform p osition below is much less than that of the m ain deck.In this o p eratin g m ode,the m ax imum stress of the hull hold section is at the to p p lace of the central lon g itudinal bulkhead,the m ax imum stress at this p lace is calculated to be262.13MPa which occurs at N o.121section.T he stress at the lon g itudinal bulkhead and the side p late shows bar-sha p ed distribution,the stress in shi p len g th direction decreases in the direction from m idshi p p lace to the stern,the stress in shi p hei g ht direction is g reater near the m ain deck and the bottom,the stress at the m iddle p lace is relativel y less and the stress at the m ain deck is g reater than that at the bottom.T he stress value of side p late of N o.3hold ran g es from198.48MPa to212.60MPa near the m ain deck p lace.T he stress value at the to p of the side lon g itudinal bulkhead of N o.3hold ran g es from225.35MPa to260.07MPa.F or the stress distribution of inner and outer bottom p lates of the hull,in this o p eratin g m ode, since N o.5hold is not loaded w ith car g oes whereas N o.3and N o.4holds are loaded w ith car g oes, the stress value is clearl y g reater than that of N o.5hold.T he stress decreases g raduall y in shi p breadth direction from the center to both sides.T he m ax imum stress of the inner bottom p late of N o.3hold is123.66MPa and occurs at N o.119section,T he m ax imum stress of the outer bottom p late is164.06MPa and occurs at N o.119section.T he stress in the bottom keel ran g es from 137.59MPa to158.77MPa.T he stress at the p i p in g p assa g ew a y of the bottom floor of N o.3hold is 56船舶力学第4卷第6期第6期Chen Q in gq ian g et al:F inite E lem ent Calculation (57)g reater than that at the other p laces.Because there ex ists car g o load on the p i p in g p assa g ew a y,to ascertain the variation of the local stress at the p i p in g p assa g ew a y,p lane finite elem ent anal y sis is m ade at N o.119section of the m ax imum stress w ith the p i p in g p assa g ew a y subdivided finel y.T he anal y ses indicate that the stress at the m id s p an of the p i p in g p assa g ew a y is113.27MPa.As the transverse m ember of hull section is less influenced b y the g irder bendin g m om ent and is chiefl y influenced b y the h y dro-d y nam ic p ressure,the stress level in g enerall y less.5.3The second o p eratin g mode:full y-loaded de p arture and the action of hold section loadIt is reco g nized b y calculatin g that the stress distribution is p rinci p all y influenced b y the car g o w ei g ht load and the h y drod y nam ic p ressure of the hull.S ince the influence of the hull g irder bendin g m om ent is not taken into account,the stress level of each p rim ar y m ember of the hull hold section is less.Because N o.5hold is sub j ected to h y drod y nam ic p ressure onl y and no car g o load,the stress is relativel y g reater in com p arison w ith these of the other tw o holds.In this o p eratin g m ode,the deck stress distribution is less influenced b y the car g o w ei g ht load and the h y drod y nam ic p ressure of the hull and the stress in N o.5hold is g reater.T he g reater stress of the lon g itudinal bulkhead occurs at the p lace near the hull bottom and b y discardin g the influence of the boundar y constraint,the m ax imum stress of the central lon g itudinal bulkhead is35.70MPa at N o.65section near the bottom,whereas the m ax imum stress of the side bulkhead is37.66MPa at N o.65section and at the hei g ht of4096mm.T he stress value of the side p late in this area is27.95MPa.F or the stress distribution of inner and outer bottom p lates of the hull,in this o p eratin g m ode, since N o.5hold is not loaded w ith car g oes and onl y sub j ected to h y drod y nam ic p ressure,therefore, the m ax imum stress occurs at the m iddle p art of N o.5hold.T he m ax imum stress of the inner bottom p late of N o.5hold is19.71MPa and occurs at the central lon g itudinal p lace of N o.52section.T he m ax imum stress of the outer bottom p late is31.38MPa and occurs at N o.54section at a distance 3230mm from the central lon g itudinal p lace.T he bottom keel is m ore influenced b y car g o load.T he stress at the p i p in g p assa g ew a y p lace of N o.3hold of bottom floor is g reater than that at the other p laces.5.4The third o p eratin g mode:full y-loaded de p arture and the action of hold sectionload and derrick loadT he third o p eratin g m ode adds the load action of the derricks betw een N o.4and N o.5holds and betw een N o.3and N o.4holds to the o p eratin g m ode for the calculation in full y-loaded de p arture and the action of the hold section load.Because g reater load of the derricks exerts influence on the local p lace of the hull,in p articular on the transverse bulkhead p lace,therefore,stren g th anal y sis of the hull structure influenced b y the derricks is m ade on the basis of the second o p eratin g m ode.In this o p eratin g m ode,derrick force and bendin g m om ent act p rinci p all y on the su pp ortin g bulkheads below the derricks and exert som e influence on the m ain deck and the second deck throu g h the j uncture of the su pp ortin g bulkhead and the deck.It is reco g nized b y calculatin g that under the action of the derrick load,the stress value at the j uncture of the m ain deck and the su pp ortin g bulkhead of the derrick is18.83MPa.T he stress of the second deck is g reater than that58船舶力学第4卷第6期of the m ain deck because the second deck carries the load transm itted from the su pp ortin g bulkhead of the derricks betw een N o.62and N o.66areas and the stress value ran g es from30.01MPa to 36.00MPa.T he central lon g itudinal bulkhead betw een tw o transverse bulkheads of the hold also carries derrick load,hence,the stress of the central lon g itudinal bulkhead betw een N o.62and N o.66 areas and betw een N o.103and N o.107areas is g reater than that of the other p laces,the stress of the form er p lace is u p to107.97MPa and the stress of the latter p lace is86.30MPa.T he transverse bulkheads of N o.103and N o.107areas also su pp ort the derricks and the stress value of the trans2 verse bulkhead at the derrick p lace ran g es from90.02MPa to96.59MPa.5.5The fourth o p eratin g mode:ballast de p arture and concurrent action of ho gg in gbendin g moment and hold section loadIn this o p eratin g m ode,the stress of the m ain deck of N o.3hold is m ore uniform ed distributed and the stress value ran g es from245.06MPa to282.82MPa.T he m ax imum stress of the hull hold section occurs at the to p of the central lon g itudinal bulkhead.T he m ax imum stress at the m iddle p art of N o.3is290.17MPa and occurs at N o.125section.T he stress attains to the m ax imum value at the to p of the side lon g itudinal bulkhead of N o.140section and its stress value is289.88MPa.T he m ax imum stress of the side p late near the m ain deck is255.07MPa at N o.125section.T he stress of the lon g itudinal bulkhead and the side p late shows the barsha p ed distribution sim ilar to that in the first o p eratin g m ode.In this o p eratin g m ode,the stress distribution of inner and outer bottom p late of the hull is sim ilar to that in the first o p eratin g m ode.T he m ax imum stress of inner bottom p late of N o.3hold is 118.66MPa and occurs at N o.119section.T he m ax imum stress of outer bottom p late of N o.3hold is 173.77MPa and also occurs at N o.119section.T he stress of the bottom keel ran g es from 139.16MPa to173.97MPa.5.6The fifth o p eratin g mode:ballast de p arture and the action of hold section loadIn this o p eratin g m ode,the deck stress distribution is less influenced locall y b y the h y drod y2 nam ic p ressure of the hull.T he stress of the hold near the bulkhead is relativel y g reater.T he m ax i2 mum stress of N o.4hold near the bulkhead is37.76MPa and occurs at N o.101section.T he m ax imum stress of the side bulkhead is50.80MPa and occurs at the hei g ht of4096mm of N o.61 section.T he m ax imum stress of the side p late is46.56MPa and occurs at the neutral ax is of N o.66 section.In this o p eratin g m ode,the stress distribution of inner bottom p late of the hull is sub j ected to ballast w ater,the outer bottom p late is under the action of ballast w ater and h y drod y nam ic p ressure w ithout considerin g the influence of the boundar y condition.T he m ax imum stress of the inner bottom p late occurs at the m iddle p art of N o.5hold,the m ax imum stress is29.22MPa and occurs at N o.52 section at a distance3230mm from the central lon g itudinal p lace.6Conclusions(1)Stress level and stress distribution of each p rim ar y m ember of hull hold section are derived第6期Chen Q in gq ian g et al:F inite E lem ent Calculation (59)from calculatin g and anal y zin g the stren g th of three hold section finite elem ent on30000DWT multi p ur p ose shi p in five o p eratin g m odes.T he calculations indicate that the shi p stren g th m a y be ensured sufficientl y.(2)Am on g the five o p eratin g m odes for the calculation,the first and the fourth o p eratin g m odes are the ones under the cou p lin g action of the g irder stren g th and the local stren g th,where the fourth o p eratin g m ode,that is,ballast de p arture and the action of ho gg in g w ave bendin g m om ent is the o p eratin g m ode in which the hull is under the m ax imum action of the vertical bendin g m om ent and the total stress level is g reater than that in the first o p eratin g m ode.B y summ in g u p these tw o o p2 eratin g m odes for calculatin g and anal y zin g the hull hold section,the m ax imum nom inal stress level of the deck is obtained to be282.82MPa,the m ax imum nom inal stress level of the central lon g itu2 dinal bulkhead is290.17MPa,the m ax imum nom inal stress level of the side lon g itudinal bulkhead is 289.88MPa and the m ax imum nom inal stress level of the side p late of the hull is255.07MPa.H i g h stren g th steels of AH36and DH36are used for the hull at the hi g hl y stressed p laces of these m embers,the y ield stren g th of the m aterial is353.03MPa,the p erm issible stress is319.44MPa, therefore,the stren g th at the above p laces m a y be ensured.At the bottom,the m ax imum nom inal stress level of the inner bottom p late is118.66MPa,the m ax imum nom inal stress level of the outer bottom p late is173.77MPa,the m ax imum nom inal stress level of the bottom keel is173.97MPa,the comm on steel w ith y ield stren g th235MPa is em p lo y ed at these p laces,its p erm issible stress is 225.55MPa,the stress value at these p laces is also less than the p erm issible stress,so the structural stren g th of the hold section com p lies w ith the stren g th re q uirem ents.(3)T he second and the fifth o p eratin g m odes for the calculation are the o p eratin g m odes in which the hull hold section is sub j ected to the local load and are used to anal y ze the local stren g th of each p rim ar y m ember of hull hold section and the calculations indicate that the stren g th of these m embers is less than the p erm issible standard in which the p erm issible stress of the m aterial w ith comm on stren g th is140.10MPa.(4)T he third o p eratin g m ode for the calculation is the o p eratin g m ode in which the influence of the derrick on the local stren g th of hull structure is anal y zed.T he calculation results indicate that when the derrick is in o p eration,the derrick load w ill increase the structural stress at the su pp ortin g p lace below the derrick but onl y a little and the stren g th of thses m embers com p lies w ith the stren g th re q uirem ents.R eference[1]G L Rules for C lassification and C onstruction[S].30000吨多用途船船体舱段强度的有限元计算分析陈庆强,江南,朱胜昌(中国船舶科学研究中心,上海200011)胡劲涛,吴斌(上海船舶研究院设计院,上海200032)摘要:本文对30000吨多用途船船体舱段强度进行了有限元直接计算分析。
