Directcalculationofbucklingandfatiguestrength oflargeRo...

CHINESE JOURNAL OF SHIP RESEARCH，VOL.13，NO.4，AUG 2018

Received：2017 - 10 - 26Supported by: Fund of Ministry of Education and Ministry of Finance (Teaching and Technical Letter [2013] No. 35); High-tech

Ship Research Funding Project ([2016] 545)Author(s): HE Lisi, female, born in 1988, master, engineer. Research interest: ship structure reliability and

safety. E-mail: [email protected] Deyu (Corresponding author), male, born in 1963, Ph.D., professor, doctoral supervisor. Re⁃search interest: structural mechanics of ships and ocean engineering, satellite structural mechanics,structural dynamics. E-mail: [email protected]

To cite this article：HE L S, WANG D Y. Direct calculation of buckling and fatigue strength of large Ro-Ro ship section[J/OL].Chinese Journal of Ship Research, 2018, 13(4). http://www.ship-research.com/EN/Y2018/V13/I4/33.

DOI：10.19693/j.issn.1673-3185.01085


Direct calculation of buckling and fatigue strengthof large Ro-Ro ship section

HE Lisi，WANG DeyuSchool of Naval Architecture，Ocean and Civil Engineering，Shanghai Jiao Tong University，

Shanghai 200240，ChinaAbstract：［Objectives］A Roll-on/Roll-off（Ro-Ro） ship is a modern ship type with high technology and highadded value. Due to the specification of its structure，a consensus on buckling and fatigue checking for Ro-Ro shipshas not been reached among the different classification societies of the world.［Methods］On the basis of analyzing thestructural characteristics of Ro-Ro ships，the present study considers the direct calculation of buckling strength，advanced buckling analysis and fatigue analysis of a selected section of a large Ro-Ro ship. The calculations areconducted on the basis of self-developed software from the SJTU KSHIP Project. The pretreatment of buckling andfatigue assessment are established in accordance with the DNV standard "Strength Analysis of Hull Structure ofRoll-on/Roll-off Ships and Car Carriers"，and the related CCS rules.［Results］The calculated buckling strength，advanced buckling strength and fatigue strength of the target cabin meet the requirements of the related rules.［Conclusions］The contents of this paper have a certain reference value for the related structural analysis of Ro-Roships.Key words：Ro-Ro passenger ship；buckling strength；advanced buckling analysis；fatigue strength；FEACLC number: U661.43

0 Introduction

Roll-on/Roll-off (Ro-Ro) ship is a high-techship that is different from traditional three majorship types (bulk carrier, oil tanker, container ship),mainly used to transport finished vehicles and can al⁃so carry a small number of passengers. The Ro-Roship has no transverse bulkhead in usual sense. Thestrength of hull is mainly provided by large pillarsand the height of main deck of hull is less than halfof molded depth. The vehicle deck and superstruc⁃ture are main hull structure. With wider navigationarea of Ro-Ro ship and extension of route, the struc⁃tural strength safety has been paid more and more at⁃tention within service life. In recent years, many Chi⁃nese and foreign scholars have studied the strengthof Ro-Ro ships. Vásquez et al. [1] gave a detailed cal⁃

culation method for total vertical bending momentsof Ro-Ro ship in severe sea conditions. Zhang et al. [2]

used finite element method to calculate the vibrationin roll-on process. Wang et al. [3] conducted a finiteelement strength analysis on 1 400-passengers /2 000-m Ro-Ro ship. Chen [4] analyzed the structur⁃al strength of Ro-Ro ship with different vehicledecks. Wei et al. [5] carried out finite element analysis(FEA) on the ramp structural strength of Ro-Ro ship.

In addition to safety issues of ship structure men⁃tioned above, it is also necessary to consider the ef⁃fects of buckling and fatigue on ship structure. Fortraditional three major ship types, there are clear cal⁃culation methods for buckling and fatigue in relevantspecifications, but for Ro-Ro ships, there is no clearchecking procedure for buckling and fatigue strengthin current specifications. Considering that Ro-Ro

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ship needs to provide checking calculation report ofbuckling and fatigue strength during design and clas⁃sification stage, it is necessary to analyze bucklingand fatigue strength of Ro-Ro ship. At present, thereare few related studies on buckling and fatiguestrength of Ro-Ro ships in China and abroad. Li etal. [6-7] conducted FEA for the crossflexure of pillarsand the transverse strength of cargo hold of Ro-Roship, but did not evaluate the buckling strength oflarge-span deck. Amundin [8] used a Ro-Ro shipwith 230 m long and 13-layers deck as an exampleto analyze the fatigue life of cargo hold bulkhead.Wang et al. [9] conducted a strength assessment on fa⁃tigue strength of vehicle deck of Ro-Ro ship. Xu etal. [10] compared the results of fatigue checking of sev⁃eral major classification societies in the world, andanalyzed the structural fatigue strength of largeRo-Ro ships. In a word, many scholars have nottouched the fatigue of hot spot of the cruciform jointfor the fatigue analysis of Ro-Ro ship. In view of theabove problems, this paper carries out bucklingstrength checking and cruciform hot spot fatigueanalysis of Ro-Ro ship to provide a reference basisfor solving problems of excessive deck layers and dif⁃ficulty of large span of cargo hold area in the struc⁃ture design of Ro-Ro ship.

Considering the characteristics of ship type ofRo-Ro ship, this paper gives the pretreatment meth⁃od of buckling strength checking and fatiguestrength checking. Taking the finite element modelof a large Ro-Ro ship section as an example, usingself-developed software from the SJTU KSHIP Proj⁃ect, the buckling strength, advanced buckling and fa⁃tigue strength of hot spot of the cruciform joint ofRo-Ro ship are analyzed and calculated. The re⁃search results have certain reference value for directcalculation and analysis of buckling and fatiguestrength of large Ro-Ro ships.1 Introduction to basic calculation

methods

1.1 Buckling strength checking

Ro-Ro ship is the main tool for marine transporta⁃tion of finished vehicles. Due to the specification,the structure of Ro-Ro ship is very different fromthat of conventional cargo ship. The main perfor⁃mance is that there are many deck layers, all ofwhich are large-span plate structures, and the num⁃ber of transverse bulkheads is small. At present,large-scale ships generally adopt longitudinal fram⁃

ing system, and the length-width ratio of deck pan⁃els is usually large, so the buckling problem is veryeasy to occur. According to buckling strength re⁃search method of panel in elastic range, the bucklingstrength on each deck of Ro-Ro ship is analyzed.The buckling strength is evaluated with reference tothe specified plate-thickness reduction coefficientand buckling safety factor in Appendix 1 of Chapter8 of Volume 2 of CCS standard Rules for Classifica⁃tion of Sea-going Steel Ships [11].1.1.1 Condition selection

Since buckling analysis needs to be based onstress values under various conditions, the conditionof Ro-Ro ship buckling analysis is selected as thecondition of buckling strength checking. Accordingto the DNV standard Strength Analysis of Hull Struc⁃ture in Roll on/Roll off Ships and Car Carriers [12], thecondition of buckling strength calculated directly byRo-Ro ship is determined as shown in Table 1.

LoadingconditionFull loadBallast

DescriptionEach deck below main deck reaches its maximum

cargo capacityNo vehicle loading status

Table 1 Loading conditions for buckling calculations

The received external load of ship at the time ofbuckling analysis is taken as the external load whenthe buckling strength is checked. According to DNVstandard, the load on hull can be divided into hullgirder load and local load. The hull girder load is ap⁃plied to the independent point according to bendingmoment diagram shown in Fig.1. The local load in⁃cludes three parts: self-weight, seawater load andcargo load. The application of self-weight and cargoload determines the distribution of equipment withreference to general layout or equipment diagram,and the position of center of gravity is adjusted to beconsistent with actual ship. In the following, the spe⁃cific determination methods of seawater load and car⁃go load are introduced respectively.

Fig.1 Bending moment

109876543210-1-2

Bendin

gmom

ent/（k

N·m）

20 50 80 110 140 170 200X / m

SaggingHogging×105

HE L S, et al. Direct calculation of buckling and fatigue strength of large Ro-Ro ship section 29


CHINESE JOURNAL OF SHIP RESEARCH，VOL.13，NO.4，AUG 20181.1.2 Seawater load

The DNV standard gives the calculation equationfor additional wave pressure, which is used to calcu⁃late the seawater load:

pe = 10h0 + p l - 1.2(T - z) （1）where h0 is vertical distance from waterline to calcu⁃lation point when draft is T , m; T is draft, m; z isvertical distance from baseline to calculation point,m; p l is wave additional load and can be calculatedas follows:

p l =ìíî

ï

ï

(ksCw + kf )

(ksCw + kf ) ×(0.8 + 1.5) VL V

L> 1.5（2）

ks = 3CB + 2.5 CB ， stern （3）ks = 2 ，between 0.2L and 0.7L from stern（4）ks = 3CB + 4.0 CB ， bow （5）

kf = min(T f ) （6）where Cw is wave coefficient, and its value is shownin Table 2; V is ship service speed, kn; L is stan⁃dard ship length, m; CB is square coefficient; f isvertical distance from waterline to sheer strake, m,and its value is not more than 0.8Cw .

L

L≤100100<L<300

300≤L≤350L>350

Cw

0.079 2L10.75-[（300-L）/100]3/2

10.7510.75-[（L-350）/100]3/2

Table 2 Wave coefficients

1.1.3 Cargo loadThe cargo load includes dry cargo load, liquid car⁃

go load, and crew and passenger load, wherein theweight of crews and passengers is loaded in the maindistribution area in a nodal force.

The dry load (unit: kN/m2) is vertical downwardpressure of deck and should not be less than the val⁃ue calculated by following equation:

pv = (ρH + m s)(g0 + 0.5av) （7）where ρH is distribution of cargo weight on deck indesign loading condition, t/m2; m s is self-weight ofdeck, t/m2; g0 is gravity acceleration; av is verticalacceleration, which can be calculated as follows:

av =kv g0a0

CB

（8）where kv is coefficient, and kv = 1.3 is coefficientat stern, kv = 0.7 is coefficient between 0.3L and0.6L from stern, kv = 1.5 is coefficient at bow; a0 isacceleration coefficient, calculated as follows:

a0 = 3Cw

L+ CvCv1 （9）

where Cv =L

50, which is not greater than 0.2;

Cv1 =VL

, which is not greater than 0.8.The hydrostatic pressure of liquid cargo to liquid

tank (unit: kN/m2) is calculated bypv = ρ(g0 + 0.5av)h s （10）

where h s is vertical distance from calculation pointto free liquid surface of liquid cargo, m.1.2 Advanced buckling analysis

The advanced buckling is a nonlinear bucklingproblem that is different from general bucklingstrength. In this paper, the advanced buckling check⁃ing is performed after the buckling strength analysisis completed. The middle panel on main deck ofRo-Ro ship is selected, and the basic parametersand reduction coefficients of each panel are set foradvanced buckling checking.

At present, the buckling evaluation method of stiff⁃ened panels considering nonlinear problems has alsobeen introduced into specifications of various classi⁃fication societies, resulting in various methods forcalculating advanced buckling, among which themore mature are buckling calculation method basedon Marguerre nonlinear large disturbance thin platetheory (PULS method) and advanced buckling analy⁃sis method of stiffened panels (EPM method) basedon elastic large deflection theory and rigid-plasticanalysis. In this paper, the advanced buckling ofRo-Ro ship is analyzed by advanced buckling checkmodule in hull structure buckling analysis softwaredeveloped by SJTU KSHIP Project. The module usesPULS method for advanced buckling calculations, asshown in Reference [13], and selects buckling modeof plate in accordance with rules of Chapter 8 of Part1 Rules for Classification of Sea-going Steel Ships.1.3 Fatigue strength assessment of hot

spot of the cruciform joint

Based on S-N curve and Palmgren-Miner linearcumulative damage theory, the fatigue strength analy⁃sis of Ro-Ro ship is carried out according to the rele⁃vant rules of Guidelines for Fatigue Strength of ShipStructures [14]. For Ro-Ro ships, there are many areaswhere fatigue problems may occur. This paper main⁃ly discusses the fatigue strength at cruciform weldedjoints in vehicle deck. On the one hand, the cruci⁃form joint is subjected to higher amplitude of stress

ì

í

î

ïï

ïï

30


and greater probability of fatigue failure. On the oth⁃er hand, the cruciform joint may need to be connect⁃ed to pillar, where fatigue will have a significant ad⁃verse effect on structural safety of the entire ship.Due to the lack of sufficient vehicle load data, theload generated during vehicle loading and unloadingprocess is not considered in calculation process, andthe fatigue strength of welded joint under wave cy⁃clic stress is evaluated.1.3.1 Condition selection

Since loading conditions of Ro-Ro ship are not

specified in rules, this paper refers to Guidelines forFatigue Strength of Ship Structures for selection ofconditions for bulk carriers. Considering the condi⁃tion that Ro-Ro ship has no full load of compart⁃ment, two working conditions of ballast and full loadare selected as calculation conditions, as shown inTable 3. In the table, mH refers to the actual cargoload in cargo hold under uniform loading conditions(All cargo holds are loaded and the loading ratio isthe same, and all ballast tanks are empty) when thedraft is d; vFULL is cargo hold volume, including vol⁃ume enclosed by cargo hatch coaming.

Fatigueassessment

loading conditionsUniform full loadNormal ballast

Draft

Full load draftBallast draft

Correction coefficientof still-water bending

moment CSW

0.4（sagging）0.8（hogging）

Cargo holdcapacity m/t

mH

—

Dry bulk densityρC /（t·m-3）

mH

vFULL

—

Time allocation coefficient α（no compartment loading）

0.500.35

Table 3 Loading conditions for the fatigue calculations

1.3.2 Load conditionsIn fatigue strength analysis, the load conditions

corresponding to equivalent design wave are definedin accordance with Guidelines for Fatigue Strengthof Ship Structures. There are 12 types, and the loadconditions are composed of the following regularwaves:

1) Head sea, a regular wave when vertical wavebending moment reaches its maximum (abbreviatedas "H");

2) Following sea, a regular wave when verticalwave bending moment reaches its maximum (abbrevi⁃ated as "F");

3) Regular wave when roll motion reaches the max⁃imum (abbreviated as "R");

4) Regular wave when hydrodynamic pressure atwater line reaches its maximum (abbreviated as "P") .

The stress values of the corresponding 12 loadingconditions are calculated, and the hot spot stress oftaken nodes is calculated by interpolation method.Then the cumulative damage degree of structuralnodes is obtained according to calculation equationof the fatigue cumulative damage. The specific calcu⁃lation methods are shown in Chapters 3 and 5 ofGuidelines for Fatigue Strength of Ship Structures.

As for specific load calculation, the method usedis the same as method shown in Eqs. (1)-(10). Thestill-water bending moment M sw of hull girder usedfor fatigue analysis shall be calculated as follows:

M sw = C sw M s （11）where C sw is correction coefficient of still-water

bending moment under corresponding loading condi⁃tions, as shown in Table 3; M s is permissible waterbending moment of hogging or sagging of hull girder,kN·m.2 Calculation case

2.1 Calculation model

This paper takes large Ro-Ro ship section as anexample, and uses the method given in the previouschapter to calculate buckling and fatigue. The select⁃ed section is located at 28 800 mm from the bow and21 600 mm to the stern. The longitudinal directionincludes large deck-opening and main pillar, the lat⁃eral direction is the entire width of ship, and the ver⁃tical direction is the range from baseline to upperdeck. The structure of ship section can fully reflectthe specification of Ro-Ro ship. Among them, thecrews of Ro-Ro ship are mainly distributed on No. 9deck, and the passengers are mainly distributed onNo. 7 and No. 8 decks. The dry cargo weight is main⁃ly on No. 3 and No. 5 decks, and liquid cargo weightis mainly on No. 1 deck and shell plate. According torelevant rules of DNV specification, the finite ele⁃ment model of target section is first established, asshown in Fig.2, and the grid information in model isshown in Table 4.2.2 Checking of buckling strength

2.2.1 Boundary conditionsSince there is no clear boundary condition in di⁃

rect calculation of Ro-Ro ship, according to design




conditions at the time of buckling calculation, theboundary condition of overall load specified in Ap⁃pendix 1 of Chapter 8 of Rules for Classification ofSea-going Steel Ships is selected for bucklingstrength checking. Table 5 gives the specific methodfor setting overall load boundary conditions andFig.3 shows the finite element model of ship sectionafter setting boundary conditions. The bending mo⁃ments in Table 5 are loaded according to the data giv⁃en in Fig.1.

2.2.2 Results of buckling calculationIn this paper, the self-developed buckling analy⁃

sis software of hull structure from the SJTU KSHIPProject is used for buckling calculation. Before calcu⁃lation, a series of settings such as cabin identifica⁃tion (structure grouping), parameter setting, bound⁃ary condition definition, condition setting are per⁃formed, and the load according to equation of Sec⁃tion 2.1 is applied to submit the calculated bucklingstrength and synthesize the stress. Then, each deckis selected to be divided into first-class panels ac⁃cording to the position of the strong frame. After that,the secondary panel is divided according to positionof stiffener, and the final panel for calculating thebuckling strength is obtained. Finally, the bucklingsafety factor and the reduction coefficient of eachpanel are set, and buckling analysis contours are sub⁃mitted and calculated. Fig.4 shows buckling calcula⁃tion results.

The values given in contours are buckling factorsfor each deck panel, namely the ratio of compositecritical buckling stress to the calculated actual com⁃pressive stress. According to the rules of Appendix 1of Chapter 8 of Rules for Classification of Sea-going

Fig.2 The FEA model of the selected sectionxy

z

Serialnumber

12345

ContentThe total number of elements in the partThe total number of elements in the part

Number of beam elementsNumber of four-node quadrilateral elementsNumber of three-node triangular elements

Quantity223 777144 21371 560151 434

781

Table 4 Grid information

Table 5 Boundary conditions of the buckling calculations

Position

All longitudinalmembers of frontand rear end facesIndependent pointat front end face

Independent pointat rear end face

Linear displacementconstraint

δx

Related

Fixed

—

δy

Related

Fixed

Fixed

δz

Related

Fixed

Fixed

Angulardisplacementconstraint

θx

—

Fixed

Fixed

θy

—

Bendingmoment

Bendingmoment

θz

—

—

—

Fig.3 The FEA model with the boundary conditionsfor the buckling calculations

z

y x

（a）No. 1 deck

（b）No. 3 deck

（c）No. 5 deck

8.95e+0017.84e+0016.73e+0015.62e+0014.52e+0013.41e+0012.30e+0011.19e+0018.00e-0017.71e-0017.43e-0017.14e-0016.86e-0016.57e-0016.29e-0016.00e-001xy

z


z

xy

z

4.46e+0023.91e+0023.35e+0022.79e+0022.24e+0021.68e+0021.12e+0025.65e+0018.00e-0017.71e-0017.43e-0017.14e-0016.86e-0016.57e-0016.29e-0016.00e-001

32


Steel Ships, the buckling safety factor of each deckis 0.8 and the permissible stress is 305 MPa (Thesteel of each deck of ship is made of AH36 high-strength steel with material coefficient k=0.72). Buck⁃ling factors of all panels in contours are greater thanbuckling safety factor, namely, the stability of panelis qualified. It can be seen from the figure that theplace with smallest buckling factor is located nearthe opening of panel and the compression of panel.2.3 Advanced buckling analysis

After buckling strength checking is completed, itcan be found that No. 1 deck is close to compressedstern, and the panel buckling factor is the smallest inthe whole ship section, namely the closest to buck⁃

ling safety factor, which is prone to buckling. There⁃fore, using this panel as the object, further advancedbuckling analysis is carried out. After setting mainparameters such as panel type, dynamic and staticload coefficient, reduction coefficient, and bucklingstrength of stiffener, the calculation is performed us⁃ing advanced buckling checking module in hullstructural buckling analysis software. The results ob⁃tained are shown in Fig.5 and Fig.6.

Fig.5 Advanced buckling analysis contoursunder the ballast condition

5.49e-0015.26e-0005.04e-0014.81e-0014.59e-0014.36e-0014.14e-0013.91e-0013.69e-0013.46e-0013.24e-0013.01e-0012.79e-0012.57e-0012.34e-0012.12e-001

Fig.6 Advanced buckling analysis contoursunder the full load condition

3.33e-0013.17e-0003.02e-0012.86e-0012.70e-0012.54e-0012.39e-0012.23e-0012.07e-0011.91e-0011.76e-0011.60e-0011.44e-0011.28e-0011.12e-0019.67e-002

The numerical value given in contours is the ratioof the actual buckling utilization factor to permissi⁃ble buckling utilization factor. The decrease in theratio indicates that the buckling utilization rate is de⁃creased, and the possibility of buckling of the gridduring use becomes smaller. It can be seen from fig⁃ure that the buckling utilization rate of this area isonly 0.549, namely, the ability of the area to resistbuckling has room for improvement.2.4 Fatigue strength assessment of hot

spot of the cruciform joint

2.4.1 Boundary conditionsWhen calculating fatigue strength, boundary con⁃

ditions are selected according to Guidelines for Fa⁃tigue Strength of Ship Structures. For overall load,the freedom degrees of node δx , δy , δz of longitudi⁃nal members of front and rear end faces of ship sec⁃tion should be associated with the independentpoints at neutral axis on mid-longitudinal section by

（d）No. 7 deck

（e）No. 8 deck

（f）No. 9 deck

（g）No. 10 deckFig.4 Buckling analysis contours of the decks

under synthetic conditions

xy

z

xy

z

xy

z





z



CHINESE JOURNAL OF SHIP RESEARCH，VOL.13，NO.4，AUG 2018means of MPC, namely applying vertical and horizon⁃tal bending moments at independent points. The loadcombination factors for each load condition areshown in Table 2.5.3 of Chapter 2 of Guidelines forFatigue Strength of Ship Structures. The transverseline displacement, vertical line displacement and an⁃gular displacement around longitudinal axis of inde⁃pendent point in front and rear end faces of ship sec⁃tion are constrained as δy = δz = θx = 0 . The verticalline displacement of independent point in front endface is constrained as δx = 0 . Table 6 shows specificsetting method of overall load boundary conditionsand Fig.7 shows finite element model of ship sectionafter setting overall load boundary conditions.Among them, the bending moment in Table 6 is load⁃ed according to data given in Fig.1.

For local load, the symmetry boundary conditionis applied to front and rear end face of ship section,and longitudinal line displacement of node in endface and angular displacements around two coordi⁃nate axes in end face are constrained asδx = θy = θ z = 0 . A vertical spring unit shall be ar⁃ranged on side plating, inner shell plate, longitudinalbulkhead and intersection of front and rear bulk⁃heads of middle cargo hold. The spring element hasa uniform elastic coefficient. The spring constant iscalculated by following equation:

K = 5GA6lHn

（11）where G is shear modulus of materials. For steel,G =0.792×105 N/mm2. A is shearing area of side plat⁃ing at front and rear bulkheads, inner shell plate orlongitudinal bulkhead plating, mm2. lH is length ofmiddle cargo hold, mm. When load is symmetrical, nis the number of nodes of vertical intersection lineon side plating, inner shell plate or longitudinal bulk⁃head plating, and when load is asymmetric, n is thenumber of nodes of horizontal intersection line onbottom plating and inner floor.

Table 7 shows specific boundary condition methodof local load, and Fig.8 shows the finite element mod⁃el of ship section after setting local load boundarycondition.2.4.2 Fatigue calculation results

In this paper, two cruciform joints are selected forfatigue strength calculation to verify whether fatiguestrength calculation method is suitable for welding fa⁃tigue strength analysis of Ro-Ro ships. When select⁃ed model is located at midship, the junction point ofNo. 3 deck and beam is used as the first fatigue anal⁃ysis hotspot, and the junction of No. 1 deck and cen⁃ter girder is used as the second fatigue analysis hot⁃spot.

Using self-developed software from the SJTUKSHIP Project, after completing welding node meshrefinement, cabin identification, boundary condition

Table 6 Boundary conditions of the global loadingof the fatigue calculations

Position

All longitudinalmembers of frontand rear end facesIndependent pointat front end face

Independent pointat rear end face

Linear displacementconstraint

δx

Related

Fixed

—

δy

Related

Fixed

Fixed

δz

Related

Fixed

Fixed

Angulardisplacementconstraint

θx

—

Fixed

Fixed

θy

—

Bendingmoment

Bendingmoment

θz

—

—

—

Fig.7 The FEA model with the global loading boundaryconditions for the fatigue calculations

xy

z

PositionFront and rear end faces

Interseaction of longitudinal section of front and reartransverse bulkheads with the floor of ship（symmetric load）

Horizontal intersection line of upper deck, bottomplating, inner floor with front and rear transversebulkheads（load asymmetry）Vertical intersection node of side plating, inner shellplate, longitudinal bulkhead plating and front and reartransverse bulkheads

Linear displacement constraintδx

Fixed—

—

—

δy

—

Fixed

Transversespring

—

δz

—

—

—

Vertical spring

Angular displacement constraintθx

—

—

—

—

θy

Fixed—

—

—

θz

Fixed—

—

—

Table 7 Boundary conditions of the local loading of the fatigue calculations

34


definition, and working condition load setting, thecalculation is submitted and the stress is synthe⁃sized. Then, main parameters such as length of filletof hot spot, intersection angle of intersecting plate,and surface where crack is located are input. The netthickness of checkpoint plate is less than 22 mm,and no thickness correction is needed. Since the leftand right sides of ship are symmetrical, only the portside is selected as upwind side. The model is theship section of midship model. Since the bending mo⁃ment of head sea and following sea is the maximumat midship, only the following sea is selected as loadcondition for calculation. Finally, the fatiguestrength checking is performed to obtain total cumu⁃lative damage degree and fatigue life of hot spot.Fig.9 and Fig.10 show two fatigue hot spots, and Ta⁃ble 8 and Table 9 give the fatigue evaluation resultsof hot spot.

It can be seen from Table 8 and Table 9 that totalcumulative damage degree of No. 3 deck is D=0.006 70 + 0.002 06 = 0.008 76, and the fatigue lifeis T = 20/D = 2 283.1 years. Namely, during the ser⁃vice period of 20 years, the node will not experiencefatigue damage. The total cumulative damage degreeof No. 1 deck is D = 5.631 23×10-7, and fatigue lifeis T=20/D=35 516 156.3 years. The fatigue strengthmeets the requirements.

In addition, it can be seen from the table thatstress range of No. 3 deck hotspot is 26.1 MPa, andthat of No. 1 deck hotspot is 3.77 MPa. It can beseen that No. 3 deck is under pressure from load ofcargo (vehicle), and the No. 1 deck is not directlystressed there. In the case of ballast, the pressure onNo. 3 deck is greater than that on No. 1 deck, so thecumulative damage on No. 3 deck is larger than thaton No. 1 deck. Since the stress at deck hotspot is notlarge, the total cumulative damage is also small.3 Conclusions

Based on analysis of specification of Ro-Ro shipand buckling and fatigue checking calculation meth⁃od, the pretreatment setting is carried out with refer⁃ence to the related rules of DNV and CCS, and the fi⁃nite element model of large Ro-Ro ship section is se⁃lected for buckling strength checking, advanced

Fig.8 The FEA model with the local loading boundary conditionsfor the fatigue calculations（load symmetry）

xy

z

Fig.9 Hot spot of the cruciform joint on No.3 deckxy

z

Fig.10 Hot spot of the cruciform joint on No.1 deckxy

z

Table 8 Fatigue evaluation of the hot spot on No.3 deck

Loading condition（leading load

condition）Hot spot stress range

/MPaCorrection coefficient

of plate thicknessCorrection coefficient

of average stressDesign stress range

/MPaCumulative damage

degree

Uniform full load（portalmaximum externalpressure（PP））

0~37.29

1.00

0.70

0~26.10

0.006 70

Normal ballast（maximum bendingmoment（H）in head

seas）0~37.28

1.00

0.70

0~26.10

0.002 06

Loading condition（leading load

condition）Hot spot stress range

/MPaCorrection coefficient

of plate thicknessCorrection coefficient

of average stressDesign stress range

/MPaCumulative damage

degree

Uniform full load（maximum external

pressure（PP））0~3.77

1.00

1.00

0~3.77

4.306 43×10-7

Normal ballast（maximum bendingmoment（H）in head

seas）0~3.77

1.00

1.00

0~3.77

1.324 8×10-7

Table 9 Fatigue evaluation of the hot spot on No.1 deck




大型客滚船舱段屈曲和疲劳强度直接计算

何丽丝，王德禹上海交通大学船舶海洋与建筑工程学院，上海 200240

摘要：［目的目的］客滚船是一种高技术、高附加值的船型。由于其结构的特殊性，目前各国船级社还未形成统一

的有关客滚船屈曲和疲劳强度的计算规范。［方法方法］在充分分析客滚船结构特点的基础上，基于项目组自主研发

的软件，依照挪威船级社（DNV）的客滚船屈服强度直接计算规范，并参考中国船级社（CCS）有关其他船型的相

关规范，对某大型客滚船舱段进行屈曲强度、高级屈曲、热点疲劳 3方面的直接计算，并详细介绍直接计算前处

理设定方法，［结果结果］结果表明，目标舱段的屈曲强度、高级屈曲强度及疲劳强度的直接计算结果全部满足规范

值。［结论结论］研究结果对大型客滚船的相关结构分析具有一定的参考价值。

关键词：客滚船；屈曲强度；高级屈曲分析；疲劳强度；有限元分析

buckling analysis and cruciform hot spot fatiguestrength check.

In buckling calculation, this paper summarizesstandard calculation methods of various loads, andintroduces the setting method of boundary conditionin the actual calculation process.

Based on calculation of buckling, this paper alsoselects the panel with the smallest buckling factor incalculated section, and further calculates advancedbuckling. Based on calculation results, the bucklingutilization of calculated plate is discussed.

In fatigue hotspot checking, this paper discussesin detail the setting method of boundary conditionsof total load and local load, and gives the fatigue hotspot calculation results by taking two typical cruci⁃form positions as an example, which proves that thefatigue life of the calculated hot spot is satisfied to re⁃quirements.

In general, the calculation method used in this pa⁃per is feasible and effective in buckling, advancedbuckling and fatigue check of Ro-Ro ships. In theabsence of a clear specification of buckling and fa⁃tigue calculation of Ro-Ro ship, using this method todirectly calculate buckling and fatigue strength ofRo-Ro ships has certain reference value.References［1］ VÁSQUEZ G，FONSECA N，SOARES C G. Experimen⁃

tal and numerical vertical bending moments of a bulkcarrier and a Roll-on/Roll-off ship in extreme waves［J］. Ocean Engineering，2016，124：404-418.

［2］ ZHANG W B，WAN S M，LIN B，et al. Analysis of theship loader's vibration mode in the roll-on process andthe reinforcement scheme［J］. Advanced Materials Re⁃search，2013，721：536-540.

［3］ WANG Y C，ZHANG X W. Structural design and anal⁃ysis of 1 400-passenger/2 000-meter Ro/Ro passenger

vessel［J］. Ship Engineering，2012，34（5）：13-16（inChinese）.

［4］ CHEN D Y. Study on structure strength of large PCTCunder the different design concepts of decks［D］.Zhoushan：Zhejiang Ocean University，2016（in Chi⁃nese）.

［5］ WEI N，SUN H X. Ramp structure design and FEManalysis for Ropax ship［J］. Journal of Ship Design，2015（Supp 2）：32-35（in Chinese）.

［6］ LI K F，ZHANG Q M. FEM transversal rackingstrength analysis and structure optimization about pil⁃lar in PCTC cargo hold［J］. Journal of Ship Design，2016（1）：54-58（in Chinese）.

［7］ LI K F，ZHOU L. Transverse strength analysis ofRo-Ro passenger vessel with FEM［J］. Journal of ShipDesign，2014（Supp 1）：40-42，62（in Chinese）.

［8］ AMUNDIN E. Modeling of fatigue in Ro-Ro ships［D］.Sweden：KTH Royal Institute of Technology，2012.

［9］ WANG N，XIAO S M，CHEN Z B，et al. Fatiguestrength assessment for vehicle deck of Ro-Ro passen⁃ger ships［J］. Ship & Ocean Engineering，2014，43（2）：

16-18，22（in Chinese）.［10］ XU X D，HUANG X P，CUI W C. A procedure for fa⁃

tigue strength assessment of large Ro/Ro passengership［J］. Shipbuilding of China，2010，51（2）：35-46（in Chinese）.

［11］ China Classification Society. Rules for Classificationof Sea-going Steel Ships［M］. Beijing: China Commu⁃nications Press，2015（in Chinese）.

［12］ DNV. Strength analysis of hull structure in Roll on/Roll off ships and car carriers：31.2-2011［S］. Nor⁃way：DNV，2011.

［13］ HONG Y，QIAN F，GU Y X，et al. The advancedbuckling analysis method in IACS CSR for doublehull oil tankers and a new generation of CCS platepanel buckling assessment system［J］. Shanghai Ship⁃building，2008（4）：32-38（in Chinese）.

［14］ CCS. Guidelines for fatigue strength of ship structure［S］. Shanghai：CCS，2015（in Chinese）.

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