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doi:10.1016/j.oceaneng.200
Tel.: +61-3-6335-4741; fax: +61-3-6335-4720.
@mte.amc.edu.au (B. Gangadhara Prusty).
tter # 2003 Elsevier Ltd. All rights reserved.
3.08.008
Ocean Engineering 31 (2004) 901–929
www.elsevier.com/locate/oceaneng
Finite element investigation on the staticresponse of a composite catamaran under
slamming loads
Roberto Ojeda a, B. Gangadhara Prusty b,�, Marcos Salas a
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 Norske
Veritas 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; Ship’s 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
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929902
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 vessel’s structure. One of the
most critical of this additional loads is slamming, which occurs when the vessel’smotion 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 vessel’s 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 INCAT’s 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 structural
analysis, 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 Lloyd’sRegister rules and deflections and stress distribution were studied.However, above works have been focused on large high-speed catamarans built
using isotropic materials such as aluminium alloys.Hughes (1997) presented a strategy for achieving first principles optimum structural
design 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 thedesign to be all composite. DNV HSLC (1999) rules were used to perform the analysis.The author highlighted the dramatic structural weight saving that can be
achieved 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 optimum
design 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 withlength 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.
903R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
A designer’s 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 Olbjørn et al. (1991). The authors men-tioned that for the case of planning and semi-planning craft (V=
ffiffiffiffiL
pi3) 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.
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929904
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 outer
and inner skins and closed cell foam as the sandwich core material. Table 2 pre-sents eight different lamination schemes for different parts of the vessel’s 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 zaxes. 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 2
Laminations 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
0.032Lamination 5-no watertight bulkheads
0.021Lamination 6-watertight bulkheads
0.023Lamination 7-accommodation floor
0.022Lamination 8-keel
0.105Table 1
Principal parameters of the catamaran
Parameter
Dimension/detailsLength overall
16.76 m (55 ft)Length waterline
14.10 mBeam overall
6.00 mBeam waterline
5.88 mDraft (cwl)
0.80 mDisplacement (cwl)
18.00 metric tonEngines
2� 225 kWPropulsion
Two water jets905R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
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.
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929906
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 each
element 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 3
SHELL99 real constant table
SHELL99 real constant number
Item1
Hull sides and bottom2
Underwing3
Deck and superstructure sides4
Superstructure roof5
No watertight bulkheads6
Watertight bulkheads7
Accommodation decks8
Keel9
Windows10
Water jetsFig. 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 5
Material list table
Number
Material Type1
Chop strand mat Isotropic2
Unidirectional Orthotropic3
Woven roving Orthotropic4
Biaxial DB170 Orthotropic5
Triaxial CDB 200 Orthotropic6
Triaxial CDB 340 Orthotropic7
Divinycell H80 Orthotropic8
Coremat Isotropic9
Glass Isotropic10
Steel IsotropicTable 4
MASS21 real constant table
MASS21 real
constant number
Item N
umberof nodes
N
odal mass (kg)11
Engine 8 2 12.512
Galley and dining room area 63 42.513
Toilets 40 31.214
Bridge 87 31.015
Daily fuel tank 28 33.016
Main fuel tank 1 50 24.017
Fresh water tank 32 31.3R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929908
tions for both load cases are preformed according to the method presented by
Kastak (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 ¼VffiffiffiffiL
p � 3:2
L0:76� fg � g0 m=s2 ð1Þ
where fg is an acceleration factor dependent on the type of service notation and
service 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 is
assumed 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.
909R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
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, according
to DNV rules, is calculated as below.
Mb ¼D2ðg0 þ acgÞðer ewÞ kN m ð2Þ
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 bending
moments 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.
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929910
the design vertical acceleration. These equilibrium conditions, shown in Fig. 7, maybe written as a set of two linear equations as:
Fa þ Fb ¼ ðMaft þMforeÞðg0 þ acgÞ ð3Þ
Fadaft Maftðg0 þ acgÞlaft ¼ Fbdfore Mforeðg0 þ acgÞlfore ð4Þ
On solving the simultaneous equations the forces are calculated as
Fa ¼ 208 kN
Fb ¼ 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 ¼ 25 kPa
Pb ¼ 26 kPa
So for the midship bending moment, the calculation is,
Fadaft Maftðg0 þ acgÞlaft ¼ 330 kN m
or
Fbdfore Mforeðg0 þ acgÞlfore ¼ 330 kN m ð5Þ
Hence, a close agreement has been obtained between the resulting bendingmoments 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 wave
crest, 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 theLCG 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 ¼D2
g0 þ acg� �
ew ls4
� �kN m ð6Þ
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.
911R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
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 ¼ ðMÞðg0 þ acgÞ ð7Þ
On solving Eq. (7) the force obtained is
F ¼ 400 kN
Fig. 9. Crest landing area.
Fig. 8. Hollow landing loads in the FE model.
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929912
meaning that the force to be applied to each hull is
Fh ¼ 200 kN
Hence, the slamming pressure, for the crest landing case, is obtained by dividingthis force into the crest landing reference area of each hull.
P ¼ 20:3 kPa
The midship bending moment is calculated by splitting the hull weight and thecrest landing area into two parts at the midship section.
Fadaft Maftðg0 þ acgÞlaft � 140 kN m
or
Fbdfore Mforeðg0 þ acgÞlfore � 140 kN m ð8ÞThis 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 themodel, 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.
913R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
Fig. 12. Crest landing loads in the FE model.
Fig. 11. Weight distribution plot.
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929914
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 clearer
indication 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.
915R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
Fig. 14. Maximum axial stress by section plot for HL condition.
Fig. 15. Maximum stress concentration plots for HL condition (tension).
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929916
Fig. 16. Maximum stress concentration plots for HL condition (compresion).
Fig. 17. Maximum axial stress by lamination plot for HL condition.
917R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
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 vessel
in hollow landing condition.
Fig. 18. Vertical deflection of the hull girder in CL condition.
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929918
Fig. 20. Maximum stress concentration plots for CL condition (tension).
Fig. 19. Maximum axial stress by section plot for CL condition.
919R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
Fig. 22. Maximum axial stress by lamination plot for CL condition.
Fig. 21. Maximum stress concentration plots for CL condition (compresion).
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929920
Table 6
Change in ply orientation
Item O
riginal orientation (frames) Proposed orientation (frames)Biaxial fibre DB170 4
5 0Core –
–Biaxial fibre DB170 4
5 0Fig. 24. Maximum axial transverse stresses by lamination/crest landing.
Fig. 23. Maximum axial transverse stresses by lamination/hollow landing.
921R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
5.3. Optimisation study
From both load cases, it can be seen that the maximum vaules of axial stressoccurs 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 and
crest 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 DNV
HSLC (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 the
vessel 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. 25–28.
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929922
Table 7
Geometry of the problem
Geometry of the panel
Length (m)
0.02540Width (m)
0.02540Geometry of the stiffener
Height (m)
0.00254Thickness (m)
0.00025Table 8
Lamination schemes of the problem
Name
Panel S tiffenerI-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.
923R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
Fig. 26. Results, lamination I-a.
Fig. 27. Results, lamination II.
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929924
A.2. Shell deflections
See Wung (1997), Tables 9–13, Figs. 29–31.
Fig. 28. Results, lamination III.
Table 9
Material properties of the problem
Ex (N/m2) 1
:32Eþ 11Ey (N/m2) 1
:08Eþ 10Ez (N/m2) 1
:08Eþ 10Gxy (N/m2) 5
:65Eþ 09Gxz (N/m2) 5
:65Eþ 09Gyz (N/m2) 3
:38Eþ 09Prxy 0
.24Prxz 0
.24Pryz 0
.49Thickness (m) 0
.000127Table 10
Load
UDL ¼ 620:5 kN=m2
Table 11
Geometry of the problem
Geometry
r (m)
7.62h (degrees)
40l (m)
15.24t (m)
0.0762925R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
Fig. 29. Description of the problem.
Table 12
Material properties of the problem
Material Properties
E1 (N/m2)
13:4Eþ 9E2 (N/m2)
336:1Eþ 6E3 (N/m2)
336:1Eþ 6G12 (N/m2)
201:7Eþ 6G13 (N/m2)
201:7Eþ 6G23 (N/m2)
168:1Eþ 6Pr12
0.25Pr13
0.25Pr23
0.25Table 13
Lamination scheme of the problem
Lamination scheme
[0 0 0 45 45 90 90 90 45 45 0 0 0]
R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929926
Fig. 31. Vertical deflection.
Fig. 30. Lateral deflection.
927R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929
A.3. Plate moments
See Chen and Lui (1990), Tables 14–16, Figs. 32 and 33.
Fig. 32. Description of the problem.
Table 14
Geometry definition of the problem
Geometry Definition
a=b
1a=h
10Table 15
Geometry of the problem and load
Model Geometry
a (m)
0.127b (m)
0.127h (m)
0.0127Load
qo (N/m2)
68:9Eþ 3R. Ojeda et al. / Ocean Engineering 31 (2004) 901–929928
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Table 16
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13:4Eþ 9E2 (N/m2)
336:1Eþ 6E3 (N/m2)
336:1Eþ 6G12 (N/m2)
201:7Eþ 6G13 (N/m2)
201:7Eþ 6G23 (N/m2)
168:1Eþ 6Pr12
0.25Pr13
0.25Pr23
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