Post on 26-Oct-2021
October 18, 2017
Reinier Bos (TU Delft), Mathieu Castaing (GTT), Mirek Kaminski (TU Delft)
Selecting potentially critical sloshingloads on an LNG cargo containment system
CCS assessment
Structural capac-ity using FEA
Apply calibrationbased on opera-tional experience
Hydrodynamicloads using smallscale (1:20-1:40)model tests
C
d
D
C/D
A
Details: Gervaise, De Sèze, and Maillard 2009
This could be improved if we know what the structure feels.
1 of 22
CCS assessment
Structural capac-ity using FEA
Apply calibrationbased on opera-tional experience
Hydrodynamicloads using smallscale (1:20-1:40)model tests
C
d
D
C/D
A
Details: Gervaise, De Sèze, and Maillard 2009
This could be improved if we know what the structure feels.
1 of 22
Demands critical load selection
Compared to failure analysis:
• Easy to arrange
• Quick to judge
• Pessimistic
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Background
Sketch of the Mk III cargo containment system (CCS) as designed by GTT
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Simplified response model
• Sandwich theory (Carlsson and Kardomateas 2011)
• Beam on elastic foundation (Hetenyi 1946)
• Beam on elastic foundation with shear (Das 2011)
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Linear analytical model
analytical FEA
w*(z)
z
(ρpAp +1
3ρf h
2f )∂2w(x , t)
∂t2︸ ︷︷ ︸inertia
+EpIp∂4w(x , t)
∂x4︸ ︷︷ ︸beam bending
− Ef hf6(1+ νf )
∂2w(x , t)
∂x2+
Ef
hf (1− ν2f )w(x , t)︸ ︷︷ ︸
foundation shear and compression
= p(x , t)
Coe�cients using Finlayson 1972
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Linear analytical model
analytical FEA
w*(z)
z
(ρpAp +1
3ρf h
2f )∂2w(x , t)
∂t2︸ ︷︷ ︸inertia
+EpIp∂4w(x , t)
∂x4︸ ︷︷ ︸beam bending
− Ef hf6(1+ νf )
∂2w(x , t)
∂x2+
Ef
hf (1− ν2f )w(x , t)︸ ︷︷ ︸
foundation shear and compression
= p(x , t)
Coe�cients using Finlayson 1972
5 of 22
Analytical model
0.014 0.085 0.17 0.34
−0.1
−0.05
0
position (m)
displacement(m
m)
AnaSFMTSFBTMFBTMFMT
0.014 0.085 0.17 0.340
0.5
1
load
(MPa)
Indentation at top (sliding)
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Analytical model
0.014 0.085 0.17 0.34
−0.1
−0.05
0
position (m)
stress
(MPa) Ana
SFMTSFBTMFBTMFMT
0.014 0.085 0.17 0.340
0.5
1
load
(MPa)
Stress at top (sliding)
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Analytical model
0.014 0.085 0.17 0.34
−0.2
−0.1
0
position (m)
stress
(MPa) Ana
SFMTSFBTMFBTMFMT
0.014 0.085 0.17 0.340
0.5
1
load
(MPa)
Stress at top (free) � edge shear force?
6 of 22
Analytical model
0.014 0.085 0.17 0.34
0.8
1
1.2
1.4
position (m)
SCF(-)
AnaSFMTSFBTMFBTMFMT
Stress concentration factor at mastic
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Solution procedure
1. Vibration modes and frequencies
2. Integrate vibration over time, for each mode
3. Reconstruct deformation to obtain stresses
σz(x , z = h) =
(Ef
hf(1− ν2f
)) · w −(
Ef hf6(1+ νf )
)·(∂2w
∂x2
)
σz(x , z = 0) =
(Ef
hf(1− ν2f
)) · w
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Response to a single load
Vibration modes and frequencies
0.00 0.17 0.34position (m)
1.0
0.5
0.0
0.5
1.0
modal sh
ape (
m)
1000 2000 3000 4000 5000frequency (Hz)
First �ve modes are colored, rest in grey, total 31 modes
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Displacement
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030ti
me (
s)
0
150000
300000
450000
600000
750000
900000
1050000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0.00018
0.00015
0.00012
0.00009
0.00006
0.00003
0.00000
0.00003
0.00006
Load (Pa) and displacement (m)
A local load induces a not-so-local response
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Displacement
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030ti
me (
s)
0
150000
300000
450000
600000
750000
900000
1050000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0.00018
0.00015
0.00012
0.00009
0.00006
0.00003
0.00000
0.00003
0.00006
Load (Pa) and displacement (m)
A local load induces a not-so-local response
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Stresses
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030ti
me (
s)
210000
180000
150000
120000
90000
60000
30000
0
30000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
75000
60000
45000
30000
15000
0
15000
Top and bottom stress (Pa)
Response at the top is more concentrated and therefore higher than at the bottom.
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Stresses
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030ti
me (
s)
210000
180000
150000
120000
90000
60000
30000
0
30000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
75000
60000
45000
30000
15000
0
15000
Top and bottom stress (Pa)
Response at the top is more concentrated and therefore higher than at the bottom.
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Time integral of modes
0.0001 0.0011 0.0021 0.0030time (s)
0.0002
0.0001
0.0000
0.0001
0.0002
0.0003
exci
tati
on (
-)
Only three modes (seem to) contribute to the response.
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Time integral of modes
0.0001 0.0011 0.0021 0.0030time (s)
0.0002
0.0001
0.0000
0.0001
0.0002
0.0003
exci
tati
on (
-)
Only three modes (seem to) contribute to the response.
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Systematic study
Load cases
All combinations of:
• Location [0, 0.06, 0.12, 0.17] m from side
• Width [0.01, 0.05, 0.10, 0.17] m build up (triangular)
• Time [0.001, 0.01, 0.1, 1] s rise time
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Results: maximum top and bottom stress
0
0.01
0.05
0.1
0.17
0.06 0.12 0.17
Load center
Load
width
maxσ=
0.2,0.5,1.0MPa
Rise time 10(−3,−2,−1,0) s
• Load width is mostimportant
• Load center is notimportant
• Rise time could beimportant
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Results: maximum top and bottom stress
0
0.01
0.05
0.1
0.17
0.06 0.12 0.17
Load center
Load
width
maxσ=
0.2,0.5,1.0MPa
Rise time 10(−3,−2,−1,0) s
• Load width is mostimportant
• Load center is notimportant
• Rise time could beimportant
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Results: maximum top and bottom stress
0
0.01
0.05
0.1
0.17
0.06 0.12 0.17
Load center
Load
width
maxσ=
0.2,0.5,1.0MPa
Rise time 10(−3,−2,−1,0) s
• Load width is mostimportant
• Load center is notimportant
• Rise time could beimportant
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Displacement (loc: 0 m, width: 0.17 m, time:0.001 s)
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0
150000
300000
450000
600000
750000
900000
1050000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0.0018
0.0015
0.0012
0.0009
0.0006
0.0003
0.0000
0.0003
0.0006
Load (Pa) and displacement (m)
A relatively wide load (half width) excites response over entire width.
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Displacement (loc: 0 m, width: 0.17 m, time:0.001 s)
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0
150000
300000
450000
600000
750000
900000
1050000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0.0018
0.0015
0.0012
0.0009
0.0006
0.0003
0.0000
0.0003
0.0006
Load (Pa) and displacement (m)
A relatively wide load (half width) excites response over entire width.
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Stresses (loc: 0 m, width: 0.17 m, time:0.001 s)
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
900000
750000
600000
450000
300000
150000
0
150000
300000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
700000
600000
500000
400000
300000
200000
100000
0
100000
200000
Top and bottom stress (Pa)
Maximum top stress is localized not at the edge, due to curvature.
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Stresses (loc: 0 m, width: 0.17 m, time:0.001 s)
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
900000
750000
600000
450000
300000
150000
0
150000
300000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
700000
600000
500000
400000
300000
200000
100000
0
100000
200000
Top and bottom stress (Pa)
Maximum top stress is localized not at the edge, due to curvature.
15 of 22
Displacement (loc: 0.17 m, width: 0.01 m,time: 0.001 s)
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0
150000
300000
450000
600000
750000
900000
1050000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0.000150
0.000125
0.000100
0.000075
0.000050
0.000025
0.000000
0.000025
0.000050
Load (Pa) and displacement (m)
A concentrated center load excites response mostly in two point bending.
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Displacement (loc: 0.17 m, width: 0.01 m,time: 0.001 s)
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0
150000
300000
450000
600000
750000
900000
1050000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
0.000150
0.000125
0.000100
0.000075
0.000050
0.000025
0.000000
0.000025
0.000050
Load (Pa) and displacement (m)
A concentrated center load excites response mostly in two point bending.
16 of 22
Stresses (loc: 0.17 m, width: 0.01 m, time:0.001 s)
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
210000
180000
150000
120000
90000
60000
30000
0
30000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
60000
50000
40000
30000
20000
10000
0
10000
20000
Top and bottom stress (Pa)
Top stresses are highly local, but small compared to loading.
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Stresses (loc: 0.17 m, width: 0.01 m, time:0.001 s)
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
210000
180000
150000
120000
90000
60000
30000
0
30000
0.00 0.17 0.34position (m)
0.0001
0.0011
0.0021
0.0030
tim
e (
s)
60000
50000
40000
30000
20000
10000
0
10000
20000
Top and bottom stress (Pa)
Top stresses are highly local, but small compared to loading.
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Comparison of modal excitation
0.0001 0.0011 0.0021 0.0030time (s)
0.002
0.001
0.000
0.001
0.002
0.003
exci
tati
on (
-)
0.0001 0.0011 0.0021 0.0030time (s)
0.0001
0.0000
0.0001
0.0002
0.0003
exci
tati
on (
-)
0.0001 0.0011 0.0021 0.0030time (s)
0.0002
0.0001
0.0000
0.0001
0.0002
0.0003
exci
tati
on (
-)
Only three modes (seem to) contribute to the response.
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Comparison of modal excitation
0.0001 0.0011 0.0021 0.0030time (s)
0.002
0.001
0.000
0.001
0.002
0.003
exci
tati
on (
-)
0.0001 0.0011 0.0021 0.0030time (s)
0.0001
0.0000
0.0001
0.0002
0.0003
exci
tati
on (
-)
0.0001 0.0011 0.0021 0.0030time (s)
0.0002
0.0001
0.0000
0.0001
0.0002
0.0003
exci
tati
on (
-)
Only three modes (seem to) contribute to the response.
18 of 22
Alternative solution
Results using first five modes
0
0.01
0.05
0.1
0.17
0.06 0.12 0.17
Load center
Load
width
maxσ=
0.2,0.5,1.0MPa
Rise time 10(−3,−2,−1,0) s
• Five modes areenough for globalloads
• Di�erence for localloads a di�erence(25%) is observed
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Results using first five modes
0
0.01
0.05
0.1
0.17
0.06 0.12 0.17
Load center
Load
width
maxσ=
0.2,0.5,1.0MPa
Rise time 10(−3,−2,−1,0) s
• Five modes areenough for globalloads
• Di�erence for localloads a di�erence(25%) is observed
19 of 22
Closing
Conclusion
In this case:
• Response is dominated by �rst �ve vibration modes
• Stress levels require the higher modes, although these modes behave statically• Ranking of importance of load parameters
1. load width
2. rise time
3. impact location
• This model can be used for '�rst estimate' of importance
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Conclusion
In this case:
• Response is dominated by �rst �ve vibration modes
• Stress levels require the higher modes, although these modes behave statically• Ranking of importance of load parameters
1. load width
2. rise time
3. impact location
• This model can be used for '�rst estimate' of importance
20 of 22
Remarks
• Added mass and damping
• Sti�ness and strength gradient due to temperature
• Linear superposition of thermal stress, ship global bending
• Bottom: stress concentration by mastic
• Center: stress concentration by groove
• Top: stress concentration peel
21 of 22
References I
Carlsson, L. and G. Kardomateas (2011). Structural and Failure Mechanics of Sandwich
Composites. Springer.Das, B. (2011). Geotechnical Engineering Handbook. J. Ross Publishing Inc.Finlayson, B. (1972). The Method of Weighted Residuals and Variational Principles.Academic Press.
Gervaise, E., P.-E. De Sèze, and S. Maillard (2009). �Reliability-based methodology forsloshing assessment of membrane LNG vessels�. In: cited By 2. URL:https://www.scopus.com/inward/record.uri?eid=2-s2.0-
73849107843&partnerID=40&md5=b85c8435d7f46256309282bb42e2506d.Hetenyi, M. (1946). Beams on elastic foundation. Waverly press, Baltimore.
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Thank you