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Ocean Engineering 31 (2004) 901929

www.elsevier.com/locate/oceaneng

Finite element investigation on the staticresponse of a composite catamaran under

slamming loads

Roberto Ojedaa

, B. Gangadhara Prustyb,

, Marcos Salasa

a Institute of Naval and Maritime Sciences, University Austral of Chile, Casilla 567, Valdivia, Chileb Department of Maritime Engineering, Australian Maritime College, P.O. Box: 986,

Launceston, TAS 7250, Australia

Received 7 April 2003; accepted 13 August 2003

Abstract

This paper presents the structural response of a fast and relatively small, composite mate-

rials catamaran to slamming loads. Finite element method is used to provide valuable infor-mation in order to optimise the design of the catamaran. The analysis is carried out usingANSYS 6.0 finite element software.

The response of the structure to quasi-static slamming loads according to Det NorskeVeritas High Speed and Light Craft crest landing and hollow landing rules [DNV, 1999] hasbeen implemented and studied. An optimisation study for the structural response is carriedout by changing the ply orientation in the vessel and suitable recommendations are made.# 2003 Elsevier Ltd. All rights reserved.

Keywords: Finite element analysis; Fibre-reinforced composite; Ships structures; High-speed crafts;Slamming loads

1. Introduction

The demand for high-speed sea transportation has increased dramatically in the

last 15 years.Since high speed is very closely related to the weight of the vessel, to achieve

these new speed requirements, designers began to use lightweight materials in place

Corresponding author. Tel.: +61-3-6335-4741; fax: +61-3-6335-4720.

E-mail address: [email protected] (B. Gangadhara Prusty).

0029-8018/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.oceaneng.2003.08.008


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of steel. One of the most common materials used to achieve lightweight structuresin small to medium size high-speed vessels are composites.

Higher speed also means additional loads to the vessels structure. One of the

most critical of this additional loads is slamming, which occurs when the vesselsmotion causes an impact between her bottom or bow flare plating (also cross deckstructure in multihulls), and the water surface.

The behaviour of a composite vessel structure under these loads is studied apply-ing the finite element method. Classification societies recommended design loadsand load cases were used to perform the analysis of the vessels structure.

This paper reports on a finite element analysis of the behaviour of a small com-posite vessel under such loads, according to DNV HSLC (1999) crest landing andhollow landing loadings.

2. Literature review

Case studies on the state-of-the-art computer simulation and modelling techni-ques, using I-DEAS Master Series mechanical aided engineering software, appliedon the design of INCATs large wave piercing aluminium catamarans was pre-sented by Yakimoff (1997). The author highlights the importance of the use ofsophisticated computer techniques to prove new concepts, improving safety and toquickly optimise structures of this kind of vessels.

Morris (1991) carried out a three-dimensional finite element model structuralanalysis, using NASTRAN finite element package, of the entire hull and super-

structure of a large aluminium alloy wave-piercing catamaran. Quasi-dynamicanalysis was used to identify field and concentrated stresses within suitable globaland local structural models. Loading patterns were applied according to LloydsRegister rules and deflections and stress distribution were studied.

However, above works have been focused on large high-speed catamarans builtusing isotropic materials such as aluminium alloys.

Hughes (1997) presented a strategy for achieving first principles optimum structuraldesign of a ship, using MAESTRO finite element software. He demonstrates that strat-egy for a large monohull fast ferry, first using all aluminium and then adapting the

design to be all composite. DNV HSLC (1999) rules were used to perform the analysis.The author highlighted the dramatic structural weight saving that can beachieved by using composite materials (13% of the total displacement of a 100 mlength monohull fast ferry).

He also remarks that there was not enough time available to do a true optimumdesign for the composite ship model, which means that no change in scantlings orply orientations were implemented on the sandwich panels of the model.

Pettersen and Wiklund (1999) have explained different levels of direct calcula-tions, according to DNV HSLC (1999) rules, applicable for various sizes and typesof crafts. They have mentioned that the global strength of a high-speed craft with

length above 50 m shall be analysed using a global finite element model, extendingover the total hull length and have a mesh size which can represent the overall stiff-ness and global stress distribution in the primary hull structure.

R. Ojeda et al. / Ocean Engineering 31 (2004) 901929902


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A designers guide to the methodology used in the development and application ofthe required design loads according to the DNV (1999) rules for classifying highspeed and light crafts have been presented by Olbjrn et al. (1991). The authors men-

tioned that for the case of planning and semi-planning craft (V=ffiffiffiffiLp i3) two quasi-sta-

tic slamming load cases should be analysed: crest landing and hollow landing.Formulations for transverse bending moment, vertical shear force and also twin hullpitch connection moment (due to torsion loading) are also given for multihull vessels.

Direct calculation methods for the global strength analysis of high-speed com-posite crafts with length less than 50 m and a length to depth ratio less than 12have not been recommended by any authors or rules so far. However, Kastak(1998) carried out an FE global strength analysis of a small aluminium catamaran(7.9 m length) using DNV HSLC (1999) rules.

The same approach is used in the analysis of the present vessel, which is only

17 m long.

3. Description of the vessel

The vessel used for this analysis was built in Chile by Alwoplast according to aCrowther Multihulls design. She is a 16.76 m long, high speed, composite materi-als, power-yacht catamaran. She is capable of achieving a maximum speed of 28knots. The general arrangement of the vessel is shown in Fig. 1.

Fig. 1. General arrangement of the composite catamaran.

903R. Ojeda et al. / Ocean Engineering 31 (2004) 901929


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This vessel operates as a pleasure craft in the inland, inshore and coastal watersof the bays and channels of Chiloe, in the southern part of Chile (South America).The principal parameters of the vessel are presented in Table 1.

The vessel was constructed using glass fibre-reinforced composites for the outerand inner skins and closed cell foam as the sandwich core material. Table 2 pre-sents eight different lamination schemes for different parts of the vessels structureand the total thickness of each one, including the inner and outer skin and sand-wich core. All curved panel laminations were made by hand layout method infemale mould. Vacuum bag process was used in flat areas, such as bulkheads.

4. Finite element analysis using ANSYS 6.0

Two different element types (SHELL99 and MASS21) are utilised to create thefinite element model. The full structure of the composite vessel was representedusing SHELL99 layered shell elements (shown in Fig. 2). This element is an 8-node, 3-D shell, layered element with six degrees of freedom at each node: trans-lation in the nodal x, y and z directions and rotations about the nodal x, y and z

axes. It is designed to model thin to moderately thick plate and shell structureswith a side-to-thickness ratio of roughly 10 or greater. The SHELL99 elementallows a total of 250 uniform-thickness layers.

Table 2Laminations schemes

Lamination Thickness (m)

Lamination 1-hull bottom and sides 0.034Lamination 2-underwing 0.044Lamination 3-deck and superstructure sides 0.022Lamination 4-superstructure roof 0.032

Lamination 5-no watertight bulkheads 0.021Lamination 6-watertight bulkheads 0.023Lamination 7-accommodation floor 0.022

Lamination 8-keel 0.105

Table 1Principal parameters of the catamaran

Parameter Dimension/details

Length overall 16.76 m (55 ft)Length waterline 14.10 mBeam overall 6.00 mBeam waterline 5.88 m

Draft (cwl) 0.80 mDisplacement (cwl) 18.00 metric tonEngines 2 225 kWPropulsion Two water jets



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The performance of the element has been validated by running some benchmark

examples from the open literature (see Appendix A).The element SHELL99 was defined at seven different sections (Fig. 3) of the hull.

This method is useful to check the geometry and attributes during pre-processing

and to have a quick access to the results in the post-processing stage.MASS21, shown in Fig. 4, is selected as the element to define lumped masses in

the vessel, such as engines, fuel, fresh water, etc. This is a point element having six

degrees of freedom: translations in the nodal x, y, and z directions and rotations

about the nodal x, y, and z axes.

Fig. 2. SHELL99 element.

Fig. 3. FE model sections.



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The element is defined by a single node and concentrated mass components(Force Time2=Length) in the element coordinate directions. Real constants areused in SHELL99 to define numbers of layers, layer orientation angle, layermaterial and layer thickness. Ten different real constants, shown in Table 3, aredefined to represent the eight different lamination schemes of the vessel structureplus the windows and the water jets.

Real constants are used in MASS21 to define the lumped mass applied to eachelement in x, y and z directions of the different items such as engines and compo-nents of the deadweight.

All the seven different real constants are presented in Table 4.Material property directions for orthotropic materials are parallel to the layer

coordinate system, which is defined by the element coordinate system and the layerorientation angle (defined in the real constants). A list of all the materials used inthe finite element model is presented in Table 5.

Table 3SHELL99 real constant table

SHELL99 real constant number Item

1 Hull sides and bottom2 Underwing3 Deck and superstructure sides4 Superstructure roof

5 No watertight bulkheads6 Watertight bulkheads7 Accommodation decks

8 Keel9 Windows10 Water jets

Fig. 4. MASS21 element.



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4.1. Mesh generation

The geometry of the model, shown in Fig. 5, is created by defining keypoints

from the table of offsets of the hull. Areas are then defined in terms of those key-

points and attributes (element type, element coordinate system orientation, real

constant) are assigned to the areas and keypoints based on the information pro-

vided by the designer. Then, a mesh is generated, using the automatic meshing

facility of the pre-processor module of ANSYS 6.0.The ANSYS 6.0, finite element model consists of 10 620 nodes with six degrees

of freedom per node and 4868 elements (4461 SHELL99 and 408 MASS21).

4.2. Boundary conditions

Global constraining of the loaded model was avoided by adoption of a free body

support, which was arranged to provide the necessary reference point for the

Inertia Relief [3] facility of the ANSYS program.

4.3. DNV hollow landing and crest landing slamming load cases

Within the global loads recommended by DNV (1999), two static slamming load

cases, hollow landing (HL) and crest landing (CL), are specified. The load calcula-

Table 5Material list table

Number Material Type

1 Chop strand mat Isotropic2 Unidirectional Orthotropic

3 Woven roving Orthotropic4 Biaxial DB170 Orthotropic5 Triaxial CDB 200 Orthotropic6 Triaxial CDB 340 Orthotropic7 Divinycell H80 Orthotropic8 Coremat Isotropic9 Glass Isotropic

10 Steel Isotropic

Table 4MASS21 real constant table

MASS21 real

constant number

Item Number

of nodes

Nodal mass (kg)

11 Engine 8 212.512 Galley and dining room area 63 42.513 Toilets 40 31.2

14 Bridge 87 31.015 Daily fuel tank 28 33.016 Main fuel tank 150 24.0

17 Fresh water tank 32 31.3



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tions for both load cases are preformed according to the method presented byKastak (1998).

For both cases, the hull girder is considered out of the water and the weight of

the structure is to be increased by the design vertical acceleration at longitudinal

centre of gravity (LCG).The design vertical acceleration may be calculated according to the rules.

acg V

ffiffiffiffiL

p 3:2L0:76

fg g0 m=s2 1

where fg is an acceleration factor dependent on the type of service notation andservice area restriction. Yacht vessel type and coastal service area restriction deter-

mine a factor of 1.0; g0 is the acceleration of gravity, 9.81 m/s2; L is the length of

the craft in metres defined as the distance between perpendiculars, which for this

case is 14.10 m.V=

ffiffiffiffiL

pneed not to be taken greater than 3.0 for this case.

Thus, substituting these values into Eq. (1), the vertical design acceleration yields

12.6 m/s2.In hollow landing condition, it is assumed that the vessel is settled down on a

hollow wave, which is positioned along the length of the vessel. Thus, the vessel isassumed to be supported on the hollow landing reference areas, placed at the bow

and stern of the ship (Fig. 6). The value of the reference area, based on DNV

Fig. 5. Catamaran FE model.



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HSLC (1999) rules for hollow landing, was found to be 16.05 m2. Each hull carriedhalf of this area, divided in a fore and aft area, with a surface 4.01 m2 each.

A longitudinal midship bending moment for the hollow landing case, accordingto DNV rules, is calculated as below.

Mb D2

g0 acger ew kN m 2

where D is the displacement of the vessel in tonnes, 18 ton for the studied vessel; g0is the acceleration of gravity, 9.81 m/s2; acg is the design vertical acceleration, 12.6m/s2; er is the mean distance from the centre of the hollow landing reference areasto the vessel LCG in metres, 4.5 m; ew is half the distance from LCG of the forehalf body of the vessel to the LCG of the aft body of the vessel in metres, 2.95 m.

On appropriate substitution of values in Eq. (2), the longitudinal midship bend-ing moment was found to be 313 kN m.

For this static and freely supported ship structure, the values of bendingmoments calculated from either end (fore and aft half bodies) have to be equal toeach other and also similar to the moment value calculated using the DNV (1999)rules. Also the sum of the forces due to the slamming pressure acting on the hollowlanding reference areas must be equal to the weight of the structure increased by

Fig. 6. Hollow landing areas.

Fig. 7. Hollow landing loading condition.



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the design vertical acceleration. These equilibrium conditions, shown in Fig. 7, maybe written as a set of two linear equations as:

FaFb

Maft

Mfore

g0

acg

3

Fadaft Maftg0 acglaft Fbdfore Mforeg0 acglfore 4

On solving the simultaneous equations the forces are calculated as

Fa 208 kNFb 194 kN

The force acting on each hull is obtained by dividing each force by 2. Thus, theslamming pressures, for the hollow landing case, were obtained by dividing theforces acting in each hull into the hollow landing reference areas.

Pa 25 kPaPb 26 kPa

So for the midship bending moment, the calculation is,

Fadaft Maftg0 acglaft 330 kN m

or

Fbdfore Mforeg0 acglfore 330 kN m 5Hence, a close agreement has been obtained between the resulting bending

moments for aft and fore bodies and the rule bending moment.The slamming pressure for hollow landing was applied, to the finite element

model, on the elements within the hollow landing reference areas as presented inFig. 8.

In crest landing condition, it is assumed that the vessel is settled down on a wavecrest, which is positioned along the length of the vessel. Thus, the vessel is assumedto be supported over crest landing reference area placed with its centroid at the

LCG of the vessel, as shown in Fig. 9. The value of the reference area, based inDNV HSLC (1999) rules, for crest landing was found to be 19.75 m2. Thus, eachhull carried half of this area, which was a surface of 9.87 m2.

The longitudinal midship bending moment for the crest landing case is calcu-lated as shown below

Mb D2

g0 acg

ew ls4

kN m 6

where D, g0 and acg have been previously defined; ew is half the distance from LCGof the fore half body of the vessel to the LCG of the aft body of the vessel inmetres, 2.95 m; ls is longitudinal slamming reference area, 6.7 m.



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Thus, on substitution of values into Eq. (6), the longitudinal midship bendingmoment yield 255 kN m.

Following the same procedure adopted for hollow landing case, equilibrium con-dition (Fig. 10) for crest landing case is written as a linear equation as:

F Mg0 acg 7On solving Eq. (7) the force obtained is

F 400 kN

Fig. 9. Crest landing area.

Fig. 8. Hollow landing loads in the FE model.



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meaning that the force to be applied to each hull is

Fh 200 kNHence, the slamming pressure, for the crest landing case, is obtained by dividing

this force into the crest landing reference area of each hull.

P 20:3 kPaThe midship bending moment is calculated by splitting the hull weight and the

crest landing area into two parts at the midship section.

Fadaft Maftg0 acglaft % 140 kN mor

Fbdfore Mforeg0 acglfore % 140 kN m 8This bending moment is found to be almost 37% less than the one calculated

using the DNV (1999) crest landing rules. However, the difference can be attributedto the concentration of the ship weight (Fig. 11), over the crest landing referencearea.

The slamming pressure for crest landing is applied, to the finite element model,on the elements within the crest landing reference areas as presented in Fig. 12.

5. Analysis and discussion

The finite element model is analysed for each load case using ANSYS 6.0 sparsematrix solver in a Intel Pentium IV Proccessor. Deflection and stresses, for theDNV HSLC (1999) load cases are analysed. In order to check imbalances of the

model, the accelerations applied by the inertia relief facility were checked and arefound to be very small in magnitude, which confirm that only minor force imbal-ances were present on the model.

Fig. 10. Crest landing loading condition.



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Fig. 12. Crest landing loads in the FE model.

Fig. 11. Weight distribution plot.



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5.1. Hollow landing load case

The deformed plot of the model for the hollow landing load case is presented in

Fig. 13. Displacements have been increased by a factor of 20 to provide a clearerindication of the deformed shape. The deflections at both ends of the vessel are

found to be non symmetrical, that attributed to the non uniform mass distribution

presented in Fig. 15. The maximum vertical deflection, of about 39 mm, is noted to

occur at the forward end of the vessel.Maximum axial (tension and compression) stresses were studied along each sec-

tion and lamination scheme of the vessel. High stress concentration points are

identified. Fig. 14 shows the distribution of the maximum axial stresses in x, y and

z axes for each section of the vessel in hollow landing condition. Maximum axial

stress in tension (76 MPa) and maximum axial stress in compresion (51 MPa) are

found to occur at the ring frame in the forward part of Section 1. The stress con-

centration points are shown in Figs. 15 and 16, respectively. Fig. 17 shows the dis-

tribution of the maximum axial stresses in x, y and z axes for each lamination of

the vessel in hollow landing condition.

Fig. 13. Vertical deflection of the hull girder in HL condition.



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Fig. 14. Maximum axial stress by section plot for HL condition.

Fig. 15. Maximum stress concentration plots for HL condition (tension).



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Fig. 16. Maximum stress concentration plots for HL condition (compresion).

Fig. 17. Maximum axial stress by lamination plot for HL condition.



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5.2. Crest landing case

The deformed plot of the model for the crest landing load case is presented in

Fig. 18. Displacements have been increased by a factor of 20 as in the hollow land-

ing case. The maximum vertical deflection, of about 22 mm, is observed to occur at

the forward end of the vessel.In this case also, the maximum axial (tension and compression) stresses are

plotted along each section and lamination scheme of the vessel. High stress con-centration points are identifed. Fig. 19 shows the distribution of the maximum

axial stresses in x, y and z axes for each section of the vessel in crest landing con-

dition.The maximum axial stress in tension (55 MPa) is found to occur at the line of

union of the acomodation deck floor and the hull side in Section 5 (Fig. 20). The

maximum axial stress in compresion (37.5 MPa) is observed to occur at the acomo-

dation floor at the centreline in Section 3 (Fig. 21). Fig. 22 shows the distribution

of the maximum axial stresses in x, y and z axes for each lamination of the vesselin hollow landing condition.

Fig. 18. Vertical deflection of the hull girder in CL condition.



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Fig. 22. Maximum axial stress by lamination plot for CL condition.

Fig. 21. Maximum stress concentration plots for CL condition (compresion).



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Table 6Change in ply orientation

Item Original orientation (frames) Proposed orientation (frames)

Biaxial fibre DB170 45 0Core Biaxial fibre DB170 45 0

Fig. 24. Maximum axial transverse stresses by lamination/crest landing.

Fig. 23. Maximum axial transverse stresses by lamination/hollow landing.



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5.3. Optimisation study

From both load cases, it can be seen that the maximum vaules of axial stress

occurs in the frames (transvese axial stresses (SX) in tension). The greatest occur-ing in the hollow landing case. In order to observe the global behaviour, a studyhas been performed by changing the ply orientation. The change in the ply orien-tation, shown in Table 6, was applied to the frames lamination scheme, in the finiteelement model. The model is then again solved for crest and hollow landing loadcases.

The maximum transverse stress (SX) in the frames for the hollow landing andcrest landing cases is found to reduce by 34% and 21%, respectively, as shown inFigs. 23 and 24.

Through out the remainder of the structure only minor changes, less than 5%,

were achieved, hence the plots are not presented.

6. Conclusions

A full, 3-D shell element, model of a small composite catamaran is created usingANSYS 6.0.

The SHELL99 3-D shell element is satisfactorily tested and used to model lami-nated composite structures. MASS21 nodal mass element is used for modellingconcentrated and distributed items of the ship weight.

The applications of two quasi-static slamming load cases according to the DNVHSLC (1999) rules, hollow landing and crest landing, were studied. Both loadcases were solved under a static linear approach using ANSYS 6.0.

Deflection and stresses along the hull are studied to check the integrity of thevessel structure. High stress concentration points were highlighted and changes inlamination schemes were trailed and maximum stress values were significantlyreduced.

Acknowledgements

The first author gratefully acknowledges the Australian Maritime College Coun-cil for awarding the Tom Fink Scholarship 2002 to carry out this investigation.

The authors wish to thank Crowther Multihulls and Alwoplast S.A. for provid-ing the information required to carry out this investigation.

Appendix A

A.1. Stiffened panel deflections

See Chattopadhyay et al. (1993), Tables 7 and 8, Figs. 2528.



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Table 7Geometry of the problem

Geometry of the panel

Length (m) 0.02540Width (m) 0.02540

Geometry of the stiffenerHeight (m) 0.00254Thickness (m) 0.00025

Table 8Lamination schemes of the problem

Name Panel Stiffener

I-a [0/0] [90/90]II [90/0/90] [90/0/90]III [0/90/0/90] [0/90/0/90]

Fig. 25. Description of the problem.



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Fig. 26. Results, lamination I-a.

Fig. 27. Results, lamination II.



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A.2. Shell deflections

See Wung (1997), Tables 913, Figs. 2931.

Fig. 28. Results, lamination III.

Table 9

Material properties of the problem

Ex (N/m2) 1:32E 11

Ey (N/m2) 1:08E 10

Ez (N/m2) 1:08E 10

Gxy (N/m2) 5:65E 09

Gxz (N/m2) 5:65E 09

Gyz (N/m2) 3:38E 09

Prxy 0.24Prxz 0.24Pryz 0.49Thickness (m) 0.000127

Table 10Load

UDL 620:5 kN=m2

Table 11Geometry of the problem

Geometry

r (m) 7.62h (degrees) 40l(m) 15.24t (m) 0.0762



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Table 12Material properties of the problem

Material Properties

E1 (N/m2) 13:4E 9E2 (N/m

2) 336:1E 6E3 (N/m

2) 336:1E 6G12 (N/m

2) 201:7E 6G13 (N/m

2) 201:7E 6G23 (N/m

2) 168:1E 6Pr12 0.25Pr13 0.25Pr23 0.25

Table 13Lamination scheme of the problem

Lamination scheme

[0 0 0 45 45 90 90 90 45 45 0 0 0]



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Fig. 31. Vertical deflection.

Fig. 30. Lateral deflection.



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A.3. Plate moments

See Chen and Lui (1990), Tables 1416, Figs. 32 and 33.


Table 14Geometry definition of the problem

Geometry Definition

a=b 1a=h 10

Table 15

Geometry of the problem and load

Model Geometry

a (m) 0.127b (m) 0.127h (m) 0.0127

Loadqo (N/m

2) 68:9E 3



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References

Chattopadhyay, B., Sinha, P.K., Mulkhopadhyay, M., 1993. Finite element analysis of blade-stiffenedcomposite plates under transverse loads. Journal of Reinforced Plastics and Composites 12 (1), 76100.

Chen, W.C., Lui, W.H., 1990. Deflections and free vibrations of laminated plates-Levy type solutions.International Journal of Mechanical Sciences 3 (9), 779793.

DNV, 1999. Rules for classification of high speed and light crafts. Det Norske Veritas rules.Hughes, O., 1997. Two first principles structural designs of a fast ferry all-aluminum and all-composite.

FAST 97.

Fig. 33. Moment results.

Table 16Material properties of the problem

E1 (N/m2) 13:4E 9

E2 (N/m2

) 336:1E 6E3 (N/m

2) 336:1E 6G12 (N/m

2) 201:7E 6G13 (N/m

2) 201:7E 6G23 (N/m

2) 168:1E 6Pr12 0.25Pr13 0.25Pr23 0.25



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Kastak, D., 1998. Finite element model of a 7.9 m training/research vessel-Educat Report 98/2,AMECRC, IR.

Morris, J.A., 1991. A three dimensional structural analysis of a large wave piercing catamaran design.IMAS 91 High Speed Marine Transportation.

Olbjrn, E.H., Hughes, C.T., Govindasamy, B.N., 1991. Classification of high-speed marine transpor-tation with particular emphasis on structural strength. IMAS 91 High Speed Marine Transportation.

Pettersen, ., Wiklund, K.M., 1999. Det Norske Veritas requirements for direct calculation methods ofhigh speed and light craft. FAST 99.

Wung, P.M., 1997. Laminated composite structures by continuum-based shell elements with transversedeformations. Computers & Structures 62 (6), 10731090.

Yakimoff, P., 1997. State-of-art computer simulation for structural analysis of high speed catamarans.FAST 97.


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