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8/11/2019 FE Simulation of a Double-bottom Grounding on a Conical Rock
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HELSINKI UNIVERSITY OF TECNOLOGYShip Laboratory / Kristjan Tabri
FE simulation of a double-bottom grounding on a conical rock
Report
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CONTENTS:
1. INTRODUCTION .......................................................................................................................................4
2. MODELING OF THE DOUBLE-BOTTOM............. ............ .............. ............. .............. ............ .............. 43. SIMULATION PROCEDURE............ ............. ............. ............. .............. ............. ............ .............. ........... 8
4. DATA PROCESSING ............................................................................................................................... 11
5. RESULTS AND DISCUSSION ................................................................................................................ 11
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ABSTRACT
Current simulations are a part of a research project FSAKARI. The objective of the
simulations is to investigate how double-bottoms with different designs behave in case of a
grounding on a conical rock. To evaluate the effect of the different factors like double-bottom
construction and rock penetration to the double bottom five different double-bottom designs
are modeled. The simulations are carried out with different rock penetrations. After post-
processing the simulation data will be used in FSA analysis. Simulations are carried out in the
Ship Laboratory of the Helsinki University of Technology. For FE simulation explicit finite
element code LS-Dyna is used.
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1. Introduction
To estimate the risks in a case of a ship grounding on a rock it should be possible to estimate
how the ship behaves in grounding event. (As there is straight connection between the ship
and its double-bottom behaviour, also behaviour of the double-bottom should be known. To
investigate the behaviour of the double-bottom several FE simulations, where a rigid obstacle
(rock) penetrates to the double-bottom, are carried out. As it is too laborious to carry out a FE
simulation for the whole double-bottom of the ship only a small part of the ship is modelled.
During the simulation the model is fixed on the sides and is not moving, but the rock has a
horizontal and a vertical displacement. By the simulation, contact force and extent of the
damage are determined for the model. Based on that information forces and extent of the
damage can also be estimated for the whole ship. In current simulations main interest are on
the following points: How the depth of the rock penetration affects the contact force and the damage
Rock penetration needed for tearing
Average contact force
Extent of the tearing in outer and inner bottom plating
Force history during the contact event
This report includes descriptions of the different double-bottom models and FE simulation
process. Resulting data is presented for every simulation.
2. Modeling of the double-bottom
For the simulation five different double-bottom models are created. For modelling and three-
dimensional meshing FE program LS-Ingrid is used. LS-Ingrid is also used as a translator to
convert a database into LS-Dyna input file. Part of the ship is modelled according to the
structural drawings for a RO-RO vessel.
Main particles of the vessel are:
LWL: 150.47 [m]
LPP: 146.27 [m]
B: 25.35 [m]
T: 7.35 [m]
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Main particles of the double-bottom of the ship:
Girder spacing: 4.26 [m]
Floor spacing: 2.4 [m]
Height: 1.6 [m]
For the simulation, a small part from the middle of the ship is modeled (Figure 1). The model
included 4 floors and 3 girders, and its length was 12 meters and width 17 meters. Height of
the model depends on a particular case and varies from 1.6 [m] to 2.4 [m]. Altogether five
different double-bottom designs were used. The basic case is denominated as a case A. Cases
B, C, D are created by changing only one parameter in the case A. Case E has a different
designs than other cases. In the case E model has longitudinal girders instead of longitudinal
stiffeners and also transversal floors are removed. General picture of the cases A, B, C and Dis given in figure 2 and for the case E in figure 3.
Figure 1. Modeled part
Main parameters and particles for the different double-bottom models:
1. CASE A
Length 12 [m]
Breath 17 [m]
Height 1.6 [m]
Thickness:
floors 11 [mm]
girders 11 [mm]
Modeled part
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external plating 12 [mm]
internal plating 17 [mm]
Rock radius 1.1 [m]
Mass of the bottom model 75.7 [ton]
2. CASE B (db height)
Height of the double-bottom increased by 50% 1.62.4 [m]
Rock radius 1.1 [m]
Mass of the bottom model 82.6 [ton]
3. CASE C (plating)
Bottom plating thickness increased by 50 % 12 18 [mm]
Rock radius 1.1 [m]
Mass of the bottom model 85.6 [ton]
4. CASE D (stiffeners)
Bottom stiffeners moment of inertia increased by 90 % 2477 4720 [cm4]
Moment of inertia is increased by changing cross-
sectional area of the stiffener. Stiffener type is
changed from HP 260x10 to HP 300x13.
Rock radius 1.1 [m]
Mass of the bottom model 78.6 [ton]
5. CASE E (girders)
Longitudinal stiffeners are replaced by longitudinal girders. Transversal floors are removed.
Longitudinal girders:
Thickness 10 [mm]
Girder spacing 710 [mm]
Rock radius 1.1 [m]
Mass of the bottom model 84.6 [ton]
6. CASE A2
Same as the case A, but rock radius is 2 metres
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7. CASE A3
Same as the case A, but rock radius is 3 metres
The model depending on a particular case has 70,000- 85,000 elements. The size of the
prevailing element is 10x10 [mm2]. For the precise simulation of tearing, fracture criteria for
the prevailing element size is calculated. For that we modelled a specimen and carried out
several tensile tests and looked for correct failure criteria by comparing real and calculated
stress curves. The model had boundary conditions at both ends and on both sides (Figure.2),
where all degrees of freedom are fixed.
Figure 2.Double-bottom model (Cases A, B, C, D)
As it can be seen from the figure 2, x-axis points to longitudinal direction and z-axis points to
vertical direction. Same notifications are later used in appendices with time-histories.
Longitudinal direction,
boundary conditions
Breath,
boundary conditions
Floor
Centre girder
Tank-top (inner plating)
Outer plating
X
Z
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Figure 3.Double-bottom model (Case E)
3. Simulation procedure
To simulate the grounding event a conical rock is modelled. Cone angle is 45 and radius ofthe top cone of the rock is 1.1 meters for the cases A, B, C and D, and 2 and 3 meters for the
cases A2 and A3. In figure 4, modelled rock is shown graphically. The rock is given a
horizontal and a vertical displacement as a function of time as follows (figure 5):
vertical displacement =15t
horizontal displacement = MAXPt
0.026-0.24
026.0cos1
2
1
where
t -time
PMAX -maximum (final) rock penetration to the double-bottom
0.026 -time when rock starts to penetrate to the double-bottom
0.24 -time when rock attains its final penetration
As forces close to boundary conditions may cause some disturbances and inaccuracy, the rock
starts to penetrate the double-bottom not exactly at the first end of the model but 0.39 [m]
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(t=0.026 [s]) from it. In the same reason longitudinal displacement of the rock terminates 2.4
[m] before the end of the model. Total longitudinal displacement of the rock is 9.6 [m]
(tTOTAL=0.64 [s]). The simulations are carried out for 7 different rock penetrations- from 0.5 to
3.5 [m] with 0.5 [m] spacing. In every case the rock attained final penetration value 3.6
meters (t=0.24 [s]) from the first end of the model. Centre of the rock is always moving along
the centre girder. Horizontal velocity of the rock is 15 [m/s], but as the force calculation
process is quasi-static, velocity of the rock does not have any effect to the force values. In
figure 5 rock movements with corresponding temporal values are presented graphically.
The double-bottom model, the shape and the movements of the rock are described in input file
for LS-Ingrid. For the simulation initial input file is converted into input file for explicit finite
element code LS-Dyna. In LS-Dyna calculations contact force between rock and the double-
bottom is calculated by usingpenalty method. In thepenalty methodnormal interface springs
are placed between all penetrating nodes and surfaces, and forces are calculated by using
springs. Better description of thepenalty methodand other matters concerning the simulation
procedure are given in LS-Dyna theoretical manual [1].Computer used for simulation is dual
195 MHz processor Silicon Graphics Octane2 UNIX Workstation with 512 MB memory.
Operation system used in workstation is IRIX.
Figure 4. Modeled rock
45
R
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Figure 5. Rock movements respect to the double-bottom
Rock displacement
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.80 1.60 2.40 3.20 4.00 4.80 5.60 6.40 7.20 8.00 8.80 9.60
Horizontal displacement (m)
Verticaldisplacement(m)
Figure 6. Rock displacement
Maximum penetration
t=0.24 [s]
Termination of the
rock displacement
Rock starts to penetrate to
the double-bottom t=0.026
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4. Data processing
Resulting data is given in time domain after every 1.29E-3 seconds (1.93E-2 [m]). Single
simulation takes about 20-35 hours depending on a particular case and rock penetration. The
amount of the resulting data in single simulation is about 100 KB in text files and 30 MB in
video files. Videos of outer and inner bottom plating damages are taken for every simulation.
For more convenient and comprehensible processing, the simulation data is converted from
time domain into displacement domain. To evaluate the effect of different design, force
histories are analysed after each simulation. Forces needed for tearing both in outer and inner
bottom plating and also average grounding force were calculated and presented in every
simulation. Average force is calculated during the time when rock has attained its final
penetration value and moves horizontally in longitudinal direction. To evaluate the extent of
the damage average breath of the tearing is measured as well as temporal initiation of the
tearing. In some simulations also deformation energy is measured.
5. Results and discussion
According to recorded time histories and above-mentioned calculated values some general
conclusions can be drawn and behaviour of the different designs can be presented. On
analysis cases are divided into two halves- cases with same rock radius (cases A, B, C and D)
and cases with different rock radius (cases A, A2 and A3). Both halves are investigated
separately. On comparison main interests are on following points:
Average vertical and horizontal grounding forces
Tearing width
Penetration depth and force values at the moment of tear initiation
Cases A, B, C, D
First the results for the cases A, B, C and D are presented and analysed. Results are both
presented on graphical and numerical mode.
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Average vertical and horizontal impact forces
Values for the average vertical grounding force are presented on graphs 1 and 2, and
numerically on table 1. Graphs 3, 4 and table 2 present the values for horizontal forces. On the
graphs 1 and 3 vertical and horizontal impact forces are presented as a function of final
penetration depth as it gives good overview how are the relations between the different
designs on different final penetration values. Graphs 2 and 4 basically present the same
values, but on mode where it is easier to see how much the values on different penetration
values differ from the average value. Average values on graphs 1 and 3 are presented with
dots in corresponding colour and on graphs 2 and 4 with blue rectangles.
-3,0E+07
-2,5E+07
-2,0E+07
-1,5E+07
-1,0E+07
-5,0E+06
0,0E+00
0 0,5 1 1,5 2 2,5 3 3,5 4
Penetration [m]
Force[N]
CASE A
CASE B
CASE C
CASE D
CASE E
Graph 1. Average vertical forces for cases A, B, C, D
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-3,0E+07
-2,5E+07
-2,0E+07
-1,5E+07
-1,0E+07
-5,0E+06
0,0E+00
CASE A CASE B CASE C CASE D CASE E
Force[N]
3,5
3
2,5
2
1,5
1
0.5
Average
Graph 2. Average vertical forces for cases A, B, C, D (sorted by cases)
Average force values shown in the graphs are calculated by using force values from the
middle range.
In the middle range only three penetration values are considered- 1.5, 2.0 and 2.5 metres.
Therefore average force value on the graphs is simply average of the three force values on
mentioned penetration depths. The middle range reflects the situation where outer plating of
the double-bottom is widely damaged and inner plating is slightly damaged or still intact.
From the graphs it can be seen that case B gives lowest average force value in the middle
range. Reason is that compared to other cases case B gives much lower force values on
penetration depths from 1.5 to 3.0 metres. It can be explained by the fact that on mrntioned
range (1.5-3.0) other cases (except B) are already deforming (lower penetration values) or
tearing (higher values) the inner plating, but in case B rock contacts with the inner plating no
before the penetration value 2.5.
If the beginning of the graph is considered it can be seen that on penetration value 0.5 case B
gives quite average value. Only cases D (stiffeners) and C give higher value, which can be
explained by their higher stiffness. It can be seen that on penetration value 1.0 case B gives
almost highest value (equal to case C).
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Case C gives highest average force values and has also highest values in most of the
penetration values. On penetration value 0.5 case C is the only double-bottom version, which
stays intact. It reflects also on its high force value on that point.
Case E (girders) has second highest average force value. As its construction is quite stiff,
tearing on penetration value 0.5 occurs very early and because of that also force value on that
penetration depth is the lowest.
Table 1. Vertical force values
Penetration/ case A B C D E
0,5 -5,448E+06 -5,824E+06 -8,592E+06 -7,444E+06 -4,538E+06
1 -6,349E+06 -7,261E+06 -7,413E+06 -6,757E+06 -6,794E+06
1,5 -9,320E+06 -8,631E+06 -1,053E+07 -9,657E+06 -1,120E+07
2 -1,424E+07 -1,090E+07 -1,658E+07 -1,482E+07 -1,547E+07
2,5 -1,868E+07 -1,437E+07 -2,212E+07 -2,022E+07 -2,007E+07
3 -2,065E+07 -1,992E+07 -2,277E+07 -2,155E+07 -2,387E+07
3,5 -2,232E+07 -2,316E+07 -2,641E+07 -2,335E+07 -2,391E+07
Average (1.5-2.5 [m]) -1,408E+07 -1,130E+07 -1,641E+07 -1,490E+07 -1,558E+07
-2,0E+07
-1,8E+07
-1,6E+07
-1,4E+07
-1,2E+07
-1,0E+07
-8,0E+06
-6,0E+06
-4,0E+06
-2,0E+06
0,0E+000 0,5 1 1,5 2 2,5 3 3,5 4
Penetration [m]
Force[N]
CASE A
CASE B
CASE C
CASE D
CASE E
Average
Graph 3. Average horizontal forces for cases A, B, C, D
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-2,0E+07
-1,6E+07
-1,2E+07
-8,0E+06
-4,0E+06
0,0E+00
CASE A CASE B CASE C CASE D CASE E
Force[N]
3,5
3
2,5
2
1,5
1
0.5
Average
Graph 4. Average horizontal forces for cases A, B, C, D (sorted by the cases)
As it can be seen, graphs for horizontal force values (graphs 3 and 4) are quite similar to those
in case of vertical forces. On penetration values 0.5 to 1.5 all cases give quite similar results.
On higher penetrations it can be seen that case B gives clearly lower values (average 13%) on
all penetration depths. Reason for that is quite same as it was on case of the vertical forces.
From the table 3 comes out that in case B tearing in inner plating occurs not before the
penetration depth 3.5, which indicates that contact between the inner plating, and rock occurs
later compared to other cases.
Cases C and D give average force values equal to each other and slightly higher than cases D
and A.
Table 2. Horizontal force valuesPenetration/ case A B C D E
0,5 -2,977E+06 -3,245E+06 -3,657E+06 -3,303E+06 -2,773E+06
1 -4,606E+06 -5,206E+06 -5,237E+06 -4,854E+06 -4,796E+06
1,5 -6,496E+06 -6,152E+06 -7,163E+06 -6,775E+06 -7,394E+06
2 -9,157E+06 -7,562E+06 -1,040E+07 -9,348E+06 -1,062E+07
2,5 -1,275E+07 -9,928E+06 -1,456E+07 -1,356E+07 -1,407E+07
3 -1,500E+07 -1,291E+07 -1,577E+07 -1,498E+07 -1,713E+07
3,5 -1,734E+07 -1,550E+07 -1,903E+07 -1,679E+07 -1,806E+07
Average (1.5-2.5 [m]) -9,466E+06 -7,881E+06 -1,071E+07 -9,894E+06 -1,069E+07
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Tearing width
Flowingly tear widths are analysed. For every simulation tearing width was measured using
measures only from that part of the model where rock was moving only horizontally and
width of the rupture changing only slightly or was almost constant. It is necessary to do it so
as in some cases at the very beginning of the rupture tearing width is several times higher than
it is at the constant part. So conclusively it can be said that tear widths given in graphs x to x
and on tables x and x describes only that part of the rupture where rock was moving only
horizontally and not the very beginning of the rock. On appendices 1 to 6 measures are given
both for constant width of the tearing as well as for the widest breath. Figure 7 helps to
understand the above-described phenomena.
Figure 7.Tearing width
Values for the tearing widths are given in graphs 5 (outer plating) and 6 (inner plating).
Numerically results are presented in table 3.
CONSTANT PART
WIDEST BREATH
DIRECTION OF
THE ROCK
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1,490 1,4661,349
1,506
1,654
0
0,5
1
1,5
2
2,5
3
CASE A CASE B CASE C CASE D CASE E
Rockpenetration[m]
3.5
3
2.5
2
1.5
1
0.5
Average
Graph 5. Average breaths of the outer plating tears
1,647
0,490
1,377
0,824
1,070
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
CASE A CASE B CASE C CASE D CASE E
Rockpenetration[m]
2.5
3
3.5
Average
Graph 6. Average breaths of the inner plating tears
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Outer plating tearing
As it can be seen from the graph 5 differences in average tearing width values are quite small.
Cases A, B and D give nearly similar values. Case C (plating) gives little smaller (9 %) and
case E (girders) higher values (11 %) than other 3 cases. In case E higher tearing width can be
explained by the higher stiffness of the double-bottom. In case of double-bottom version E
greater number of longitudinal girders increases stiffness of the double-bottom and also rock
causes greater damage to the double-bottom, as bottom does not follow rock movements as
well as in other cases. In case C greater plating thickness (18 [mm]) does not ruptures as
easily as in case of thinner (12 [mm]) plates and stronger plating also deforms inner
constructions more easily.
Inner plating tearing
In case of inner bottom tearing, differences between the tearing widths are bigger. Values forthe case B (higher double-bottom) are not straight comparable to the other cases as double-
bottom heights are different and so it gives clearly the slowest tear width value. If other four
cases are compared it can be seen that case D (stiffeners) gives smallest and case A highest
value. Average tear width for the case A is twice as big as it is in case of the D version. Also
the case E (girders) gives good values compared to the cases A (35 % narrower tear) and C
(22 % narrower). In case of the bottom version D stronger stiffeners are dividing contact force
into a larger area and plating is deformed more widely and smoothly.
Table 3. Values for tearing widths
FINAL PENETRATION [m] CASE
Outer plating A B C D E
0,5 0,36 0,23 0,00 0,30 0,40
1,0 0,95 0,95 0,93 0,94 0,98
1,5 1,13 1,17 1,09 1,19 1,48
2,0 1,47 1,46 1,27 1,46 1,70
2,5 1,90 1,90 1,75 1,69 2,09
3,0 1,87 2,10 2,17 2,16 2,20
3,5 2,75 2,45 2,23 2,80 2,73
Average 1,49 1,47 1,35 1,51 1,65Inner plating A B C D E
0,5 0 0 0 0 0
1 0 0 0 0 0
1,5 0 0 0 0 0
2 0 0 0 0 0
2,5 0,32 0 0,28 0,141 0,31
3 1,87 0 1,05 0,78 1,25
3,5 2,75 0,49 2,8 1,55 1,65
Average 1,647 0,490 1,377 0,824 1,070
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Penetration depth and force values at the moment of tear initiation
In every simulation rock achieves its final penetration value during the same period of time,
but as the final penetration value is different for every simulation, rock meets structural
members like floors, girders and stiffeners in every simulations at different positions. That is
the reason why there is a quite big scatter in penetration values necessary to cause tearing to
the plating. To smooth the effect the above described problem average penetration values are
calculated and compared. Same applies also to force values at the moment of tear initiation. It
should be noted that average values are calculated using only those values where tearing has
already occurred.
0,5270,493
0,619
0,556
0,460
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
CASE A CASE B CASE C CASE D CASE E
Roc
kpenetration[m]
0.5
1
1.5
2
2.5
3
3.5
Average
Graph 7. Penetration needed to cause tearing to the outer plating
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-1,25E+07-1,17E+07
-1,96E+07
-1,38E+07
-1,10E+07
-2,5E+07
-2,0E+07
-1,5E+07
-1,0E+07
-5,0E+06
0,0E+00CASE A CASE B CASE C CASE D CASE E
Force[N]
3.5
3
2
2.5
1.5
10.5
Average
Graph 8. Force values at the moment of outer plating tear initiation
Table 4. Penetrations at the moment of outer plating tear initiation
Finalpenetration A B C D E
0,5 0,47 0,479 - 0,472 0,306
1 0,534 0,482 0,561 0,533 0,435
1,5 0,529 0,504 0,722 0,636 0,424
2 0,524 0,473 0,555 0,524 0,483
2,5 0,509 0,529 0,59 0,604 0,451
3 0,541 0,534 0,654 0,541 0,608
3,5 0,582 0,448 0,6313 0,581 0,510
Average 0,527 0,493 0,619 0,556 0,460
Outer plating
It can be seen from the graphs 7 and 8 that case E has lowest value for the penetration
necessary to cause tearing to the outer plating. Case E is very weak especially at low final
penetration values- 0.5 to 1.5 [m], where it ruptures in much lower penetration values
compared to other cases. Scatter between the case E and the other cases is large-
approximately 39 % on lower final penetration values. Scatter is decreasing when higher final
penetration values are considered and at the end it is roughly 10 %. Cases C and D are having
highest values for penetration before cracking occurs.
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Table 5. Force values at the moment of outer plating tear initiation
Final
penetration A B C D E
0,5 -6,91E+06 -7,80E+06 - -7,26E+06 -6,385E+06
1 -1,13E+07 -1,00E+07 -1,52E+07 -1,26E+07 -1,030E+07
1,5 -1,24E+07 -1,29E+07 -1,88E+07 -1,49E+07 -1,034E+07
2 -1,25E+07 -1,22E+07 -1,67E+07 -1,38E+07 -1,028E+072,5 -1,35E+07 -1,43E+07 -1,93E+07 -1,61E+07 -1,273E+07
3 -1,50E+07 -1,34E+07 -2,34E+07 -1,54E+07 -1,225E+07
3,5 -1,58E+07 -1,15E+07 -2,40E+07 -1,65E+07 -1,447E+07
Average -1,25E+07 -1,17E+07 -1,96E+07 -1,38E+07 -1,10E+07
If forces at the moment of outer plating tear initiation are under the consideration it can be
seen that case C (plating) gives 1.4 to 1.8 times higher force level than the other cases. Result
is quite obvious as it indicates that to cause tearing to the 18 [mm] plating needs much higher
force level than to cause tearing to the same type of material, but 12 [mm] in thickness. Case
E has lowest force values and scatter between the case E and other cases is approximately
25%. Reason for that is in small penetration values structure in case E does not bend so
widely as it does in other cases and tearing occurs easily.
Inner plating
Results for the necessary penetration values and forces at the moment of tear initiation are
given at graphs 9 and 10. Numerical results are in table 6.
Penetration needed to cause tearing to the inner plating is quite same for all the cases except
case B, which is obvious as case B has 50% higher double-bottom. Scatter between the cases
A, C, D, E is approximately 5% and again case E has the lowest value.
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2,363
3,100
2,351 2,3432,221
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
CASE A CASE B CASE C CASE D CASE E
Rockpenetration[m]
0.5
1
1.5
2
2.5
33.5
Average
Graph 9. Penetration needed to cause tearing to the inner plating
-2,89E+07
-3,13E+07
-3,85E+07
-3,35E+07
-3,85E+07
-5,0E+07
-4,5E+07
-4,0E+07
-3,5E+07
-3,0E+07
-2,5E+07
-2,0E+07
-1,5E+07
-1,0E+07
-5,0E+06
0,0E+00CASE A CASE B CASE C CASE D CASE E
Force[N]
0.5
1
1.5
2
2.5
3
3.5
Average
Graph 10.Forces at the moment of inner plating tear initiation
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23
In case of the force values at the moment of tear initiation differences are much bigger. Also
relations between the cases are different as they were in case of the penetrations. Case A gives
the lowest value and cases C and E are having equal force value, which is also the highest
value. In both cases (C and E) it can be explained by the fact that amount of the deformation
work to be done in order to cause tearing to the inner plating is higher and the double-bottom
still has high resistance against further rock movements.
Table 6. Penetration needed to cause tearing to the inner plating
Finalpenetration A B C D E
0,5 - - - - -
1 - - - - -
1,5 - - - - -
2 - - - - -
2,5 2,36 - 2,35 2,43 2,36
3 2,3 - 2,4 2,3 2,42
3,5 2,43 3,1 2,302 2,3 1,88
Average 2,363 3,100 2,351 2,343 2,221
Table 7. Force values at the moment of inner plating tear initiation
Finalpenetration A B C D E
0,5 - - - - -
1 - - - - -1,5 - - - - -
2 - - - - -
2,5 -2,33E+07 - -2,86E+07 -2,56E+07 -3,379E+07
3 -3,63E+07 - -4,33E+07 -3,55E+07 -4,556E+07
3,5 -2,72E+07 -3,13E+07 -4,37E+07 -3,93E+07 -3,625E+07
Average -2,89E+07 -3,13E+07 -3,85E+07 -3,35E+07 -3,85E+07
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24
CASES A, A2, A3
In cases A, A2 and A3 double-bottom design remains the same, but rock radius is changed
and has values 1.1, 2 and 3 [m]. By comparing those 3 cases it is possible to evaluate what
kind of effect rock radius has to tearing properties and force values.
Average vertical and horizontal forces
Average vertical and horizontal forces are presented on graphs 11, 12 and in table 8.
-3,5E+07
-3,0E+07
-2,5E+07
-2,0E+07
-1,5E+07
-1,0E+07
-5,0E+06
0,0E+00
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0
Penetration (m)
Force(N)
CASE A (r=1.1)
CASE A2 (r=2)
CASE A3 (r=3)
Graph 11.Average vertical forces
If vertical force values are considered (graph 11) it can be seen that increasing rock radius
from 1.1 [m] to 2 [m] increases force level approximately 1.25 times and increasing radius
from 1.1 to 3 [m] increases force level 1.6 times.
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Tear width
If tear width values are considered it can be seen that in case of outer plating it is hard to find
some trend how rock radius affects the tear width. Average tear width values are 1.49, 1.38,
1.54 [m] for rock radiuses respectively 1.1, 2.0 and 3.0 [m]. As it can be seen from the results
that increasing the rock radius decreases the tear width or vice versa. It can be explained by
the fact that rocks with different radiuses meet the structural members (especially girders) on
different positions and girders and plates are deformed by different mechanisms.
0
0,5
1
1,5
2
2,5
3
CASE A CASE A2 CASE A3
Penetration[m]
3,5
3
2,5
2
1,5
1
0,5
Average
Graph 13. Average breaths of the outer plating tears
In case of inner plating tearing it is easy to see that higher rock radiuses decrease the tear
width. In case of larger rock double-bottom is bended more heavily and rock also does not
start to cut the inner plating so early.
1.49
1.38
1.54
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0
0,5
1
1,5
2
2,5
3
CASE A CASE A2 CASE A3
Penetration[m]
3,5
3
2,5
Average
Graph 14.Average breaths of the inner plating tears
Numerical results for the outer and inner plating tear breaths are given in table 9.
Table 9. Tear breaths
OUTER PLATING INNER PLATINGPenetration A A2 A3 A A2 A3
0,5 0,36 - - - - -
1,0 0,95 0,61 - - - -
1,5 1,13 1,09 0,84 - - -
2,0 1,47 1,356 1,25 - - -
2,5 1,9 1,56 1,48 0,32 - -
3,0 1,87 1,256 1,935 0,6687 0,69 0,49
3,5 2,75 2,4 2,21 2,73 1,66 1,27
Average 1,49 1,38 1,543 1,24 1,18 0,88
1.241.18
0.88
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Penetration depth and force values at the moment of tear initiation
Penetration and force values at the moment of outer plating tear initiation are given on graphs
15, 16 and in table 10.
0,527
0,881
1,341
0,0
0,5
1,0
1,5
2,0
2,5
CASE A CASE A2 CASE A3
Pe
netration[m]
3,5
3
2,5
2
1,5
1
0,5
Average
Graph 15.Necessary penetration values to cause tearing to the outer plating
From the graphs for the outer plating penetration and forces comes out that increasing rock
radius clearly increases force level and also rock goes deeper to the double-bottom before its
plating starts tearing. Reason for that is obviously larger deformable volume and wider
bending of the whole double-bottom.
In case of penetration values there is almost linear correlation between the rock radius and the
necessary penetration. When rock radius is increased 1.8 times (2/1.1) average necessary
penetration value increases 1.67 times (0.881/0.527) and when rock radius is increased 2.7times (3/1.1) average necessary penetration value increases 2.55 times (1.341/0.527).
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-1,25E+07
-2,20E+07-2,32E+07
-3,5E+07
-3,0E+07
-2,5E+07
-2,0E+07
-1,5E+07
-1,0E+07
-5,0E+06
0,0E+00
CASE A CASE A2 CASE A3
Force[m]
3,5
3
2,5
2
1,5
1
0,5
Average
Graph 16.Forces at the moment of outer plating tear initiation
In case of the force values linear correlation does not apply anymore and changing radius
from 1.1 to 2 [m] increases average force level 1.76 times, but increase from 1.1 to 3 [m]
increases it only 1.86 times.
Table 10. Penetration depths and force values at the moment of outer plating tear
initiation
Penetration Force
Finalpenetration A A2 A3 A A2 A3
0,5 0,470 - - -6,91E+06 - -
1,0 0,534 0,776 - -1,13E+07 -1,84E+07 -
1,5 0,529 0,836 0,905 -1,24E+07 -2,16E+07 -3,13E+07
2,0 0,524 0,852 1,298 -1,25E+07 -2,64E+07 -2,49E+07
2,5 0,509 0,815 1,042 -1,35E+07 -2,56E+07 -1,76E+07
3,0 0,541 0,926 1,250 -1,50E+07 -2,01E+07 -1,85E+07
3,5 0,580 1,080 2,210 -1,58E+07 -1,97E+07 -2,37E+07
Average 0,527 0,881 1,341 -1,25E+07 -2,20E+07 -2,32E+07
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Inner plating
Penetration depths and force values at the moment of inner plating tear initiation are given on
graphs 17, 18 and in table 11.
2,365
2,564
2,754
0,0
0,5
1,0
1,5
2,0
2,5
3,0
CASE A CASE A2 CASE A3
Penetration[m]
3,5
3
2,5
Average
Graph 17.Necessary penetration values to cause tearing to the inner plating
As it can be seen from the graph 17 rock radius clearly increases the necessary penetration
values, but not as strongly as it was in case of the outer plating tear. Increasing radius from
1.1 to 2 or to 3[m] necessary penetration values increase respectively 1.08 or 1.16 times.
In case of the force values (graph 18) appear that effect of the rock radius is different from the
effect in case of the outer plating. Changing rock radius from 1.1 to 2 [m] increases the force
level 1.5 times and when radius is changed to 3 [m] force level rises 2.0 times.
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-2,90E+07
-4,40E+07
-5,90E+07
-7,0E+07
-6,0E+07
-5,0E+07
-4,0E+07
-3,0E+07
-2,0E+07
-1,0E+07
0,0E+00
CASE A CASE A2 CASE A3
Force[m]
3,5
3
2,5
Average
Graph 18.Forces at the moment of inner plating tear initiation
Table 11. Penetration depths and force values at the moment of inner plating tear
initiation
Necessary penetration Forces at the moment of tear initiationFinal
penetration A A2 A3 A A2 A3
0,5 - - - - - -
1,0 - - - - - -
1,5 - - - - - -
2,0 - - - - - -
2,5 2,362 - - -2,33E+07 - -
3,0 2,304 2,643 2,712 -3,63E+07 -4,55E+07 -5,47E+07
3,5 2,430 2,486 2,796 -2,72E+07 -4,24E+07 -6,32E+07
Average 2,365 2,564 2,754 -2,90E+07 -4,40E+07 -5,90E+07
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32
Literature
1. LS-Dyna theoretical manual
2. LS-Dyna user manual
Appendices
Appendix 1 Case A
Appendix 2 Case B
Appendix 3 Case C
Appendix 4 Case D
Appendix 5 Case A2
Appendix 6 Case A3
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A1.1 APPENDIX 1. Case A (Basic)
DB I CASE A (Basic)
Measures
Cone top radius 1.1 [m]Double-bottom
Lenght 12 [m]
Breath 17 [m]Height 1.6 [m]
Girders
Thickness 0.011 [m]
Spacing 4.26
Girder stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing0.8
[m]
Floors
Thickness 0.011 [m]
Spacing 2.4 [m]
Floor stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.71 [m]
External platingThickness 0.012 [m]
Internal plating
Thickness 0.017 [m]
Plating stiffeners
bottom
Height 0.26 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
tank-top
Height 0.26 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
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A1.2 APPENDIX 1. Case A (Basic)
DB I CASE A (Basic)
Velocity of the ship 15 m/s
Approach of the rock to db 0.5 m
Tear to outer plating (values in the moment ofinitiation)
time 2.18E-01 sec
x-disp 3.25E+00 m
z-disp 4.70E-01 m
x-force -2.56E+06 N
z-force -6.91E+06 N
Average breath of the tear 3.60E-01 m
Average X- force -2.98E+06 N
Average Z-force -5.45E+06 N
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A1.3 APPENDIX 1. Case A (Basic)
X-force (H=0.5 m)
-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
Initiation of op tear
x-force
Average
Z- force (H=0.5 m)-1.E+07
-9.E+06
-8.E+06
-7.E+06
-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+00
0 1 2 3 4 5 6 7 8 9 10
x- displacement (m)
z-force(N)
Z-force
Initiation of op tear
Average
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A1.4 APPENDIX 1. Case A (Basic)
DB I CASE A
Velocity of the ship 15 m/s
Approach of the rock to db 1.0 m
Tear to outer plating (values in themoment of initiation)
time 1.40E-01 sec
x-disp 2.08E+00 m
z-disp 5.34E-01 m
x-force -3.37E+06 N
z-force -1.13E+07 N
Average breath of the tear 9.50E-01 m
Average X- force -4.61E+06 N
Average Z-force -6.35E+06 N
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A1.5 APPENDIX 1. Case A (Basic)
X-force (H=1.0 m)
-8.E+06
-7.E+06
-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
x-force
Initation of op tear
Average
Z- force (H=1.0 m)
-1.25E+07
-1.05E+07
-8.50E+06
-6.50E+06
-4.50E+06
-2.50E+06
-5.00E+05
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force(n)
z-force
Initation of op tear
Average
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A1.6 APPENDIX 1. Case A (Basic)
DB I CASE A
Velocity of the ship 15 m/s
Approach of the rock to db 1.5 m
Tear to outer plating (values in the moment ofinitiation)
time 1.13E-01 sec
x-disp 1.69E+00 m
z-disp 5.29E-01 m
x-force -3.74E+06 N
z-force -1.24E+07 N
Average breath of the tear 1.13E+00 m
Average X- force -6.50E+06 N
Average Z-force -9.32E+06 N
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A1.7 APPENDIX 1. Case A (Basic)
X-force (H=1.5 m)
-9.E+06
-8.E+06
-7.E+06
-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+000 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force(N)
X-force
Initation of op tear
Average
Z- force (H=1.5 m)
-1.3E+07
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displaceme nt (m )
z-force
(N)
Z-force
Initation o f op tear
Average
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A1.8 APPENDIX 1. Case A (Basic)
DB I CASE A
Velocity of the ship 15 m/s
Approach of the rock to db 2.0 m
Tear to outer plating (values in the moment of initiation)
time 9.98E-02 sec
x-disp 1.49E+00 m
z-disp 5.24E-01 m
x-force -3.23E+06 N
z-force -1.25E+07 N
Average breath of the tear 1.47E+00 m
Average X- force -9.16E+06 N
Average Z-force -1.42E+07 N
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A1.9 APPENDIX 1. Case A (Basic)
X-force (H=2.0 m)
-1.35E+07
-1.15E+07
-9.50E+06
-7.50E+06
-5.50E+06
-3.50E+06
-1.50E+06
0 1 2 3 4 5 6 7 8 9 10
x-displaceme nt (m)
x-force
(N)
x-force
Initiation of op tear
Average
Z- force (H=2.0 m )
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force(N)
Z-force
Initiation of op tear
Average
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A1.10 APPENDIX 1. Case A (Basic)
DB I CASE A
Velocity of the ship 15 m/s
Approach of the rock to db 2.5 m
Tear to outer plating (values in the moment ofinitiation)
time 9.09E-02 sec
x-disp 1.35E+00 m
z-disp 5.09E-01 m
x-force -2.33E+06 N
z-force -1.35E+07 N
Average breath of the op tear 1.90E+00 m
Tear to inner bottom (values in the moment ofinitiation)
time 2.11E-01 sec
x-disp 3.15E+00 m
z-disp 2.36E+00 m
x-force -1.03E+07 N
z-force -2.33E+07 N
Average breath of the ib tear 3.20E-01 m
Average X- force -1.27E+07 N
Average Z-force -1.87E+07 N
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A1.11 APPENDIX 1. Case A (Basic)
x-force (H=2.5 m)
-1.8E+07
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
x-force(N)
X-force
Initation of op tearInitation of ib tear
Average
Z- force (H=2.5 m)-2.6E+07
-2.1E+07
-1.6E+07
-1.1E+07
-6.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A1.12 APPENDIX 1. Case A (Basic)
DB I CASE AVelocity of the ship 15 m/s
Approach of the rock to db 3.0 m
Tear to outer plating (values in the moment ofinitiation)
time 8.58E-02 sec
x-disp 1.29E+00 m
z-disp 5.41E-01 m
x-force - N
z-force -1.50E+07 N
Average breath of the op tear 5,178x1,87 m
Tear to inner bottom (values in the moment ofinitiation)
time 1.72E-01 sec
x-disp 2.57E+00 m
z-disp 2.30E+00 m
x-force - N
z-force -3.63E+07 N
Average breath of the ib tear 6.69E-01 m
Average X- force 0.00E+00 N
Average Z-force -2.06E+07 N
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A1.13 APPENDIX 1. Case A (Basic)
Z- force (H=3.0 m)
-3.9E+07
-3.4E+07
-2.9E+07
-2.4E+07
-1.9E+07
-1.4E+07
-9.0E+06
-4.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-displacement(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A1.14 APPENDIX 1. Case A (Basic)
DB I CASE A
29-Nov-01
Velocity of the ship 15 m/sApproach of the rock to db 3.5 m
Tear to outer plating (values in the moment ofinitiation)
time 8.32E-02 sec
x-disp 1.25E+00 m
z-disp 5.82E-01 m
x-force -1.17E+06 N
z-force -1.58E+07 NAverage breath of the op tear 6.91x2.75 m
Tear to inner bottom (values in the moment ofinitiation)
time 1.60E-01 sec
x-disp 2.40E+00 m
z-disp 2.43E+00 m
x-force -9.64E+06 N
z-force -2.72E+07 NAverage breath of the ib tear 2.73 m
Average X- force -1.73E+07 N
Average Z-force -2.23E+07 N
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A1.15 APPENDIX 1. Case A (Basic)
x-force (H=3.5 m)
-2.2E+07
-2.0E+07
-1.7E+07
-1.5E+07
-1.2E+07
-9.5E+06
-7.0E+06
-4.5E+06
-2.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force(N)
X-force
Initation of op tear
Initation of ib tear
Average
Z- force (H=3.5 m)
-4.0E+07
-3.5E+07
-3.0E+07
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Initation of op tearInitation of ib tear
Average
z-force
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A2.1 APPENDIX 2. Case B (DB height)
DB I CASE B
Measures
Double-bottom
Lenght 12 [m]
Breath 17 [m]
Height 2.4 [m]
Girders
Thickness 0.011 [m]
Spacing 4.26
Girder stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.8 [m]
FloorsThickness 0.011 [m]
Spacing 2.4 [m]
Floor stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.71 [m]
External plating
Thickness 0.012 [m]
Internal plating
Thickness 0.017 [m]
Plating stiffeners
bottom
Height 0.3 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
tank-top
Height 0.26 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
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A2.2 APPENDIX 2. Case B (DB height)
DB I CASE B
Velocity of the ship 15 m/s
Approach of the rock to db 0.5 m
Tear to outer plating (values in the moment of initiation)
time 2.47E-01 sec
x-disp 3.69E+00 m
z-disp 4.79E-01 m
x-force -3.18E+06 N
z-force -7.80E+06 N
Average breath of the tear 2.30E-01 m
Average X- force -3.24E+06 N
Average Z-force -5.82E+06 N
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A2.3 APPENDIX 2. Case B (DB height)
X-force (H=0.5 m)-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+00
0 1 2 3 4 5 6 7 8 9 10x-displacement (m)
x-force
(N)
Initiation o f op tear
x-forceAverage
Z- force (H=0.5 m )-1.E+07
-9.E+06
-8.E+06
-7.E+06
-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+00
0 1 2 3 4 5 6 7 8 9 10
x- displacement (m)
z-force
(N)
Z-force
Initiation of op tear
Average
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A2.4 APPENDIX 2. Case B (DB height)
DB I CASE B
Velocity of the ship 15 m/s
Approach of the rock to db 1.0 m
Tear to outer plating (values in the moment ofinitiation)
time 1.32E-01 sec
x-disp 1.97E+00 m
z-disp 4.82E-01 m
x-force -3.41E+06 N
z-force -1.00E+07 N
Average breath of the tear 9.50E-01 m
Average X- force -5.21E+06 N
Average Z-force -7.26E+06 N
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A2.5 APPENDIX 2. Case B (DB height)
X-force (H=1.0 m)
-8.E+06
-7.E+06
-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
x-force
(N)
x-force
Initation of op tearAverage
Z- force (H=1.0 m)
-1.25E+07
-1.05E+07
-8.50E+06
-6.50E+06
-4.50E+06
-2.50E+06
-5.00E+05
0 1 2 3 4 5 6 7 8 9 10
x-displacement(m)
z-force
(n)
z-force
Initation of op tear
Average
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A2.6 APPENDIX 2. Case B (DB height)
DB I CASE B
Velocity of the ship 15 m/s
Approach of the rock to db 1.5 m
Tear to outer plating (values in the moment ofinitiation)
time 1.11E-01 sec
x-disp 1.66E+00 m
z-disp 5.04E-01 m
x-force -3.91E+06 N
z-force -1.29E+07 N
Average breath of the tear 1.17E+00 m
Average X- force -6.15E+06 N
Average Z-force -8.63E+06 N
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A2.7 APPENDIX 2. Case B (DB height)
X-force (H=1.5 m)
-9.E+06
-8.E+06
-7.E+06
-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X- force
Initation of op tear
Average
Z- force (H=1.5 m)
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Z-force
Initation of op tear
Average
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A2.8 APPENDIX 2. Case B (DB height)
DB I CASE B
Velocity of the ship 15 m/s
Approach of the rock to db 2.0 m
Tear to outer plating (values in the moment ofinitiation)
time 9.60E-02 sec
x-disp 1.43E+00 m
z-disp 4.73E-01 m
x-force -2.88E+06 N
z-force -1.22E+07 N
Average breath of the tear 1.46E+00 m
Average X- force -7.56E+06 N
Average Z-force -1.09E+07 N
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A2.9 APPENDIX 2. Case B (DB height)
X-force (H=2.0 m)-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
x-force
Initiation o f op tear
Average
Z- force (H=2.0 m)
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
z-force(N)
Z-force
Initiation of op tear
Average
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A2.10 APPENDIX 2. Case B (DB height)
DB I CASE B
Velocity of the ship 15 m/s
Approach of the rock to db 2.5 m
Tear to outer plating (values in the moment ofinitiation)
time 9.22E-02 sec
x-disp 1.37E+00 m
z-disp 5.29E-01 m
x-force -2.41E+06 N
z-force -1.43E+07 N
Average breath of the tear 1.90E+00 m
Average X- force -9.93E+06 N
Average Z-force -1.44E+07 N
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A2.11 APPENDIX 2. Case B (DB height)
X-force (H=2.5 m)
-1.30E+07
-1.10E+07
-9.00E+06
-7.00E+06
-5.00E+06
-3.00E+06
-1.00E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
x-forceInitiation of op tear
Average
Z- force (H=2.5 m)
-2.0E+07
-1.8E+07
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Z-force
Initiation of op tear
Average
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A2.12 APPENDIX 2. Case B (DB height)
DB I CASE B
Velocity of the ship 15 m/s
Approach of the rock to db 3.0 m
Tear to outer plating (values in the moment of initiation)
time 8.58E-02 sec
x-disp 1.28E+00 m
z-disp 5.34E-01 m
x-force -1.88E+06 N
z-force -1.34E+07 N
Average breath of the tear 2.10E+00 m
Average X- force -1.29E+07 N
Average Z-force -1.99E+07 N
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A2.13 APPENDIX 2. Case B (DB height)
X-force (H=3.0 m)
-1.7E+07
-1.5E+07
-1.3E+07
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
x-force
(N)
X- force
Initation of op tear
Average
Z- force (H=3.0 m)
-2.5E+07
-2.3E+07
-2.0E+07
-1.8E+07
-1.5E+07
-1.3E+07
-1.0E+07
-7.5E+06
-5.0E+06
-2.5E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Z- force
Initation of op tear
Average
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A2.14 APPENDIX 2. Case B (DB height)
DB I CASE B
23-Oct-01
Velocity of the ship 15 m/sApproach of the rock to db 3.5 m
Tear to outer plating (values in the moment ofinitiation)
time 7.68E-02 sec
x-disp 1.14E+00 m
z-disp 4.48E-01 m
x-force -1.73E+06 N
z-force -1.15E+07 NAverage breath of the op tear 2.45E+00 m
Tear to inner bottom (values in the moment ofinitiation)
time 1.95E-01 sec
x-disp 2.89E+00 m
z-disp 3.10E+00 m
x-force -1.17E+07 N
z-force -3.13E+07 NAverage breath of the ib tear 4.90E-01 m
Average X- force -1.55E+07 N
Average Z-force -2.32E+07 N
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A2.15 APPENDIX 2. Case B (DB height)
X-force (H=3.5 m)
-1.9E+07
-1.7E+07
-1.5E+07
-1.3E+07
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
x-force
(N)
X- force
Initiation of op tear
Average
Initiation of IB tear
Z- force (H=3.5 m)
-3.6E+07
-3.1E+07
-2.6E+07
-2.1E+07
-1.6E+07
-1.1E+07
-6.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
z-force
(N)
Z- force
Average
Initiation of op tear
Initiation of IB tear
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A3.1 APPENDIX 3. Case C (Plating thickness)
DB I CASE C
Measures
Double-bottom
Lenght 12 [m]
Breath 17 [m]
Height 1.6 [m]
Girders
Thickness 0.011 [m]
Spacing 4.26
Girder stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.8 [m]
FloorsThickness 0.011 [m]
Spacing 2.4 [m]
Floor stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.71 [m]
External plating
Thickness 0.018 [m]
Internal plating
Thickness 0.017 [m]
Plating stiffeners
bottom
Height 0.26 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
inner bottom
Height 0.26 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
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A3.2 APPENDIX 3. Case C (Plating thickness)
DB I CASE C
Velocity of the ship 15 m/s
Approach of the rock to db 0.5 m
Tear to outer plating (values in the moment of initiation)
time no tear to op. sec
x-disp no tear to op. m
z-disp no tear to op. m
x-force no tear to op. N
z-force no tear to op. N
Average breath of the tear no tear to op. m
Average X- force -3.66E+06 N
Average Z-force -8.59E+06 N
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A3.3 APPENDIX 3. Case C (Plating thickness)
X-force (H=0.5 m)
-6.0E+06
-5.0E+06
-4.0E+06
-3.0E+06
-2.0E+06
-1.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
x-force
(N)
x-force
Average
Z- force (H=0.5 m)
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x- displacement (m)
z-force
(N)
Z-force
Average
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A3.4 APPENDIX 3. Case C (Plating thickness)
DB I CASE C
Velocity of the ship 15 m/s
Approach of the rock to db 1.0 m
Tear to outer plating (values in the moment ofinitiation)
time 1.43E-01 sec
x-disp 2.14E+00 m
z-disp 5.61E-01 m
x-force -3.77E+06 N
z-force -1.52E+07 N
Average breath of the tear 9.30E-01 m
Average X- force -5.24E+06 N
Average Z-force -7.41E+06 N
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A3.5 APPENDIX 3. Case C (Plating thickness)
X-force (H=1.0 m)
-8.E+06
-7.E+06
-6.E+06
-5.E+06
-4.E+06
-3.E+06
-2.E+06
-1.E+06
0.E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
x-force
Initation of op tear
Average
Z- force (H=1.0 m )
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 2 4 6 8 10
x-displacem ent (m)
z-force
(n)
z-force
Average
Initation of op. tear
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A3.6 APPENDIX 3. Case C (Plating thickness)
DB I CASE C
Velocity of the ship 15 m/s
Approach of the rock to db 1.5 m
Tear to outer plating (values in the moment of initiation)
time 1.32E-01 sec
x-disp 1.96E+00 m
z-disp 7.22E-01 m
x-force -3.86E+06 N
z-force -1.88E+07 N
Average breath of the tear 1.09E+00 m
Average X- force -7.16E+06 N
Average Z-force -1.05E+07 N
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A3.7 APPENDIX 3. Case C (Plating thickness)
X-force (H=1.5 m)
-1.0E+07
-9.0E+06
-8.0E+06
-7.0E+06
-6.0E+06
-5.0E+06
-4.0E+06
-3.0E+06
-2.0E+06
-1.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation of op tear
Average
Z- force (H=1.5 m)
-2.0E+07
-1.8E+07
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Z-force
Initation of op tear
Average
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A3.8 APPENDIX 3. Case C (Plating thickness)
DB I CASE C
Velocity of the ship 15 m/s
Approach of the rock to db 2.0 m
Tear to outer plating (values in the moment of initiation)
time 1.02E-01 sec
x-disp 1.52E+00 m
z-disp 5.55E-01 m
x-force -3.96E+06 N
z-force -1.67E+07 N
Average breath of the tear 1.27E+00 m
Average X- force -1.04E+07 N
Average Z-force -1.66E+07 N
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A3.9 APPENDIX 3. Case C (Plating thickness)
X-force (H=2.0 m)
-1.5E+07
-1.3E+07
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
x-force
Initiation of op tearAverage
Z- force (H=2.0 m)
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Z-force
Initiation of op tear
Average
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A3.10 APPENDIX 3. Case C (Plating thickness)
DB I CASE C
Velocity of the ship 15 m/s
Approach of the rock to db 2.5 m
Tear to outer plating (values in the moment ofinitiation)
time 9.60E-02 sec
x-disp 1.43E+00 m
z-disp 5.90E-01 m
x-force -4.05E+06 N
z-force -1.93E+07 N
Average breath of the op tear 1.75E+00 m
Tear to inner bottom (values in the moment ofinitiation)
time 2.11E-01 sec
x-disp 3.14E+00 m
z-disp 2.35E+00 m
x-force -1.16E+07 N
z-force -2.86E+07 N
Average breath of the ib tear 2.80E-01 m
Average X- force -1.46E+07 N
Average Z-force -2.21E+07 N
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A3.11 APPENDIX 3. Case C (Plating thickness)
x-force (H=2.5 m)
-2.1E+07
-1.9E+07
-1.6E+07
-1.4E+07
-1.1E+07
-8.5E+06
-6.0E+06
-3.5E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation of op tearInitation of ib tear
Average
Z- force (H=2.5 m)-3.1E+07
-2.6E+07
-2.1E+07
-1.6E+07
-1.1E+07
-6.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A3.12 APPENDIX 3. Case C (Plating thickness)
DB I CASE C
Velocity of the ship 15 m/s
Approach of the rock to db 3.0 m
Tear to outer plating (values in the moment of initiation)
time 9.216E-02 sec
x-disp 1.382E+00 m
z-disp 6.54E-01 m
x-force -1.822E+06 N
z-force -2.34E+07 N
Average breath of the op tear 6.01x2,1725 m
Tear to inner bottom (values in the moment of initiation)
time 1.766E-01 sec
x-disp 2.650E+00 m
z-disp 2.40E+00 m
x-force -1.242E+06 N
z-force -4.33E+07 N
Average breath of the ib tear 1.05E+00 m
Average X- force -1.58E+07 N
Average Z-force -2.28E+07 N
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A3.13 APPENDIX 3. Case C (Plating thickness)
x-force (H=3.0 m)
-2.3E+07
-2.1E+07
-1.8E+07
-1.6E+07
-1.3E+07
-1.1E+07
-8.0E+06
-5.5E+06
-3.0E+06
-5.0E+05
0 1 2 3 4 5 6 7 8 9 10
x-displaceme nt (m)
x-force
(N)
X-force
Initation of op tear
Initation o f ib tear
Average
Z- force (H=3.0 m)
-4.5E+07
-4.0E+07
-3.5E+07
-3.0E+07
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A3.15 APPENDIX 3. Case C (Plating thickness)
x-force (H=3.5 m)
-2.5E+07
-2.3E+07
-2.0E+07
-1.8E+07
-1.5E+07
-1.3E+07
-1.0E+07
-7.5E+06
-5.0E+06
-2.5E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displaceme nt (m)
x-force(N)
X-force
Initation of op tear
Initation of ib tear
Average
Z- force (H=3.5 m)
-5.0E+07
-4.5E+07
-4.0E+07
-3.5E+07
-3.0E+07
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displaceme nt (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A4.1 APPENDIX 4. Case D (Stiffeners)
DB I CASE D
Measures
Double-bottom
Lenght 12 [m]
Breath 17 [m]
Height 1.6 [m]
Girders
Thickness 0.011 [m]
Spacing 4.26
Girder stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.8 [m]
FloorsThickness 0.011 [m]
Spacing 2.4 [m]
Floor stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.71 [m]
External plating
Thickness 0.012 [m]
Inner bottom plating
Thickness 0.017 [m]
Plating stiffeners
bottom
Height 0.3 [m]
Thickness 0.00528/0.30 [m]
Spacing 0.71 [m]
inner bottom
Height 0.26 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
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A4.2 APPENDIX 4. Case D (Stiffeners)
DB I CASE D
Velocity of the ship 15 m/s
Approach of the rock to db 0.5 m
Tear to outer plating (values in the moment of initiation)
INITATION
time 3.07E-01 sec
x-disp 4.59E+00 m
z-disp 4.72E-01 m
x-force -3.67E+06 N
z-force -7.26E+06N
TERMINATION
time 3.14E-01 sec
x-disp 4.68E+00 m
z-disp 4.72E-01 m
x-force -2.86E+06 N
z-force -6.81E+06 N
Average breath of the tear 1.15E-01 m
Length of the tear 3.04E-01 m
Average X- force -3.30E+06 N
Average Z-force -7.44E+06 N
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A4.4 APPENDIX 4. Case D (Stiffeners)
DB I CASE D
Velocity of the ship 15 m/s
Approach of the rock to db 1.0 m
Tear to outer plating (values in the moment ofinitiation)
time 1.40E-01 sec
x-disp 2.08E+00 m
z-disp 5.33E-01 m
x-force -3.72E+06 N
z-force -1.26E+07 N
Average breath of the tear 9.40E-01 m
Average X- force -4.85E+06 N
Average Z-force -6.76E+06 N
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A4.5 APPENDIX 4. Case D (Stiffeners)
X-force (H=1.0 m )
-8.0E+06
-7.0E+06
-6.0E+06
-5.0E+06
-4.0E+06
-3.0E+06
-2.0E+06
-1.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacemen t (m)
x-force
(N)
x-force
Initation of op tear
Average
Z- force (H=1.0 m)
-1.3E+07
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement(m)
z-force
(n)
z-force
Initation of op tear
Average
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A4.6 APPENDIX 4. Case D (Stiffeners)
DB I CASE D
Velocity of the ship 15 m/s
Approach of the rock todb
1.5 m
Tear to outer plating (values in the moment ofinitiation)
time 1.24E-01 sec
x-disp 1.85E+00 m
z-disp 6.36E-01 m
x-force -4.43E+06 N
z-force -1.49E+07 N
Average breath of the
tear
1.19E+00 m
Average X- force -6.77E+06 N
Average Z-force -9.66E+06 N
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A4.8 APPENDIX 4. Case D (Stiffeners)
DB I CASE D
Velocity of the ship 15 m/s
Approach of the rock to db 2.0 m
Tear to outer plating (values in the moment of initiation)
time 9.98E-02 sec
x-disp 1.49E+00 m
z-disp 5.24E-01 m
x-force -3.56E+06 N
z-force -1.38E+07 N
Average breath of the tear 1.46E+00 m
Average X- force -9.35E+06 N
Average Z-force -1.48E+07 N
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A4.9 APPENDIX 4. Case D (Stiffeners)
X-force (H=2.0 m)
-1.3E+07
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
x-force
Initiation of op tear
Average
Z- force (H=2.0 m)
-2.0E+07
-1.8E+07
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displaceme nt (m)
z-force
(N)
Z-force
Initiation of op tear
Average
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A4.10 APPENDIX 4. Case D (Stiffeners)
DB I CASE D
Velocity of the ship 15 m/s
Approach of the rock to db 2.5 m
Tear to outer plating (values in the moment of initiation)
time 9.60E-02 sec
x-disp 1.44E+00 m
z-disp 6.04E-01 m
x-force -2.63E+06 N
z-force -1.61E+07 N
Average breath of the op tear 1.69E+00 m
1 st tear to inner bottom (values in the moment ofinitiation)
time 2.18E-01 sec
x-disp 3.26E+00 m
z-disp 2.43E+00 m
x-force -1.04E+07 N
z-force -2.56E+07 N
length of the tear 2.20 m
Average breath of the ib tear 0.50m
2nd tear to inner bottom (values in the moment ofinitiation)
time 5.03E-01 sec
x-disp 7.55E+00 m
z-disp 2.50E+00 m
x-force -1.24E+07 N
z-force -1.93E+07 N
length of the tear 2.25 mAverage breath of the ib tear 0.14 m
Average X- force -1.36E+07 N
Average Z-force -2.02E+07 N
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A4.11 APPENDIX 4. Case D (Stiffeners)
x-force (H=2.5 m)
-1.7E+07
-1.5E+07
-1.3E+07
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-forceInitation of op tear
Initation of1st ib tear
Average
Z- force (H=2.5 m)-3.0E+07
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
Z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A4.12 APPENDIX 4. Case D (Stiffeners)
DB I CASE D
Velocity of the ship 15 m/s
Approach of the rock todb
3.0 m
Tear to outer plating (values in the moment ofinitiation)
time 8.58E-02 sec
x-disp 1.29E+00 m
z-disp 5.41E-01 m
x-force -1.53E+06 N
z-force -1.54E+07 N
Average breath of the op
tear
5.05x2,16 m
Tear to inner bottom (values in the moment ofinitiation)
time 1.72E-01 sec
x-disp 2.57E+00 m
z-disp 2.30E+00 m
x-force -1.02E+07 N
z-force -3.55E+07 N
Average breath of the ibtear
7.80E-01 m
Average X- force -1.50E+07 N
Average Z-force -2.15E+07 N
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A4.13 APPENDIX 4. Case D (Stiffeners)
x-force (H=3.0 m)
-2.0E+07
-1.8E+07
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation of op tear
Initation o f ib tear
Average
Z- force (H=3.0 m)-3.9E+07
-3.4E+07
-2.9E+07
-2.4E+07
-1.9E+07
-1.4E+07
-9.0E+06
-4.0E+06
0 1 2 3 4 5 6 7 8 9 10x-displacem ent (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A4.14 APPENDIX 4. Case D (Stiffeners)
DB I CASE D
Velocity of the ship 15 m/s
Approach of the rock to db 3.5 m
Tear to outer plating (values in the moment ofinitiation)
time 8.32E-02 sec
x-disp 1.25E+00 m
z-disp 5.81E-01 m
x-force -1.39E+06 N
z-force -1.65E+07 N
Average breath of the op tear 6.7x2.8 m
Tear to inner bottom (values in the moment ofinitiation)
time 1.55E-01 sec
x-disp 2.32E+00 m
z-disp 2.30E+00 m
x-force -1.01E+07 N
z-force -3.93E+07 N
Average breath of the ib tear 1.55 m
Average X- force -1.68E+07 N
Average Z-force -2.33E+07 N
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A4.15 APPENDIX 4. Case D (Stiffeners)
x-force (H=3.5 m)
-2.2E+07
-2.0E+07
-1.7E+07
-1.5E+07
-1.2E+07
-9.5E+06
-7.0E+06
-4.5E+06
-2.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation of op tear
Initation of ib tear
Average
Z- force (H=3.5 m)
-4.0E+07
-3.5E+07
-3.0E+07
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A5.1 APPENDIX 5. Case A2 (rock radius=2 [m])
DB I CASE A2 (rock radius= 2[m])
Measures
Cone top radius 2 [m]Double-bottom
Lenght 12 [m]
Breath 17 [m]
Height 1.6 [m]
Girders
Thickness 0.011 [m]
Spacing 4.26
Girder stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.8 [m]
Floors
Thickness 0.011 [m]
Spacing 2.4 [m]
Floor stiffeners
Thickness 0.012 [m]
Breath 0.15 [m]
Spacing 0.71 [m]
External plating
Thickness 0.012 [m]
Internal plating
Thickness 0.017 [m]
Plating stiffeners
bottom
Height 0.26 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
tank-top
Height 0.26 [m]
Thickness 0.00361/0.26 [m]
Spacing 0.71 [m]
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A5.2 APPENDIX 5. Case A2 (rock radius=2 [m])
DB I CASE A2
Velocity of the ship 15 m/s
Approach of the rock to db 0.5 m
Tear to outer plating (values in the momentof initiation)
time #N/A sec NO TEAR
x-disp #N/A m
z-disp #N/A m
x-force #N/A N
z-force #N/A N
Average breath of the op tear m
Tear to inner bottom (values in themoment of initiation)
time #N/A sec NO TEAR
x-disp #N/A m
z-disp #N/A m
x-force #N/A N
z-force #N/A N
Average breath of the ib tear m
Average X- force -3.05E+06 N
Average Z-force -8.22E+06 N
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A5.3 APPENDIX 5. Case A2 (rock radius=2 [m])
x-force (H=0.5 m)
-5.0E+06
-4.5E+06
-4.0E+06
-3.5E+06
-3.0E+06
-2.5E+06
-2.0E+06
-1.5E+06
-1.0E+06
-5.0E+05
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation of op tear
Initation of ib tear
Average
Z- force (H=0.5 m)
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Initation of op tearInitation o f ib tear
Average
z-force
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A5.4 APPENDIX 5. Case A2 (rock radius=2 [m])
DB I CASE A2
Velocity of the ship 15 m/s
Approach of the rock to db 1 m
Tear to outer plating (values in the moment ofinitiation)
time 1.728E-01 sec
x-disp 2.592E+00 m
z-disp 7.757E-01 m
x-force -2.701E+06 N
z-force -1.840E+07 N
Average breath of the op tear 6.10E-01 m
Tear to inner bottom (values in the moment ofinitiation)
time #N/A sec NO TEAR
x-disp #N/A m
z-disp #N/A m
x-force #N/A N
z-force #N/A N
Average breath of the ib tear m
Average X- force -4.93E+06 N
Average Z-force -7.40E+06 N
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A5.5 APPENDIX 5. Case A2 (rock radius=2 [m])
x-force (H=1.0 m)
-8.0E+06
-7.0E+06
-6.0E+06
-5.0E+06
-4.0E+06
-3.0E+06
-2.0E+06
-1.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force(N)
X-force
Initation of op tea rInitation o f ib tear
Average
Z- force (H=1.0 m)-1.9E+07
-1.7E+07
-1.5E+07
-1.3E+07
-1.1E+07
-9.0E+06
-7.0E+06
-5.0E+06
-3.0E+06
-1.0E+06
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A5.6 APPENDIX 5. Case A2 (rock radius=2 [m])
DB I CASE A2
Velocity of the ship 15 m/s
Approach of the rock to db 1.5 m
Tear to outer plating (values in the moment ofinitiation)
time 1.408E-01 sec
x-disp 2.112E+00 m
z-disp 8.356E-01 m
x-force -1.770E+06 N
z-force -2.155E+07 N
Average breath of the op tear 1.09E+00 m
Tear to inner bottom (values in the moment ofinitiation)
time #N/A sec NO TEAR
x-disp #N/A m
z-disp #N/A m
x-force #N/A N
z-force #N/A N
Average breath of the ib tear m
Average X- force -7.13E+06 N
Average Z-force -1.09E+07 N
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A5.7 APPENDIX 5. Case A2 (rock radius=2 [m])
x-force (H=1.5 m)
-1.0E+07
-9.0E+06
-8.0E+06
-7.0E+06
-6.0E+06
-5.0E+06
-4.0E+06
-3.0E+06
-2.0E+06
-1.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation of op tear
Initation of ib tear
Average
Z- force (H=1.5 m )
-2.3E+07
-2.1E+07
-1.8E+07
-1.6E+07
-1.3E+07
-1.1E+07
-8.0E+06
-5.5E+06
-3.0E+06
-5.0E+05
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A5.8 APPENDIX 5. Case A2 (rock radius=2 [m])
DB I CASE A2
Velocity of the ship 15 m/s
Approach of the rock to db 2 m
Tear to outer plating (values in the momentof initiation)
time 1.229E-01 sec
x-disp 1.843E+00 m
z-disp 8.519E-01 m
x-force -1.263E+06 N
z-force -2.640E+07 N
Average breath of the op tear 3.52x1.356 m
Tear to inner bottom (values in the momentof initiation)
time #N/A sec NO TEAR
x-disp #N/A m
z-disp #N/A m
x-force #N/A N
z-force #N/A N
Average breath of the ib tear m
Average X- force -1.03E+07 N
Average Z-force -1.73E+07 N
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A5.10 APPENDIX 5. Case A2 (rock radius=2 [m])
DB I CASE A2
Velocity of the ship 15 m/s
Approach of the rock to db 2.5 m
Tear to outer plating (values in the moment ofinitiation)
time 1.088E-01 sec
x-disp 1.632E+00 m
z-disp 8.150E-01 m
x-force -1.070E+06 N
z-force -2.559E+07 N
Average breath of the op tear 5.22x1.56 m
Tear to inner bottom (values in the moment ofinitiation)
time #N/A sec NO TEAR
x-disp #N/A m
z-disp #N/A m
x-force #N/A N
z-force #N/A N
Average breath of the ib tear m
Average X- force -1.42E+07 N
Average Z-force -2.41E+07 N
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A5.11 APPENDIX 5. Case A2 (rock radius=2 [m])
x-force (H=2.5 m)
-1.8E+07
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation of op tear
Initation of ib tear
Average
Z- force (H=2.5 m )
-3.5E+07
-3.0E+07
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
z-force
(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A5.12 APPENDIX 5. Case A2 (rock radius=2 [m])
DB I CASE A2
Velocity of the ship 15 m/s
Approach of the rock to db 3 m
Tear to outer plating (values in the moment of initiation)
time 1.062E-01 sec
x-disp 1.594E+00 m
z-disp 9.258E-01 m
x-force -4.875E+06 N
z-force -2.013E+07 N
Average breath of the op tear 6.78x2.08 m
Tear to inner bottom (values in the moment of initiation)
time 1.920E-01 sec
x-disp 2.880E+00 m
z-disp 2.643E+00 m
x-force 0.000E+00 N
z-force -4.554E+07 N
Average breath of the ib tear 0.69 m
Average X- force -1.57E+07 N
Average Z-force -2.32E+07 N
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A5.13 APPENDIX 5. Case A2 (rock radius=2 [m])
x-force (H=3.0 m)
-2.0E+07
-1.8E+07
-1.6E+07
-1.4E+07
-1.2E+07
-1.0E+07
-8.0E+06
-6.0E+06
-4.0E+06
-2.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation of op tear
Initation of ib tear
Average
Z- force (H=3.0 m )
-5.0E+07
-4.5E+07
-4.0E+07
-3.5E+07
-3.0E+07
-2.5E+07
-2.0E+07
-1.5E+07
-1.0E+07
-5.0E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacem ent (m)
z-force(N)
Initation of op tear
Initation of ib tear
Average
z-force
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A5.14 APPENDIX 5. Case A2 (rock radius=2 [m])
DB I CASE A2
Velocity of the ship 15 m/s
Approach of the rock to db 3.5 m
Tear to outer plating (values in the moment of initiation)
time 1.062E-01 sec
x-disp 1.594E+00 m
z-disp 1.080E+00 m
x-force -6.371E+06 N
z-force -1.969E+07 N
Average breath of the op tear 5.32x2.4 m
Tear to inner bottom (values in the moment of initiation)
time 1.626E-01 sec
x-disp 2.438E+00 m
z-disp 2.486E+00 m
x-force 0.000E+00 N
z-force -4.237E+07 N
Average breath of the ib tear 3.84x1.66 m
Average X- force -1.80E+07 N
Average Z-force -2.64E+07 N
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A5.15 APPENDIX 5. Case A2 (rock radius=2 [m])
x-force (H=3.5 m)-2.5E+07
-2.3E+07
-2.0E+07
-1.8E+07
-1.5E+07
-1.3E+07
-1.0E+07
-7.5E+06
-5.0E+06
-2.5E+06
0.0E+00
0 1 2 3 4 5 6 7 8 9 10
x-displacement (m)
x-force
(N)
X-force
Initation o f op tear
Initation o f ib tear
Average
Z- force (H=3.5 m)-4.8E+07
-4.3E+07
-3.8E+07
-3.3E+07
-2.8E+07
-2.3E+07
-1.8E+07
-1.3E+07
-8.0E+06