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Large deflection elastic-plastic

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e ne concep

for plates

Plate strips

Plastic hinge concept extended to 2 dimensions

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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,

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Rigid-plastic resistance for platesAxially fixed or free boundaries

60]

qz z

1

3 212

2 ( )

4

5

pacity

[q/

5

3

q

qz

zz

Pinned ends

c

c

2 1

2

3

1

31 1

2

( )( )

:

2

3

carrying

c

1z

w

hq

h

a

Clampd ends

cY 2

6 2

2 2

:

0

0 1 2 3Load-

zw

hq

h

ac

Y 12 2

2 2

a a a

3 2( )

Unlike beams no simple solution exists for plates with finite

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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Rigid-plastic resistance for platesAxially fixed or free boundaries

0]

4

5

pacity[

q/q a =

5

3 6

78

capaci

ty

strip]

1 = a/b

3, 2

2

3

arr

ying

ca 2

1

23

4

5

-carrying

[q/q

c

plat

,

0

0 1 2 3Load-

0

1

0 1 2 3

Loa

The membrane effect is relatively larger for long plate

Relative displacement [w/h]

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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Plastic analysis- comparison with NLFEA

14

16

8

10

adfactor

2

4

6L

Fixed-060 plast 0.6Fixed-090 plast 0.9

Fixed-120 plast 1.2Fixed-150 plast 1.5

0

0.00 0.01 0.02 0.03 0.04Deformation [m]

Fixed-180 plast 1.8

Nonlinear FE predictions and plastic analysis of uniformly loadedrectangular plates with various aspect ratios

(600/900/1200/1500/1800 x 600 x 35 mm,fY= 300 MPa). Rotationally

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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Influence of boundary conditions

16

18

20

10

12

14

oadfactor

2

4

6 Fixed-060 Straight060

Fixed-090 Straight-090

Fixed-120 Straight-120Fixed-150 Straight-150

0

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Deformation

Fixed-180 Straight-180

(600/900/1200/1500/1800 600 x 35 mm,fY= 300 MPa for

(1): rotationally clamped and axially fixed boundaries

(2): rotationally clamped and axially free, but straight boundaries.

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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oa actor x a .

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Non-linear finite element simulation of latessubjected uniform patch loading

Membrane effect

.

Load

patch

Load

patch

Same load patch different plate length

Boundaries fixed or straight

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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16

Plate boundary

8

12

factor Resistance

converges

4

Loa

patch-0.60

patch-0.90-

as o a o

uniformly

loaded plate

Load patch L

0

0.00 0.01 0.02 0.03 0.04

.

s

Nonlinear FE predictions of resistance versus deformation of rectangularplates subjected to uniform patch loading with various width b = 600/900 and1500 mm (plate dimensions 1800 x 600 x 35 mm,fY= 300 MPa).Rotationall clam ed and axiall fixed boundaries. Load factor x 1 MPa

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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Constant load patch plate aspect ratio factor

Resistance for b = 0.60, s = 0.60 m, t = 35 mm,

IACS resistance

independent of

Plate boundary fy= 300 MPa20

aspect ratio

No gain in reducing

Lb10

ure

[MPa]

DNV aspect ratio

factor reasonable

Load patch

5

Pres

L/b=1.0 DnV-fact

L/b=1.5 DnV-fact

L/b=2.0 DnV-fact

0

0.000 0.010 0.020 0.030 0.040 0.050

Deformation [m]

. -

IACS

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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Constant load patch plate aspect ratio factor

IACS resistance

independent ofaspect ratio

a e oun ary Resistance for b = 0.90, s = 0.60 m, t = 35 mm,

fy= 300 MPa15

No gain in

reducing girder

spacingLb

10

sure

[MPa]

DNV aspect ratio

factor less

reasonable for

Load patch 5Pres

L/b=1.0 DnV-fact

L/b=4/3 DnV-fact

L/b=2.0 DnV-fact

IACS

long patchs 0.000 0.010 0.020 0.030 0.040 0.050Deformation [m]

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Local plate resistance

Resistance increases with increasing

e orma ons ue o e mem rane

effect Can we allow permanent deformations

and how much is acce table?

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Equivalent strain vs. load patch

Plate boundary

0.20

0.25Patch-0.60

Patch-0.90

Load patch L 0.10

0.15

Str

ainN

Patch-1.20

Staright edge 0.60

0.05

s

.

0.000 0.020 0.040 0.060 0.080

Deformation [m]

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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qu va ent stra n v rtua y n epen ent o oa patc

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Local plate resistanceResistance for L=1.80 m, s = 0.60 m, t = 35 mm,

fy= 300 MPa

versus max. equivalent strain

1214

or

Plate boundary q. s ra n . .

6

8

Loadfac

- -Load patch L

0

2

. .

patch-0.90 IACS0.90 DnV-fact'

patch-1.50 IACS1.50 DnV-fact

. . . . .

Deformation [m]s

Potential for reduced plate thickness if permanent

NUS July 10-12, 2006 Analysis and Design for Robustness of Offshore StructuresNUS Keppel Short Course

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deformations are allowed