Practical Implications of Hydroelasticity in Ship DesignA. Bereznitski

Ship Structures Laboratory, Delft University of Technology, Delft, The NetherlandsM.L. Kaminski

Trials & Monitoring Group, MARIN, Wageningen, The Netherlands

ABSTRACT

The review of research on the hydroelasticity shows that understandingof the subject has been increased but discussions of practicalimplications of hydroelasticity to ship design are rare. The authorsaimed to chanfe this and investigated how allowance for thehydroelasticity affects assessment of ship performance. This has beenillustrated by analyzing a modern cruiseship in the aftship slammingcondition with and without hydro-structural interaction. The scope ofwork included analysis of a simplified hydro-structural model thatreproduces important structural ship properties as whipping and localaftship vibration modes. The hydro-structural interaction has * beenmodeled at the slamming position only. The following ship designcriteria have been considered: passengers discomfort, overall hullgirder strength and local plating strength. The analysis has beendescribed to facilitate the reader with a possibility to carry out a similaranalysis of his design.

KEY WORDS: aftship slamming; hydroelasticity; hydrodynamicloads; fluid-structure interaction; local response; global response,discomfort.

INTRODUCTION

First a clear definition of the term hydroelasticity will be given. Thehydroelasticity can be defined in a very simple way. The hydroelasticityis a fluid-structure interaction (Fig. 1). This means that the systemincludes two parts: the water/air domain and the structure. During theimpact the water pressure acts on the structure and the structuredeforms. At the same time the speed of the structural deformationinfluences the pressure in the water.

If no hydroelasticity is present (Fig. 2) the problem is solved in thetraditional two steps approach. First, the hydrodynamic loads aredefined assuming that the structure penetrating the water is rigid. Then,these loads are applied to the structure to find the structural response.So there is no interaction between the structural response and the waterbehavior.

In Bereznitski (2001a, 2001b) the effect of hydroelasticity wasinvestigated for a 2D-slamming problem. The following conclusionshave been made:

The effect of hydroelasticity was found important for thebottom-slamming problem, when the deadrise angle is closeto zero.

Reduction of structural stiffness increases the effect ofhydroelasticity.

For small deadrise angles in a range of 0-5 degrees theentrapped air between the structure and the water surfacecontributes to the reduction of impact loads significantly.

Faltinsen (1997, 1998) had made similar conclusions earlier.

Water/Air

loads

responseStructure

Figure 1. Hydroelastic interaction.

Water/Airloads

Structure

Figure 2. No hydroelasticity.

In this paper a structure of a typical modern cruise liner is analyzed inorder to investigate the role of hydroelasticity in practical assessment ofship performance. Aftship slamming has been chosen as a case study,because several modem cruise liners are prone to it (Fig. 3). Theslamming impact can initiate ship vibrations with quite highaccelerations along the whole ship. These accelerations affectpassengers' comfort. The whipping part of vibrations produces anadditional global vertical bending moment, which has to be accounted

2002-YU-l A. Bereznitski and M.L. Kaminski Page 1 of 6

for in the strength assessment of the hull girder. In the slamming zonethe local structure can experience too high stresses.

Traditionally hydroelasticity is not taken into account in practicaldesign. The slamming contribution to the global bending moment istypically determined without consideration of the hydroelasticity(Weems et al., 1998, Lundgren et al., 1998, Ramos and Soares, 1998,Nikolaidis and Kaplan, 1992). At the same time if hydroelasticity isconsidered it is done for quite simple cases with a number oflimitations. In this paper the hydroelastic aspects are discussed for asimplified model of the whole ship including both the local and theglobal structural members.

THE MODEL

For the sake of this paper a typical modern cruise liner has beenimitated. The following ship characteristics has been selected:

Length overall - 290 m. Breadth - 32 m. Design draft - 8 m. Displacement - 42 000 t.

\=\

I slamming zone

Figure 3. A typical modern cruise liner.

The model is shown in Fig. 4. Because of the symmetry only port sideis modeled. The model consists of the hull girder, the ship transverseframe in the slamming zone, air domain and water. The frame isattached to the girder at the point where bottom and the side meet. Inother words, the model consists of a 2D-hydroelastic model for thecross-section of the ship involved in the impact and the hull girder. Thenumerical analysis is performed with application of MSC.Dytran code.The 2D-hydroelastic model includes a flexible frame (Fig. 5), water andair domains. A detailed description of a similar model can be found inBereznitski (2001c). The frame is modeled using shell elements. Thewater and air region is represented by solid elements. The hull girder ismodeled as a beam.

The first natural frequency of dry frame and girder are 7.3Hz and0.91Hz, respectively. In the beginning of the simulation the hull girderwith the attached frame falls down freely with initial velocity of 1.5nVs.The gravity is instantly applied to all members of the numerical modelas the analysis starts. In order to prevent the pressure oscillations in thewater different water density is applied depending on the distance formthe free surface. To compensate the gravity force on the structureuniform distributed force is applied to all members of the structuredepending on their weight in a direction opposite to the vector of thegravity force.

As the water penetration begins the frame experiences hydrodynamicloads. The velocity of the frame penetration decreases. This motionchange excites the hull girder. Both the frame and the girder startvibrating. The hydrodynamic force acting on the frame and thentransmitted to the girder is the only force, which changes the globalmotion of the girder. All other forces influencing the global motion of

the girder, like varying buoyancy cased by interaction of the ship withwaves, are disregarded in order to simplify the model. This assumptionis expected to be valid since the simulation covers the time period of 2seconds only. This is enough to determine the local structural responseas well as the response of the girder, while the global ship motion is noteffected much.

frame

Figure 4. The hydro-structural model

Figure 5. Aftship transverse frame at slamming area.

The frame and the hull girder being flexible members of the systemcontribute to the hydroelasticity. In order to investigate theircontribution together and separately several models have beenconsidered (Table 1):

Model 1. A full hydroelastic coupling is performed. Both the hullgirder and the frame are flexible.

Model 2. A traditional 2-step global approach is applied. First, thewater simulation is performed assuming that the hull girderand the frame are rigid. Then, the hydrodynamic force fromthe first step is used to find the response of the girder. Thisis a typical case when the slamming loads are determinednumerically or from experiments and the girder response isfound based with application of these loads.

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Model 3. The third model is the same as the second model but theframe is flexible in the structural analysis, while the girderis assumed to be rigid. Again it would be a typical casewhen the slamming loads are determined numerically orfrom experiments and the local structural response is foundbased with application of this loads.

Model 4. This model considers a hydroelastic interaction assumingthat the girder is rigid and the frame is flexible. This modelwill help to evaluate the contribution of the flexibility of thegirder to this hydroelastic interaction.

Model 5. This model is similar to the fourth model, but thecontribution of the local structure is studied.

Table 1. Description of models.

Model

1

2

3

4

5

Approach

full hydroelasticcoupling

traditional globalapproach

traditional localapproach

local hydroelasticcoupling

global hydroelasticcoupling

Structural membersin water simulation

Structural membersin structural analysis

flexible girderflexible frame

rigid girderrigid frame

rigid girderrigid frame

flexible girderrigid frame

rigid girderflexible frame

rigid girderflexible frame

flexible girderrigid frame

RESULTS

First the results obtained for the fully hydroelastic model (model 1) andthe traditional global model (model 2) are compared. Figure 6 showsthat the allowance for the hydroelastic coupling results in 33% lowermaximum midship vertical bending moment. The maximum totalvertical hydrodynamic force acting on bottom is reduced by 34% (Fig.7). In the same time the maximum absolute vertical accelerationamidships remains the same. The acceleration time trace contains,however, a dominant 7Hz component that corresponds to the firstnatural frequency of aftship frame (Fig. 8). Note that in model 2, the7Hz component cannot be present, as the frame is rigid. However,making the frame flexible in model 2 does not change the result.

After that the results obtained for the fully hydroelastic model (model1) and the traditional local model (model 3) are compared. Figures 9and 10 show that the allowance for hydroelastic coupling reduces themaximum bottom displacement and stress at CLby 30%.

Then the contributions of hull girder and frame flexibility aredetermined by comparing the local and global hydroelastic models(models 4 and 5) with fully hydroelastic model (model 1). First, thecase of rigid girder (model 4) is compared with the fully hydroelasticsolution (model 1) in Figures 11 and 12. It can be seen that the girderflexibility reduces the maximum bottom displacement and stress at CLby about 25%. Then, the model 5 with global hydroelastic coupling(flexible girder but rigid frame) is compared with the fully hydroelasticmodel (model 1). Figure 13 shows that the frame flexibility reduces themaximum midship vertical bending moment by 10%.

Therefore, it can be concluded that the girder flexibility contributesmostly to the reduction of the maximum midship bending moment andbottom stress. However, the frame flexibility contributes significantlyto the overall reduction.

IMPLICATIONS FOR SHIP DESIGN

Implications of the hydroelasticity in ship design will be nowconsidered by evaluation of the following ship design criteria forlongitudinal strength of the hull girder, local plating thickness andpassengers discomfort.

Before that it should be emphasised that the aftship slamming analysedin this paper quantitatively represents an extreme slamming. Theresulting maximum total vertical hydrodynamic force equals (model 1)about 22MN. On the one hand this value, representing more than 5% ofship displacement, equals about 75% of the design wave shear force.On the other hand the maximum average slamming pressure equalsonly 50kPa. In general, slamming design pressures for the present shipwould be one order higher. Therefore, the analysed slamming isextreme, because the whole aftship area (32m x 14m) hits the watersurface simultaneously and not because the impact velocity is high

Further, the authors are aware of the fact that present 2D hydroelastiemodel produces higher pressures than the real 3D case would do. Theauthors are recently investigating a 3D model. It can be expected thatqualitative conclusions made in this paper remain valid whereas theirquantitative content change.

Design criteria for longitudinal strength, which are specified by IACS(International Association of Classification Societies), do not explicitlyallow for additional bending moments produced by hydrodynamicimpacts. In general, the hull load carrying capacity has to be comparedwith the maximum bending moment that is defined by a jointprobability distribution of wave bending moment, still water bendingmoment and hydro-dynamic moments. Such an approach is out ofscope of the present paper and the authors restricted themselves tocomparing the maximum hydrodynamic moment with the design wavebending moment, which equals 3.75GNm for the present ship. Figure 6shows that the maximum bending moment equals about 1.3GNm and0.88GNm without and with hydroelastic coupling, respectively. In bothcases the hydrodynamic bending moment is very significant andconsumes respectively 35% and 23% of the design wave bendingmoment. This certainly is more than IACS implicitly incorporated in itsrules. On the one hand it has to be concluded that a large flat aftshiphas to be avoided in ship design. On the other hand introduction onpodded propellers desires such an aftship. This contradiction has to bebalanced in the design process. This paper gives an evidence thathydroelasticity is an important instrument in reaching that balance. Asstated before the traditional approach (without using hydroelasticcoupling) overestimates bending moments by 33% (Fig. 6).

Design criteria for local plating subjected to lateral pressure, which arespecified in different CS's rules, are based on limiting the maximumpermanent plate deflection. They relate the plate thickness to the squareroot of the slamming pressure. Figure 7 shows that reduction inmaximum average pressure over the bottom plate equals about 34%.This means, providing the plate thickness was determined based onslamming considerations in accordance with the traditional localapproach (model 3), that the allowance for hydroelasticity would resultin about 16% thinner bottom plating (20mm instead of 23mm in thepresent case).

2002-YU-1 A. Bereznitski and M.L. Kaminski Page 3 of 6

Passengers' discomfort is a crucial consideration in design of cruiseships. However, there are no rules available, which explicitly provideacceptance criteria for evaluation of passengers' discomfort when a shipis responding to hydrodynamic impacts. The authors used elements ofISO (1997) norm to assess the discomfort to whole body vibration. Thetime traces of midship accelerations, which are shown in Fig. 8, havebeen analysed. As it can be seen they include several components:0.91Hz (whipping), 7Hz (transverse frame natural frequency) andhigher components above 30Hz. Only the first two components are inthe frequency range that affects human comfort. The MTVV(Maximum Transient Vibration Value) of weighed accelerations equals2.5m/s2 irrespective of hydroelastic coupling. Such acceleration isextremely uncomfortable on board of a cruise ship and a designerwould need to reduce them by factor of five as the acceptableaccelerations are lower than 0.5m/s2. For this paper however a moreimportant conclusion is that the evaluation of discomfort criterion is notaffected by hydroelasticity. The validity of this conclusion has to befurther investigated although the result has clear physical (and notnumerical) background. One of the factors to be investigated is effect ofstructural damping, which has been disregarded, in the present analysis.

CONCLUSIONS

It has been found that applying the hydroelastic approach, instead oftraditional 2-step approach, leads to significant reduction of thehydrodynamic loading involved in aftship slamming. The hull girderflexibility contributes to that reduction twice as much as the frameflexibility. This is caused by the fact that the first period of naturalvibration of the local structure is shorter that the duration of the slampressure pulse (the ratio is about 1:7), whereas for the hull girder thisratio is 1:1.

The following conclusions have been made with respect to thelongitudinal strength, the local strength and the passengers' discomfort:

The traditional approach (without using hydroelasticcoupling) overestimates the global hydrodynamic bendingmoment by 33%. This overestimation is significant since thehydrodynamic moment can correspond to 23% (in case ofhydroelastic model) and 35% (in case of model withouthydroelastic coupling) of the design wave bending moment.

The local structural response (the response of the bottom ofthe aftship transverse frame is considered) is also less severein case of hydroelastic coupling. The reduction ofdisplacements and stresses reaches 30%.

With respect to the passengers' discomfort it has beenconcluded that the evaluation of discomfort criterion in notaffected by hydroelasticity.

REFERENCES

Bereznitski, A, Boon, B, and Postnov, V (2001a). "Hydroelasticformulation in order to achieve more accurate prediction ofhydrodynamic loads", Proceedings of 11th International Offshoreand Polar Engineering Conference, ISOPE-2001, Norway, Vol 4,pp. 337-342.

Bereznitski, A, and Postnov, V (2001b). "Hydroelastic model forbottom slamming", The 8th International symposium on Practical

Design of Ships and Other Floating Structures, PRADS'2001,China, Vol 2, pp. 911-917.

Bereznitski, A (2001c). "3D model for bottom slamming", 20thInternational Conference on Offshore Mechanics and ArcticEngineering, OMAE-2001, Brazil.

Faltinsen, OM (1997). "The effect of hydroelasticity on shipslamming", Phil. Trans. R. Soc. Lond. A(1997) 355, pp. 575-591.

Faltinsen, OM (1998). "Hydroelasticity of high-speed vessels",Hydroelasticity in Marine Technology, Proceedings of the SecondInternational Conference, pp. 1-13.

ISO-2631-1, Mechanical vibration and shock - Evaluation of humanexposure to whole-body vibrations - Part 1 - General requirements,1997.

Lundgren, J, Cheung, MC, and Hutchison, BL, (1998). "Wave-inducedmotions and loads for a tanker. Calculations and model tests", The7th International symposium on Practical Design of Ships and OtherFloating Structures, PRADS'1998, pp. 503-511.

Nikolaidis, E, and Kaplan, P (1992). "Combination of slamming andwave induced motion: a simulation study", International Conferenceon Offshore Mechanics and Arctic Engineering, OMAE-1992, pp.351-358.

Ramos, J, and Soares, CG (1998). "Vibratory response of ship hulls towave impact loads", International Shipbuilding Progress, Vol. 45, N441, pp. 71-87.

Weems, K, Zhang, S, Lin, WM, Bennett, J, and Shin, YS (1998)."Structural dynamic loading due to impact and whipping", The 7thInternational symposium on Practical Design of Ships and OtherFloating Structures, PRADS'1998, pp. 79-85.

1.5

1.0

0.5 -

cE 0.0oE 0O)I -0.5

-1.0

-1.5

hydroelastic (model 1)- no hydroelasticity (model 2)

time [s]

Figure 6. Midship vertical bending moment (comparison of modelsand 2).

2002-YU-1 A. Bereznitski and M.L. Kaminski Page 4 of 6

40

30-

I 20

I 10ra

oo

|-10

00

-20

0.5 1.0

hydroelastic (model 1)no hydroelasticity (model 2)

210

time [s]

Figure 7. Total vertical hydrodynamic force acting on bottom(comparison of models 1 and 2).

time [s]

Figure 9. Bottom displacement at CL (comparison of models 1 and 3).

2.0

1.0

co

I8 -1.0ora

-2.0 --

-3.0 -

hydroelastic (model 1)no hydroelastcity (model 2)

time [s]

200 T

-50

-100 J Jtime [s]

Figure 8. Midship vertical acceleration (comparison of models 1 and 2). F i g u r e 1 0 B o t t o m s t r e s s a t C L ( c o m p a r i s o n of models 1 and 3).

2002- YU-1 A. Bereznitski and M.L. Kaminski Page 5 of 6

Figure 11. Bottom displacement at CL (comparison of models 1 and 4).

200

150

-50

-100

0 0.5 1.0

model 1model 4

time [s]

o

time [s]

Figure 13. Midship vertical bending moment (comparison of modelsand 5).

Figure 12. Bottom stress at CL (comparison of models 1 and 4).

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