Abstract: This paper focuses on the CAD / CAE-FEM structural modelling techniques applied to double-shell ship hull strength analysis. The full length CAD / FEM models included in this study are developed for two special maritime ships: a LNG liquefied natural gas carrier and a LPG liquefied petroleum gas carrier. The ships strength analyses are carried out under the following loads: ship hull, cargo and ballast weight, still water and equivalent quasi-static head wave pressure. The ship hull equilibrium position into the surrounding water domain reference system and the ship strength assessment are based on own iterative algorithm, implemented as user procedure into the integrated CAD / CAE-FEM SolidWorks Cosmos/M program. This study has been accomplished for the Romanian Scientific Research Authority ANCS-CEEX-M1/X2C16/4409/06-09.
Key words: CAD / FEM models, liquefied gas carrier ships.
1. Introduction
The nowadays-naval architecture advanced ship design process requires developing three-dimensional 3D CAD / CAE-FEM ship hull structures models, for the assessment of the ship global strength based on the Finite Element Method (Jang & Hong, 2009). Instead of using standard structural models, extended only on several cargo-holds (Eyres, 2006, GL, 2008), in this study the new 3D-FEM full ship hull length models (Mansour & Liu, 2008) are developed, in order to increase ship structure strength assessment accuracy.
The vertical in plane equilibrium of the 3D-FEM full ship model, under onboard masses and external head quasi-static wave pressure, is acquired based on own iterative algorithm, implemented as user procedure in the SolidWorks Cosmos/M program (SWCM, 2008). This topic is approached in Chapter 2.
In this study, the numerical global strength analyses are carried out for two double-shell large maritime ship hull structures: a LNG liquefied natural gas carrier, with membrane type cargo-tanks, and a LPG liquefied petroleum gas carrier, with structural independent cargo-tanks. For both ships are considered the full cargo and ballast load cases, under head wave condition. These topics are approached in Chapters 3- 4.
The conclusions of this study are included in Chapter 5.
2. THE THEORETICAL BACKGROUND FOR THE SHIP STRENGTH ANALYSIS
The global ship strength analysis, based on 3D-FEM hull models extended over the whole length of the ship, compared to the standard several cargo-holds models (GL, 2008) and classical 1D-FEM models (Hughes, 1988), has the following main advantages:
- the real ship 3D structure is taken into account;
- a reduced number of boundary conditions;
- the 3D stress and deformation distributions are obtained, predicting the domains with higher risk.
The main steps for the ship strength analysis, based on full extended 3D-FEM models, are the following:
- the 3D-CAD ship hull offset lines generation;
- the 3D-CAD ship hull structure modelling;
- the 3D-FEM ship hull structure model meshing, using thick shell elements (Zienkiewicz & Taylor, 2000);
- the boundary conditions on the 3D-FEM model;
The following boundary conditions are applied: the symmetry conditions at the nodes disposed in the central plane of the ship (one side model); the vertical support conditions at two nodes disposed at the ship hull extremities, in the central plane, noted NDaft at aft peak and NDfore at fore peak.
- the loading conditions on the 3D-FEM model;
The loads acting over the ship hull structure are: the weight from the onboard masses and the external equivalent quasi-static head wave pressure load, hw=0, still water, and hw0, according to the Germanischer Lloyd (GL, 2008), using own iterative algorithm for the free floating and trim conditions equilibrium, with objective functions based on the two vertical reaction forces at NDaft, NDfore nodes. At the vertical equilibrium conditions, for still water or equivalent quasi-static head wave cases, the reaction forces RFZ(NDaft), RFZ(NDfore) in the two vertical supports have to become zero.
- the numerical results for ship hull strength assessment.
Based on 3D CAD / FEM models full extended over the ship hull, the following numerical results are obtained: the ship vertical equilibrium parameters, the deformation and the stress distributions, pointing out the hot spot domains over the whole ship hull length.
Figure 1 presents the main flow chart of own iterative algorithm for the ship vertical free floating and trim conditions equilibrium, implemented as user procedure file GS_PRESS.GEO in the SolidWorks Cosmos/M (SWCM, 2008) CAD /FEM program, also used at each iteration as linear static structural analysis solver.
In Figure 1 are included the following notations: L ship length; xF the water plane centre position; hw the equivalent quasi-static wave height; NDaft, NDfore the aft and fore peak nodes, where the objective functions vertical reaction forces RFZ are evaluated; dm, daft, dfore the ship draughts (at still water) and the median wave plane parameters; trim the longitudinal ship angle.
Fig.1. Main flow chart of own GS_PRESS user procedure
3. the 3D CAD / FEM LNG SHIP model
and the STRENGTH assessment
The first analysed ship is a large LNG 150000 m3 carrier, with membrane type cargo-tanks and hull scantlings according to Germanischer Lloyd (GL, 2008).
Table 1 presents the main characteristics of the LNG 3D CAD /FEM model (Figures 3.a,b,c), as following:
- L,B,H,hwGL are the ship length, breadth, depth and the wave maximum statistical height (GL, 2008);
- E,ï®,ï²,ReH,ï³adm,ï´adm are isotropic naval A, AH36 steel properties and the stress admissible values (GL, 2008);
-PTmax, CRmax, SFmax, NDmax, ELmax, EGmax, ELsize are the number of 3D CAD / FEM model objects.
Table 2 presents the LNG full cargo and ballast loading cases, where ï„ is the ship displacement; dm, daft, dfore are the ship medium, aft and fore peak draughts (still water).
Table 3 presents a synthesis of LNG hull structure strength assessment, including the maximum deck (ï³adm=175 N/mm2),bottom (ï³adm=243 N/mm2) and side neutral axis (ï´adm=110 N/mm2) stresses, hwGL=10.715m.
Table 1. Main characteristics of LNG 3D CAD/FEM model
L=289.3 m
ReH_A=235 N/mm2
PTmax=19144
B=43.30 m
ï³adm_A=175 N/mm2
CRmax=103927
H=25.60 m
ï´adm_A=110 N/mm2
SFmax=46560
hwGL=10.715 m
ReH_AH36=355 N/mm2
NDmax=27623
E=2.1 1011 N/m2
ï³adm_AH36=243 N/mm2
ELmax=93435
ï®=0.3
ï´adm_AH36=153 N/mm2
EGmax =583
ï²steel=7.7 t/m3
NDaft / NDfore=2007 / 26665
ELsize=0.8/1.6m
Table 2. The LNG 150000 m3 carrier loading cases
Load case
ï„ [t]
dm[m]
daft[m]
dfore[m]
Full cargo
105881
11.80
11.80
11.80
Ballast
73167
8.50
10.00
7.00
Table 3. The LNG 3D CAD/FEM model maximum stresses
Stress [N/mm2]
hwGL=10.715m
Full cargo load case
Ballast load case
Sagging
Hogging
Sagging
Hogging
|ï³x-max| deck
max/adm (175)
174.82
65.81
115.40
100.00
1.00
0.38
0.66
0.57
|ï³x-max| bottom
max/adm (243)
116.30
54.55
80.46
70.70
0.48
0.22
0.33
0.29
|ï´xz-max| side n-n
max/adm (110)
96.20
23.30
55.36
37.20
0.87
0.21
0.50
0.34
|ï³von-max| deck
max/adm (175)
170.20
63.55
110.70
96.34
0.97
0.36
0.66
0.55
|ï³von-max| bottom
max/adm (243)
104.90
50.18
72.87
65.35
0.43
0.21
0.30
0.27
In the next figures are included the following data:
- Figure 2, the wave profile, sagging & hogging, hwGL= 10.715 m, full cargo, from iterative procedure (Fig.1);
- Figures 3.a,b,c, the 3D CAD/FEM hull model of the LNG carrier, with cargo-holds and fore peak details;
- Figures 4.a,b, the maximum deck shell equivalent von Mises stress ï³vonDmax diagrams, based on LNG 3D CAD/FEM model, full cargo, wave height hw=012m.
Fig.2 LNG wave profile, sagging & hogging, hwGL=10.715m, full
Fig.3.a The LNG 150000 m3 carrier 3D CAD/FEM model
Fig.3.b The LNG 3D CAD/FEM model, detail in cargo-holds
Fig.3.c The LNG 3D CAD/FEM model, detail in fore peak
Fig.4.a LNG max. von Mises deck stress [N/mm2], sagging, full
Fig.4.b LNG max. von Mises deck stress [N/mm2],hogging, full
3. the 3D CAD / FEM LPG ship model
and the STRENGTH assessment
The second analysed ship is a LPG 10000 m3 carrier, with structural independent cargo-tanks and hull structure scantlings according to Germanischer Lloyd Rules (GL, 2008).
Table 4 presents the main characteristics of the LPG 3D CAD / FEM model (Figures 6.a,b,c), including the same items as in Table 1.
Table 5 presents the LPG full cargo and ballast loading cases, including the same items as in Table 2.
Table 6 presents a synthesis of LPG hull structure strength assessment, including the maximum deck (ï³adm=175 N/mm2),bottom (ï³adm=175 N/mm2) and side neutral axis (ï´adm=110 N/mm2) stresses, hwGL=8.45m.
Table 4. Main characteristics of LPG 3D CAD/FEM model
L=125.6 m
ï²steel=7.7 t/m3
PTmax=15214
B=20.50 m
ReH_A=235 N/mm2
CRmax=43672
H=12.00 m
ï³adm_A=175 N/mm2
SFmax=20326
hwGL=8.45 m
ï´adm_A=110 N/mm2
NDmax=19680
E=2.1 1011 N/m2
NDaft / NDfore=4071 / 19125
ELmax=49657
ï®=0.3
ELsize=0.8/1.6 m
EGmax =104
Table 5. The LPG 10000 m3 carrier loading cases
Load case
ï„ [t]
dm[m]
daft[m]
dfore[m]
Full cargo
13194
7.64
7.64
7.64
Ballast
8412
5.25
6.50
4.00
Table 6. The LPG 3D CAD/FEM model maximum stresses
Stress [N/mm2]
hwGL=8.45m
Full cargo load case
Ballast load case
Sagging
Hogging
Sagging
Hogging
|ï³x-max| deck
max/adm (175)
109.80
80.11
57.91
107.50
0.63
0.46
0.33
0.61
|ï³x-max| bottom
max/adm (175)
66.82
55.26
39.19
67.68
0.38
0.32
0.22
0.39
|ï´xz-max| side n-n
max/adm (110)
28.19
16.75
21.45
23.81
0.26
0.15
0.20
0.22
|ï³von-max| deck
max/adm (175)
104.10
78.46
54.84
99.80
0.59
0.45
0.31
0.57
|ï³von-max| bottom
max/adm (175)
56.77
49.30
37.22
59.98
0.32
0.28
0.21
0.34
In the next figures are included the following data:
- Figures 5.a.b, the wave profile, sagging & hogging, hwGL=8.45m, full cargo, from iterative procedure (Fig.1);
- Figures 6.a,b,c, the 3D CAD/FEM hull model of the LPG carrier, with cargo-holds and aft peak details;
- Figures 7.a,b, the maximum deck shell equivalent von Mises stress ï³vonDmax diagrams, based on LPG 3D CAD/FEM model, full cargo, wave height hw=012m.
Fig.5.a LPG wave profile, sagging hwGL=8.45m, full cargo
Fig.5.b LPG wave profile, hogging hwGL=8.45m, full cargo
Fig.6.a The LPG 10000 m3 carrier 3D CAD / FEM model
Fig.6.b The LPG 3D CAD/FEM model, detail in cargo-holds
Fig.6.c The LPG 3D CAD / FEM model, detail in aft peak
Fig.7.a LPG max. von Mises deck stress [N/mm2], sagging, full
Fig.7.b LPG max. von Mises deck stress [N/mm2],hogging, full
5. conclusions
Based on the numerical results, obtained with the method described in Chapter 2, for the LNG 150000 m3 liquefied natural gas carrier (Chapter 3) and the LPG 10000 m3 liquefied petroleum gas carrier (Chapter 4), the following conclusions result:
1. The 3D-FEM hull models full extended over the ship length (Figures 3.a-c,6.a-c) make possible to obtain the stress distribution over the whole structure (Figures 4.a-b,7.a-b), predicting the domains with higher risk, which cannot be achieved with standard several cargo-holds 3D-FEM or classical 1D-FEM models. The stress hot-spot domains are obtained mainly around the transversal bulkhead and frame structures.
2. Both gas carrier ships satisfy the strength criteria, according to the Germanischer Lloyd Rules (GL, 2008), under equivalent quasi-static head wave load. For the LNG carrier (Table 3, hwGL=10.715m) results at full cargo case stress ratio max/adm=0.211.001 and at ballast case stress ratio max/adm=0.270.66 1. For the LPG carrier (Table 6, hwGL=8.45m) results at full cargo case stress ratio max/adm=0.150.631 and at ballast case stress ratio max/adm=0.200.611.
3. The ship hull strength assessment based on the method presented in Chapter 2, with 3D CAD / FEM hull models developed over the whole ship length, requires standard computational resources, making possible to be implemented as practical procedure in the current ship structural design process.
4. The own algorithm for acquiring ship hull structure equilibrium in head waves, based on 3D CAD/FEM full length models (Chapter 2), can be developed for oblique wave cases, including as third iteration parameter the ship roll angle. Also, this strength assessment method can be applied for other ship types and loading cases.
