Ultimate Strength of Plates and Stiffened Panels …...Ultimate Strength of Plates and Stiffened Panels Prof. Jeom Kee Paik, Director The LRET Research Centre of Excellence at Pusan

1

Ultimate Strength of Plates and Stiffened Panels

by

Professor Jeom Paik

The LRET Research CollegiumSouthampton, 11 July – 2 September 2011

Ultimate Strength of Plates and Stiffened Panels

Prof. Jeom Kee Paik, DirectorThe LRET Research Centre of Excellence

at Pusan National University, Korea

Overview

Aims and Scope

Rationally-Based Structural Design

Methods used for Benchmark Study

Theory of the ALPS/ULSAP Method• Ultimate Strength of Plates

• Ultimate Strength of Stiffened Panels

Benchmark Study• Target Structure: Unstiffened panel

• Ultimate Strength of Unstiffened Plates under Biaxial Compression

• Target Structure: Stiffened panel

• Nonlinear FEA Modeling

• Ultimate Strength of Stiffened Panels

Concluding Remarks

Aims and Scope

Stiffened panel structure Stiffened panel subject to a combined in-plane and lateral pressure load

Rationally-Based Structural Design(Optimum structural design procedure based on ultimate limit state)

Modeling of Structure & Loads

Structural Response AnalysisCalculate Load Effects, Q

Limit State AnalysisCalculate Limit Values

of Load Effects, QL

Evaluation(A) Formulate constraints (B) Evaluate adequacy

γ1 γ2 γ3 Q ≤QL Constraints satisfied?Objective achieved?

Optimization Objective

Methods Used for Benchmark Study

Candidate methods

• Nonlinear finite element method (ANSYS, MSC/MARC, Abaqus)

• ALPS/ULSAP method

• DNV/PULS method

Theory of the ALPS/ULSAP Method

- ALPS/ULSAP (Analysis of Large Plated Structures / Ultimate Limit State Assessment Program), developed by Prof. J.K.Paik, Pusan National University

Theory of the ALPS/ULSAP Method

Ship Structural Analysis and Design (2010)

Hughes & Paik

Ultimate Limit State Design of Steel-Plated Structures (2003)

Paik & Thayamballi

(a) Plasticity at the corners

(b) Plasticity at the longitudinal mid-edges

(c) Plasticity at the transverse mid-edges

Ultimate Strength of Plates: σu = min.(σu1, σu2, σu3)

2 2 21 3max max max maxeq x x y y Yσ σ σ σ σ τ σ= − + + =

2 2 22 3max max min mineq x x y y Yσ σ σ σ σ τ σ= − + + =

2 2 23 3min min max maxeq x x y y Yσ σ σ σ σ τ σ= − + + =

• : Expected plasticity locationT: TensionC: Compression

Mode I – overall collapse

Mode II – plate-induced collapse

Mode III – stiffener-induced collapse by beam-column type collapse

Mode V – stiffener-induced collapse by tripping

Mode IV – stiffener-induced collapse by web buckling

Mode VI: Gross yielding

Ultimate Strength of Stiffened Panels: 6 Types of Collapse Modes

σu = min.(σuI, σu

II, σuIII, σu

IV, σuV, σu

VI)

Benchmark Study

Candidate methods

• Nonlinear finite element method (ANSYS, MSC/MARC, Abaqus)

• ALPS/ULSAP method

• DNV/PULS method

• Yield stress of plate, σYp = 313.6 N/mm2

• Yield stress of stiffener, σYs = 313.6 N/mm2

• Elastic modulus, E = 205800 N/mm2

• Poisson’s ratio, ν = 0.3

• Plate length, a = 2550 mm

• Plate breath, b = 850 mm

• Plate thickness, tp = 11, 16, 22, 33 mm

• Under biaxial compressive loads

• All edges simply supported

• No residual stress

• No lateral pressure

Target Structure: Unstiffened Panel

Material and Geometric Properties

Trans. frames

Long

. stif

fene

rs

850

25502550 2550

850

850

Unit: mm

2 2 2 2 2 2 2 2

2 2 2 2 2 2

( / 1 / ) [( 1) / 1 / ]/ / ( 1) / /

m a b m a bm a c b m a c b

+ + +≤

+ + +

where, /y xc σ σ=

σx and σy are the component of the longitudinal and transverse axial buckling stress of the plate under combined biaxial loading.

σx,1 and σy,1 are the component of the longitudinal or transverse axial buckling stress of the plate under uniaxial loading.

Buckling half-wave number

2.00.0 0.5 1.5

0.5

1.5

2.0

1.0

1.0

σy/ σy,1 a/b=3

σx/ σx,1

m=1

m=2

m=3

-1.0

-1.0

Unstiffened Plates under Biaxial Compression (1/3)

0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

FEMALPS/ULSAPDNV/PULS


a×b = 2550×850(mm)tp= 11mm a×b = 2550×850(mm)tp= 11mm

σyu

/ σY

σxu/ σY


tp=11mm tp=16mm

0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0




σyu

/ σY

σxu/ σY


tp=22mm tp=33mm

0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0




σyu

/ σY

σxu/ σY

σyu

/ σY

σxu/ σY

0 0.2 0.4 0.6 0.8 1.0 1.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2




Unit: mm

• Yield stress of plate, σYp = 313.6 N/mm2

• Yield stress of stiffener, σYs = 313.6 N/mm2

• Elastic modulus, E = 205800 N/mm2

• Poisson’s ratio, ν = 0.3

• Plate length, a = 4750 mm

• Plate breath, b = 950 mm

• Plate thickness, tp = 11, 12.5, 15, 18.5, 25, 37 mm

• Number of the stiffeners: 8 stiffeners in a panel

• No residual stress

Target Structure: Stiffened Panel (1/2)

Material and Geometric Properties

N. A. N. A. N. A.

b

tp

hw

tw

b

tp

hw

tw

b

tp

hw

tw

bf

tf

bf

tf

*N.A. = neutral axis

Flat bar Angle bar Tee bar

Flat bar (hwxtw) Angle bar (hwxbfxtw/tf) Tee bar (hwxbfxtw/tf)

Size 1 150x17 138x90x9/12 138x90x9/12

Size 2 250x25 235x90x10/15 235x90x10/15

Size 3 350x35 383x100x12/17 383x100x12/17

Size 4 550x35 580x150x15/20 580x150x15/20

Target Structure: Stiffened Panel (2/2)

Dimensions of the Stiffeners

xA'''

z

y

AA'

A''

D'

D''D'''

B

C

B'

C'Longi. gird

ers

D Trans. frames

Boundary Description

A-A''' and D-D'''

Symmetric condition with Rx=Rz=0 and

uniform displacement in the y direction (Uy=uniform),

coupled the plate part

A-D and A'''-D'''

Symmetric condition with Ry=Rz=0 and

uniform displacement in the x direction (Ux=uniform),

coupled with longitudinal stiffeners

A'-D', A''-D'',

B-B' and C-C' Uz=0

ANSYS Nonlinear FEA Modeling (1/2)

Extent of Analysis: Two bay/two span model

Boundary Conditions

ANSYS Nonlinear FEA Modeling (2/2)

Mesh Sizes Applied

Flat type(hw×tw)

150×17(mm) 250×25(mm) 350×35(mm) 550×35(mm)27600 elements 27600 elements 40400 elements 50000 elements

Angle type(hw×bf×tw/tf)

138×90×9/12(mm) 235×90×10/15(mm) 383×100×12/17(mm) 580×150×15/20(mm)30800 elements 30800 elements 43600 elements 53200 elements

Tee type(hw×bf×tw/tf)

138×90×9/12(mm) 235×90×10/15(mm) 383×100×12/17(mm) 580×150×15/20(mm)30800 elements 30800 elements 43600 elements 53200 elements

Size 1 Size 2 Size 3 Size 4

MSC/MARC Nonlinear FEA Modeling by Prof. M. Fujikubo, Osaka University

Extent of Analysis: Two bay/two span model

Mesh Sizes Applied (22753 elements)

10 mesh

6 mesh6 mesh

x

z

y

Extent of Analysis: Three bay/one span model

Mesh Sizes Applied (7740 elements)

3 mesh1 mesh

z

y

x

Abaqus Nonlinear FEA Modeling by Dr. Amlashi Hadi, DNV

sin sinoc o

x yw Ba Bπ π

=

sin sinopl om x yw A

a bπ π

=

2 0.1 ; 0.0015 ; Ypo p o o

p

bA t B C at E

σβ β= = = =

Nonlinear FEA Modeling for ANSYS and MSC/MARC

ocw

iθ

osw

Plate Initial Deflection Column Type Initial Distortion of Stiffener

0 sinosw

z xw Ch a

π=

B

Ly

xwoc

wopl

wopl

woc

b

b

b

b

a aaa

Sideways Initial Distortion of Stiffener

x

z

y

Overall deflection with amplification factor of 50x

z

y

Local deflection with amplification factor of 20

Initial deflection with amplification factor of 20

Nonlinear FEA Modeling for ANSYS and MSC/MARC

Plate Initial Deflection

Column Type Initial Distortion of Stiffener

Sideways Initial Distortion of Stiffener

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

Mode IIIIII III

III III III

σ xu/σ Y

eq

FEA (ANSYS)

Design Formula (ALPS/ULSAP)FEA (MSC/MARC)

Design Formula (DNV/PULS)

FEA (ABAQUS)

Panel C: hw×tw = 150×17 (mm) (F)

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

Mode III

IIIIII

III IV IV

σ xu/σ Y

eq


FEA (ANSYS)



Size 2Size 1

Ultimate Strength of Stiffened Panels (1/26)

Flat Bar Under Longitudinal Uniaxial Compression

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

Mode IIIIII IV

IVII

II

σ xu/σ Y

eq


FEA (ANSYS)



0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

Mode III IV

IVIV IV II

σ xu/σ Y

eq


FEA (ANSYS)



FEA (ABAQUS)

Size 4Size 3


Flat Bar Under Longitudinal Uniaxial Compression

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Mode III IIIIII

III

III IIIσ xu/σ Y

eq

Panel C: hw×bf×tw/tf = 138×90×9/12(mm) (A)

Yp( / ) σ /pb t E

FEA (ANSYS)



FEA (ABAQUS)

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

Mode IIIIII

IIIV

σ xu/σ Y

eq

V


FEA (ANSYS)



V

Size 2Size 1


Angle Bar Under Longitudinal Uniaxial Compression

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

Mode IIIIII

VV V V

σ xu/σ Y

eq


FEA (ANSYS)



0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

VMode III

VII

II II

σ xu/σ Y

eq


FEA (ANSYS)



FEA (ABAQUS)

Size 4Size 3


Angle Bar Under Longitudinal Uniaxial Compression

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

IIIMode IIIIII

III III

IIIσ xu/σ Y

eq

Panel C: hw×bf×tw/tf = 138×90×9/12(mm) (T)FEA (ANSYS)



FEA (ABAQUS)

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

III

Mode III

IIIV V V

σ xu/σ Y

eq

Panel C: hw×bf×tw/tf = 235×90×10/15(mm) (T)

FEA (ANSYS)



Size 2Size 1


Tee Bar Under Longitudinal Uniaxial Compression

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

Mode III V

V V

σ xu/σ Y

eq

VV


FEA (ANSYS)



0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

Yp( / ) σ /pb t E

VMode V

VII

II II

σ xu/σ Y

eq


FEA (ANSYS)



FEA (ABAQUS)

Size 4Size 3


Tee Bar Under Longitudinal Uniaxial Compression

Angle bar


Under Longitudinal Uniaxial Compression

σ xu/σ Y

eq

Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Flat bar under longitudinal compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)

Size 4

Size 3

Size 2

Size 1 σ xu/σ Y

eq

Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Angle bar under longitudinal compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)

Size 4

Size 3

Size 2

Size 1

Flat bar

Tee bar

σ xu/σ Y

eq

Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Tee bar under longitudinal compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)

Size 4

Size 3

Size 2

Size 1

All stiffener types


Under Longitudinal Uniaxial Compression

σ xu/σ Y

eq

Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Flat Angle TeeFEA (ANSYS)

Design formula (ALPS/ULSAP)

Size 4

Size 3

Size 2

Size 1

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

FEA (ANSYS)Design Formula (ALPS/ULSAP)


Mode I

III

III

III IIIIII

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

III

III

IV IVIII

Size 2Size 1


Flat Bar Under Transverse Uniaxial Compression

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

III

IV

IV IVIV

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

IV

IV

IV IVIV

Size 4Size 3


Flat Bar Under Transverse Uniaxial Compression

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

III

III

III IIIIII

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

III

III

V VV

Size 2Size 1


Angle Bar Under Transverse Uniaxial Compression

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

V

V

IV IVIV

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode V

IV

IV

IV IVIV

Size 4Size 3


Angle Bar Under Transverse Uniaxial Compression

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

III

III

III IIIIII

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

III

III

V VV

Size 2Size 1


Tee Bar Under Transverse Uniaxial Compression

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode III

V

V

IV IVIV

σ yu/σ Y

eq

Yp( / ) σ /pb t E0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

1.2



Mode V

IV

IV

IV IVIV

Size4Size 3


Tee Bar Under Transverse Uniaxial Compression

Angle barFlat bar


Under Transverse Uniaxial Compression

Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Flat bar under transverse compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)

Size 4 Size 3 Size 2

Size 1

σ yu/σ Y

eq

Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Angle bar under transverse compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)


σ yu/σ Y

eq

All stiffener typesTee bar


Under Transverse Uniaxial Compression

Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Tee bar under transverse compressive loadsFEA (ANSYS)Design formula (ALPS/ULSAP)


σ yu/σ Y

eq

Yeq( / ) σ /a r Eπ0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2 Flat Angle TeeFEA (ANSYS)

Design formula (ALPS/ULSAP)

Size 3Size 4 Size 2 Size 1

σ yu/σ Y

eq

2 2 2 2 2 2 2 2

2 2 2 2 2 2

( / 1 / ) [( 1) / 1 / ]/ / ( 1) / /

m a b m a bm a c b m a c b

+ + +≤

+ + +

where, /y xc σ σ=

2.00.0 0.5 1.5

0.5

1.5

2.0

1.0

1.0

σy/ σy,1 a/b=5

σx/ σx,1

m=1m=2

m=3

m=4

m=5

-1.0

-1.0

σx and σy are the component of the longitudinal and transverse axial buckling stress of the plate under combined biaxial loading.

σx,1 and σy,1 are the component of the longitudinal or transverse axial buckling stress of the plate under uniaxial loading.


Buckling half-wave number

Size 1 Size 2


Under Biaxial Compression (Flat Bar, tp=18.5mm)

σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Mode III

Design Formula (ALPS/ULSAP)

hw×tw = 150×17(mm) (F)

Panel C: tp=18.5mm

FEA (ANSYS)

0.0

σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Mode III

0.0


hw×tw = 250×25(mm) (F)

Panel C: tp=18.5mm

FEA (ANSYS)

Size 3 Size 4


Under Biaxial Compression (Flat Bar, tp=18.5mm)

σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0


hw×tw = 350×35(mm) (F)

Panel C: tp=18.5mm

FEA (ANSYS)

Mode III

Mode IV

Mode II σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0


hw×tw = 550×35(mm) (F)

Panel C: tp=18.5mm

FEA (ANSYS)

Mode IV

Mode IV

Mode II

Mode III

Size 1 Size 2


Under Biaxial Compression (Angle Bar, tp=18.5mm)

σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0


hw×bf×tw/tf = 138×90×9/12(mm) (A)

Panel C: tp=18.5mm

FEA (ANSYS)

Mode III

Mode IVσ y

u/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Mode III

0.0


hw×bf×tw/tf = 235×90×10/15(mm) (A)Panel C: tp=18.5mm

FEA (ANSYS)

Size 3 Size 4


Under Biaxial Compression (Angle Bar, tp=18.5mm)

σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0


hw×bf×tw/tf = 383×100×12/17(mm) (A)Panel C: tp=18.5mm

FEA (ANSYS)

Mode III

Mode V

Mode II σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0


hw×bf×tw/tf = 580×150×15/20(mm) (A)

Panel C: tp=18.5mm

Mode IV

Mode V

Mode II

FEA (ANSYS)

Mode III

Size 1 Size 2

σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Mode III

FEA (ANSYS)


Panel C: tp=18.5mm hw×bf×tw/tf = 138×90×9/12(mm) (T)

0.0

σ yu/σ Y

eq

σxu/ σYeq

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Mode III

hw×bf×tw/tf = 235×90×10/15(mm) (T)Panel C: tp=18.5mm

FEA (ANSYS)



Under Biaxial Compression (Tee Bar, tp=18.5mm)

Size 3 Size 4

σ yu/σ Y

eq

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

σxu/ σYeq

hw×bf×tw/tf = 383×100×12/17(mm) (T)Panel C: tp=18.5mm

FEA (ANSYS)


Mode III

Mode V

Mode II

σ yu/σ Y

eq

σxu/ σYeq

0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

0.0

hw×bf×tw/tf = 580×150×15/20(mm) (T)

Panel C: tp=18.5mm

Mode IV

Mode V

Mode II

FEA (ANSYS)



Under Biaxial Compression (Tee Bar, tp=18.5mm)

p

p

Plate-sided Pressure

Stiffener-sided Pressure


Under Combined Longitudinal Compression and Lateral Pressure Loads

N. A.

b

tp

hw

tw

bf

tf

Plate thickness, tp = 15 mm

hw×bf×tw/tf = 383×100×12/17(mm) (T)


p (MPa)

σ xu/σ Y

eq

tp=15mm

0.0 0.1 0.2 0.3 0.40.0

0.2

0.4

0.6

0.8

1.0Design Formula (ALPS/ULSAP)FEA (ANSYS) with Plate-sided PressureFEA (ANSYS) with Stiffener-sided Pressure


Mode VMode II Mode V

Mode III

Stiffener-sided Pressure

Plate-sided Pressure


Plate thickness, tp = 15 mm

hw×bf×tw/tf = 383×100×12/17(mm) (T)


Plate-sided Pressure(with p=0.25 MPa, amplification factor of 10)

Stiffener-sided Pressure(with p=-0.25 MPa, amplification factor of 10)


Concluding Remarks

Concluding RemarksThe dimension and material properties of a real ship panel was selected as a standard panel

and a wider range of plating and stiffener dimensions were considered by varying the panel’s properties.

The objective of the benchmark study reported in this paper was to check the accuracy of the ALPS/ULSAP method’s use to calculate the ultimate strength of plate and stiffened panel, compared with nonlinear finite element method.

The ALPS/ULSAP method was found in a good agreement with the nonlinear finite element method computations through a wide range of panel dimensions and different loading conditions.

The ALPS/ULSAP method is based on design formulations, the computational time required is extremely short compared to the nonlinear finite element method. So, this will be of great advantage in the structures design and safety assessment of ship structures comprising a large number of plate and panels.

Ultimate Strength of Hull Girders

Prof. Jeom Kee Paik, DirectorThe LRET Research Centre of Excellence

at Pusan National University, Korea

OverviewOverview

1. Background2. Rationally-based structural design3. Presumed stress distribution-based method4. Methods applied for the ultimate hull strength analysis5. Analysis results6. Statistical analysis7. Concluding remarks

BackgroundBackground

- To develop the modified Paik-Mansour formula method for the ultimate strength calculations of ship hulls subject to verticalbending moments.

- To validate the accuracy and applicability of modified Paik-Mansour formula method by comparing with more refined other methods.

Modeling of Structure & Loads

Structural Response AnalysisCalculate Load Effects, Q

Limit State AnalysisCalculate Limit Values

of Load Effects, QL

Evaluation(A) Formulate constraints (B) Evaluate adequacy

γ1 γ2 γ3 Q ≤QL Constraints satisfied?Objective achieved?

Optimization Objective

RationallyRationally--based structural designbased structural design(Optimum structural design procedure based on ultimate limit sta(Optimum structural design procedure based on ultimate limit state)te)

Methods for the ultimate hull strength analysisMethods for the ultimate hull strength analysis

• Numerical- Nonlinear FEM- Intelligent supersize FEM- Idealized structural unit method

• Analytical- Design formula

• Experimental

Presumed stress distributionPresumed stress distribution--based method based method (1/8)(1/8)

Sagging Hogging

Caldwell’s original formula method (1965)

0xdAσ =∫ 1

1

n

xi i ii

u n

xi ii

a zg

a

σ

σ

=

=

=∑

∑

( )

1

nvu xi i i u

i

M a z gσ=

= −∑

Longitudinal bending stress distribution of tanker hullat ULS obtained by Nonlinear FEA


Linear elasticaround N.A.

Buckling collapsedat compressed part

Yielded attensiled part

Single hull VLCCin hogging

Double hull VLCCin sagging

Suezmax-class double hull VLCC in sagging

Longitudinal bending stress distribution of ship hullat ULS obtained by Nonlinear FEA


Dow’s frigate test hullin sagging

Container shipin hogging

Bulk carrierin hogging

Original Paik-Mansour formula method (1995)

Uxσ

Exσ

Exσ

Yxσ

①

②

③

④

+ -

+-

Tens.

Comp.D-gus

gus

z

①

②

③

④

Yxσ z

D-guh

guh

+-

Tens.

Comp.

+ -

Exσ

Exσ

Uxσ

Sagging Hogging

0xdAσ =∫ 1

1

n

xi i ii

u n

xi ii

a zg

a

σ

σ

=

=

=∑

∑

( )

1

nvu xi i i u

i

M a z gσ=

= −∑


Modified Paik-Mansour formula method


0xdAσ =∫ 1

1

n

xi i ii

u n

xi ii

a zg

a

σ

σ

=

=

=∑

∑

( )

1

nvu xi i i u

i

M a z gσ=

= −∑

Sagging Hogging

2 2 2 2 4

10.995 0.936 0.170 0.188 0.067

xu

Yeq

σσ λ β λ β λ

=+ + + −

Yeqa

r Eσ

λπ

= Ypbt E

σβ =

s

IrA

=

Plate-stiffener combination element (PSC)

Plate-stiffener separation element (PSS)


(Paik and Thayamballi, 1997)

Plate element: a/b≥1 (Paik at al. 2004)

Plate element: a/b<1 (Paik at al. 2004)

Ypbt E

σβ =

Ypat E

σα =

4 2*

2

0.032 0.002 1.0 for 1.51.274 / for 1.5 3.01.248 / 0.283 for 3.0

xu

Yp

α α ασ α ασ

α α

⎧− + + ≤⎪= < ≤⎨⎪ + >⎩

4 2

2

0.032 0.002 1.0 for 1.51.274 / for 1.5 3.01.248 / 0.283 for 3.0

xu

Yp

β β βσ β βσ

β β

⎧− + + ≤⎪= < ≤⎨⎪ + >⎩

*

2

0.475 1xu xu

Yp Yp

a ab b

σ σσ σ α

⎛ ⎞= + −⎜ ⎟⎝ ⎠


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211211 212212 213213

214214 215215 216216

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Modeling: Modified Paik-Mansour formula method

Dow’s Test Hull Container Ship Bulk Carrier D/H Suezmax

S/H VLCC D/H VLCC

PSC model for hogging PSS model for sagging

PSC model for hogging PSS model for saggingPSS model

PSC model PSC model PSC model


Methods applied Methods applied for the ultimate hull strength analysis (1/5)for the ultimate hull strength analysis (1/5)

• Nonlinear FEM: ANSYS• Intelligent supersize FEM: ALPS/HULL• Idealized structural unit method (Smith method): IACS CSR by Dr. C.H. Huang

(China Corporation Register of Shipping)• Modified PaikModified Paik--MansourMansour formula methodformula method

NLFEM model ISFEM model ISUM model

Hard corner elements

ModifiedP-M method

NLFEM(ANSYS)

ISUM/Smith Method(IACS CSR)

ISFEM(ALPS/HULL)

Geometricmodeling

Finite element model Plate-stiffener combination model

Plate-stiffener separation model

Formulation technique

: Numerical formulation

[D]: Numerical formulation

:Closed-form solution : Numerical formulation

[D]: Closed-form solution

Computational cost

Expensive Cheap Cheap

Feature (1) 2 and 3-dimensional 2-dimensional 2 and 3-dimensional

Feature (2)Can deal with interaction between local and global failures

Can not deal with interaction between local and global failures

Can deal with interaction between local and global failures

[ ] [ ][ ] volTB D B dσ = ∫Yσ σ= Φ

1 11 1

1 1

edge functionforforfor

εε ε

ε

Φ =

− < −⎧⎪= − < <⎨⎪ >⎩

[ ] [ ][ ] volTB D B dσ = ∫


Extent of the analysis

Trans. bulkhead

Trans. bulkhead

Trans. frame

Trans. bulkhead

Trans. bulkhead

Trans. frame

(a) The entire hull model

(b) The three cargo hold model

(c) The two cargo hold model

(d) The one cargo hold model

(e) The two-bay sliced hull cross-section model

(f) The one-bay sliced hull cross-section model


Initial imperfections

sin sinopl om x yw A

a bπ π

=

sin sinoc ox yw B

a Bπ π

= 2where, 0.1 ; 0.0015 ; Ypo p o o

p

bA t B C at E

σβ β= = = =

0 sinosw

z xw Ch a

π=

woc

wos

wopl


Application of vertical bending moments keeping the hull cross-section plane

• g = neutral axis position from the baseline• zi = distance from the ship’s baseline

(reference position) to the horizontalneutral axis of the ith structural component

• σxi = longitudinal stress of the ith structuralcomponent following the presumed stressdistribution

• ai = cross-sectional area of the ith structuralcomponent

• n = total number of structural components

1

1

n

xi i ii

n

xi ii

a zg

a

σ

σ

=

=

=∑

∑

Displacement control with neutral axis changes


NLFEM (ANSYS) ModelingNLFEM (ANSYS) ModelingDow’s Test Hull Container Ship Bulk Carrier

D/H Suezmax S/H VLCC D/H VLCC

Total number of elements: 36,432Elements distribution:Plate: 10 Web: 4 Flange: 2





Total number of elements: 222,858Elements distibution:Plate: 10 Web: 6 Flange: 1

ISFEM (ALPS/HULL) ModelingISFEM (ALPS/HULL) ModelingDow’s Test Hull Container Ship Bulk Carrier


Total number of elements: 196Plate: 106 elementsBeam-column: 90 elements






ISUM (CSR) Modeling by Dr. C. H. HuangISUM (CSR) Modeling by Dr. C. H. Huang(China Corporation Register of Shipping, Taiwan)(China Corporation Register of Shipping, Taiwan)

Dow’s Test Hull Container Ship Bulk Carrier


Result Result -- Case I: Case I: DowDow’’s Test Hull s Test Hull (1/6)(1/6)Curvature versus vertical bending moments

Dow’stest hull

Design formula method MuANSYS(MNm)

MuALPS/HULL

(MNm)

MuCSR

(MNm)Mu(MNm)

Original P-M Modified P-MhC(mm) hY(mm) hC(mm) hY(mm)

Hogging 10.338 210.000 0.000 210.000 0.000 11.235 10.698 11.889Sagging 9.329 760.200 0.000 760.200 0.000 10.618 9.940 10.224

Note: Mu = ultimate moment, hC = height of collapsed hull part, hY = height of yielded hull part.

0.0 1.0 2.0 3.00

2

4

6

8

10

12

Test result

0.5 1.5 2.5

ANSYSALPS/HULLCSRModified Paik-Mansour formula method

Curvature(1/km)

Sagg

ing

bend

ing

mom

ent(

MN

m)

0.0 0.5 1.0 1.5 2.0 2.5 3.0Curvature(1/km)

0

2

4

6

8

10

12

ANSYSALPS/HULLCSRModified Paik-Mansour formula methodH

oggi

ng b

endi

ng m

omen

t(M

Nm

)

Result Result -- Case II: Case II: Container Ship Container Ship (2/6)(2/6)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500

1

2

3

4

5

6

7

8

9


Curvature(1/km)

Hog

ging

ben

ding

mom

ent(

GN

m)

Curvature versus vertical bending moments

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500

1

2

3

4

5

6

7

8

9


Curvature(1/km)

Sagg

ing

bend

ing

mom

ent(

GN

m)

Containership

Design formula method MuANSYS(GNm)

MuALPS/HULL

(GNm)

MuCSR

(GNm)Mu(GNm)


Hogging 6.400 698.800 0.000 698.800 0.000 6.969 6.916 8.040Sagging 7.077 10330.800 0.000 10330.800 0.000 6.951 6.635 7.843


Result Result -- Case III: Case III: Bulk Carrier Bulk Carrier (3/6)(3/6)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

4

8

12

16

20


Curvature(1/km)

Hog

ging

ben

ding

mom

ent(

GN

m)

Curvature versus vertical bending moments

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

4

8

12

16


Curvature(1/km)

Sagg

ing

bend

ing

mom

ent(

GN

m)

Bulkcarrier


MuALPS/HULL

(GNm)

MuCSR

(GNm)Mu(GNm)


Hogging 16.576 - - 1654.100 13.700 17.500 16.602 17.941Sagging 14.798 17935.000 0.000 17935.000 0.000 15.800 15.380 14.475


Result Result -- Case IV: Case IV: Double Hull Double Hull SuezmaxSuezmax Class Tanker Class Tanker (4/6)(4/6)Curvature versus vertical bending moments

0.00 0.05 0.10 0.15 0.20 0.25 0.300

2

4

6

8

10

12

14

16


Curvature(1/km)

Hog

ging

ben

ding

mom

ent(

GN

m) (PSC)

(PSS)

0.00 0.05 0.10 0.15 0.20 0.25 0.300

2

4

6

8

10

12

14


Curvature(1/km)

Sagg

ing

bend

ing

mom

ent(

GN

m)

(PSS)

(PSC)

Double hullSuezmaxtanker


MuALPS/HULL

(GNm)

MuCSR

(GNm)Mu(GNm)


Hogging 13.965 - - 12.100 2210.600 14.066 13.308 15.714Sagging 12.213 16078.500 0.000 16078.500 0.000 11.151 11.097 12.420


Result Result -- Case V: Case V: Single Hull VLCC Class Tanker Single Hull VLCC Class Tanker (5/6)(5/6)Curvature versus vertical bending moments

0.00 0.05 0.10 0.15 0.20 0.25 0.300

3

6

9

12

15

18

21


Curvature(1/km)

Hog

ging

ben

ding

mom

ent(

GN

m)

(PSS)

(PSC)

0.00 0.05 0.10 0.15 0.20 0.25 0.300

4

8

12

16

20


Curvature(1/km)

Sagg

ing

bend

ing

mom

ent(

GN

m)

(PSS)

(PSC)

Single hullVLCCtanker


MuALPS/HULL

(GNm)

MuCSR

(GNm)Mu(GNm)


Hogging 18.701 7035.200 0.000 7035.200 0.000 17.355 17.335 19.889Sagging 17.825 15225.500 0.000 15225.500 0.000 16.179 17.263 17.868


Result Result -- Case VI: Case VI: Double Hull VLCC Class Tanker Double Hull VLCC Class Tanker (6/6)(6/6)Curvature versus vertical bending moments

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400

5

10

15

20

25

30


Curvature(1/km)

Hog

ging

ben

ding

mom

ent(

GN

m) (PSC)

(PSS)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.400

5

10

15

20

25

30


Curvature(1/km)

Sagg

ing

bend

ing

mom

ent(

GN

m)

(PSS)

(PSC)

Double hullVLCCtanker


MuALPS/HULL

(GNm)

MuCSR

(GNm)Mu(GNm)


Hogging 25.667 - - 15.900 3816.000 27.335 25.600 28.352Sagging 22.390 20240.700 0.000 20240.700 0.000 22.495 22.000 24.798


Result: Result: Analysis VideoAnalysis Video

Modified PModified P--M Formula Method M Formula Method versus ANSYS Nonlinear FEA (1/2)

Ship Mp

(GNm)

Hogging Sagging

Formula ANSYSFormula/ANSYS

Formula ANSYSFormula/ANSYSMuh

(GNm)Muh/Mp

Muh

(GNm)Muh/Mp

Mus

(GNm)Mus/Mp

Mus

(GNm)Mus/Mp

Dow's test hull 0.013 0.010 0.772 0.011 0.840 0.920 0.009 0.697 0.011 0.793 0.879

Container ship 9.220 6.400 0.694 6.969 0.756 0.918 7.077 0.768 6.951 0.754 1.018

Bulk carrier 20.394 16.576 0.813 17.500 0.858 0.947 14.798 0.726 15.800 0.775 0.937

D/H Suezmax 17.677 13.965 0.790 14.066 0.796 0.993 12.213 0.691 11.151 0.631 1.095

S/H VLCC 22.578 18.701 0.828 17.355 0.769 1.078 17.825 0.789 16.179 0.717 1.102

D/H VLCC 32.667 25.667 0.786 27.335 0.837 0.939 22.390 0.685 22.495 0.689 0.995

Mean 0.966 1.004

S-D 0.061 0.088

COV 0.063 0.087

Note: Mp = fully plastic bending capacity , Muh = ultimate hogging moment, Mus = ultimate sagging moment,S-D = standard deviation, COV = coefficient of variation

Statistical analysis Statistical analysis -- Mean and COV (1/12)Mean and COV (1/12)

Modified PModified P--M Formula Method M Formula Method versus ANSYS Nonlinear FEA (2/2)

0.0 0.2 0.4 0.6 0.8 1.0(Mu/Mp)ANSYS

0.0

0.2

0.4

0.6

0.8

1.0

(Mu/M

p)Fo

rmul

a

Hog / Sag Mean : 0.966 / 1.004Standard deviation : 0.061 / 0.088COV : 0.063 / 0.087

Formula/ANSYS:

Hog / Sag: Dow’s frigate test hull: Container ship: Bulk carrier: D/H Suezmax: S/H VLCC: D/H VLCC

0 0.0125 10 15 20 25 30(Mu)ANSYS(GNm)

0

0.0125

10

15

20

25

30

(Mu)

Form

ula(G

Nm

)



Modified PModified P--M Formula Method M Formula Method versus ALPS/HULL ISFEM (1/2)

Ship Mp

(GNm)

Hogging Sagging

Formula ALPSFormula/

ALPS

Formula ALPSFormula/

ALPSMuh

(GNm)Muh/Mp

Muh

(GNm)Muh/Mp

Mus

(GNm)Mus/Mp

Mus

(GNm)Mus/Mp

Dow's test hull 0.013 0.010 0.772 0.011 0.799 0.966 0.009 0.697 0.010 0.743 0.939

Container ship 9.220 6.400 0.694 6.916 0.750 0.925 7.077 0.768 6.635 0.720 1.067

Bulk carrier 20.394 16.576 0.813 16.602 0.814 0.998 14.798 0.726 15.380 0.754 0.962

D/H Suezmax 17.677 13.965 0.790 13.308 0.753 1.049 12.213 0.691 11.097 0.628 1.101

S/H VLCC 22.578 18.701 0.828 17.335 0.768 1.079 17.825 0.789 17.263 0.765 1.033

D/H VLCC 32.667 25.667 0.786 25.600 0.784 1.003 22.390 0.685 22.000 0.673 1.018

Mean 1.003 1.020

S-D 0.055 0.061

COV 0.055 0.060



Modified PModified P--M Formula Method M Formula Method versus ALPS/HULL ISFEM (2/2)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Mean : 1.003 / 1.020Standard deviation : 0.055 / 0.061COV : 0.055 / 0.060


Formula/ALPS:

(Mu/M

p)Fo

rmul

a

(Mu/Mp)ALPS/HULL

Hog / Sag

0 0.0125 10 15 20 25 30

0

0.0125

10

15

20

25

30


(Mu)

Form

ula(G

Nm

)

(Mu)ALPS/HULL(GNm)


Modified PModified P--M Formula Method M Formula Method versus CSR ISUM (1/2)

Ship Mp

(GNm)

Hogging Sagging

Formula CSRFormula/

CSR

Formula CSRFormula/

CSRMuh

(GNm)Muh/Mp

Muh

(GNm)Muh/Mp

Mus

(GNm)Mus/Mp

Mus

(GNm)Mus/Mp

Dow's test hull 0.013 0.010 0.772 0.012 0.888 0.870 0.009 0.697 0.010 0.764 0.912

Container ship 9.220 6.400 0.694 8.040 0.872 0.796 7.077 0.768 7.843 0.851 0.902

Bulk carrier 20.394 16.576 0.813 17.941 0.880 0.924 14.798 0.726 14.475 0.710 1.022

D/H Suezmax 17.677 13.965 0.790 15.714 0.889 0.889 12.213 0.691 12.420 0.703 0.983

S/H VLCC 22.578 18.701 0.828 19.889 0.881 0.940 17.825 0.789 17.868 0.791 0.998

D/H VLCC 32.667 25.667 0.786 28.352 0.868 0.905 22.390 0.685 24.798 0.759 0.903

Mean 0.887 0.953

S-D 0.051 0.054

COV 0.058 0.056



Modified PModified P--M Formula Method M Formula Method versus CSR ISUM (2/2)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0


Formula/CSR:

(Mu/M

p)Fo

rmul

a

(Mu/Mp)CSR

Hog / Sag


0 0.0125 10 15 20 25 30

0

0.0125

10

15

20

25

30

(Mu)

Form

ula(G

Nm

)

(Mu)CSR(GNm)



ANSYS Nonlinear FEA versus ALPS/HULL ISFEM (1/2)

Ship Mp

(GNm)

Hogging Sagging

ANSYS ALPSALPS /ANSYS

ANSYS ALPSALPS /ANSYSMuh

(GNm)Muh/Mp

Muh

(GNm)Muh/Mp

Mus

(GNm)Mus/Mp

Mus

(GNm)Mus/Mp

Dow's test hull 0.013 0.011 0.840 0.011 0.799 0.952 0.011 0.793 0.010 0.743 0.936

Container ship 9.220 6.969 0.756 6.916 0.750 0.992 6.951 0.754 6.635 0.720 0.955

Bulk carrier 20.394 17.500 0.858 16.602 0.814 0.949 15.800 0.775 15.380 0.754 0.973

D/H Suezmax 17.677 14.066 0.796 13.308 0.753 0.946 11.151 0.631 11.097 0.628 0.995

S/H VLCC 22.578 17.355 0.769 17.335 0.768 0.999 16.179 0.717 17.263 0.765 1.067

D/H VLCC 32.667 27.335 0.837 25.600 0.784 0.937 22.495 0.689 22.000 0.673 0.978

Mean 0.962 0.984

S-D 0.026 0.045

COV 0.027 0.046



ANSYS Nonlinear FEA versus ALPS/HULL ISFEM (2/2)

0 0.0125 10 15 20 25 30

0

0.0125

10

15

20

25

30


(Mu)

AL

PS/H

UL

L (G

Nm

)

(Mu)ANSYS(GNm)0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0



ALPS/ANSYS:

(Mu/M

p)A

LPS

/HU

LL

(Mu/Mp)ANSYS

Hog / Sag


ANSYS Nonlinear FEA versus CSR ISUM (1/2)

Ship Mp

(GNm)

Hogging Sagging

ANSYS CSRCSR/

ANSYS

ANSYS CSRCSR/

ANSYSMuh

(GNm)Muh/Mp

Muh

(GNm)Muh/Mp

Mus

(GNm)Mus/Mp

Mus

(GNm)Mus/Mp

Dow's test hull 0.013 0.011 0.840 0.012 0.888 1.058 0.011 0.793 0.010 0.764 0.963

Container ship 9.220 6.969 0.756 8.040 0.872 1.154 6.951 0.754 7.843 0.851 1.128

Bulk carrier 20.394 17.500 0.858 17.941 0.880 1.025 15.800 0.775 14.475 0.710 0.916

D/H Suezmax 17.677 14.066 0.796 15.714 0.889 1.117 11.151 0.631 12.420 0.703 1.114

S/H VLCC 22.578 17.355 0.769 19.889 0.881 1.146 16.179 0.717 17.868 0.791 1.104

D/H VLCC 32.667 27.335 0.837 28.352 0.868 1.037 22.495 0.689 24.798 0.759 1.102

Mean 1.090 1.055

S-D 0.056 0.091

COV 0.052 0.086



ANSYS Nonlinear FEA versus CSR ISUM (2/2)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0


CSR/ANSYS:

(Mu/M

p)C

SR

(Mu/Mp)ANSYS

Hog / Sag


0 0.0125 10 15 20 25 30

0

0.0125

10

15

20

25

30

(Mu)

CSR

(GN

m)

(Mu)ANSYS(GNm)



ALPS/HULL ISFEM versus CSR ISUM (1/2)

Ship Mp

(GNm)

Hogging Sagging

ALPS CSRCSR/ALPS

ALPS CSRCSR/ALPSMuh

(GNm)Muh/Mp

Muh

(GNm)Muh/Mp

Mus

(GNm)Mus/Mp

Mus

(GNm)Mus/Mp

Dow's test hull 0.013 0.011 0.799 0.012 0.888 1.111 0.010 0.743 0.010 0.764 1.029

Container ship 9.220 6.916 0.750 8.040 0.872 1.163 6.635 0.720 7.843 0.851 1.182

Bulk carrier 20.394 16.602 0.814 17.941 0.880 1.081 15.380 0.754 14.475 0.710 0.941

D/H Suezmax 17.677 13.308 0.753 15.714 0.889 1.181 11.097 0.628 12.420 0.703 1.119

S/H VLCC 22.578 17.335 0.768 19.889 0.881 1.147 17.263 0.765 17.868 0.791 1.035

D/H VLCC 32.667 25.600 0.784 28.352 0.868 1.108 22.000 0.673 24.798 0.759 1.127

Mean 1.132 1.072

S-D 0.038 0.087

COV 0.034 0.081



ALPS/HULL ISFEM versus CSR ISUM (2/2)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0


CSR/ALPS:

(Mu/M

p)C

SR

(Mu/Mp)ALPS/HULL

Hog / Sag


0 0.0125 10 15 20 25 30

0

0.0125

10

15

20

25

30

(Mu)

CSR

(GN

m)

(Mu)ALPS/HULL (GNm)



Concluding Remarks(1/2)Concluding Remarks(1/2)

- Four methods, namely NLFEM (ANSYS), ISFEM(ALPS/HULL), ISUM(CSR method), and Modified P-M formula method have been considered.

- Modified P-M formula method calculations are in good agreement with ANSYS nonlinear FEA and ALPS/HULL progressive collapse simulations.

Concluding Remarks(2/2)Concluding Remarks(2/2)

- Statistical analysis of the hull girder ultimate strength based on comparisons among the various computation is carried out in terms of their mean values and coefficient of variation.

ShipFormula/ANSYS

Formula/ALPS

Formula/CSR

ALPS/ANSYS

CSR/ANSYS

CSR/ALPS

Hog Sag Hog Sag Hog Sag Hog Sag Hog Sag Hog Sag

Dow's test hull 0.920 0.879 0.966 0.939 0.870 0.912 0.952 0.936 1.058 0.963 1.111 1.029

Container ship 0.918 1.018 0.925 1.067 0.796 0.902 0.992 0.955 1.154 1.128 1.163 1.182

Bulk carrier 0.947 0.937 0.998 0.962 0.924 1.022 0.949 0.973 1.025 0.916 1.081 0.941

D/H Suezmax 0.993 1.095 1.049 1.101 0.889 0.983 0.946 0.995 1.117 1.114 1.181 1.119

S/H VLCC 1.078 1.102 1.079 1.033 0.940 0.998 0.999 1.067 1.146 1.104 1.147 1.035

D/H VLCC 0.939 0.995 1.003 1.018 0.905 0.903 0.937 0.978 1.037 1.102 1.108 1.127

Mean 0.966 1.004 1.003 1.020 0.887 0.953 0.962 0.984 1.090 1.055 1.132 1.072

S-D 0.061 0.088 0.055 0.061 0.051 0.054 0.026 0.045 0.056 0.091 0.038 0.087

COV 0.063 0.087 0.055 0.060 0.058 0.056 0.027 0.046 0.052 0.086 0.034 0.081

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