Selecting potentially critical sloshing loads on an LNG ...

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

PDF

D

C/D

A

Details: Gervaise, De Sèze, and Maillard 2009

This could be improved if we know what the structure feels.

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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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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?

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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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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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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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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


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


Maximum top stress is localized not at the edge, due to curvature.

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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


A concentrated center load excites response mostly in two point bending.

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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 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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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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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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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

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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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Selecting potentially critical sloshing loads on an LNG ...

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