A Comparison of Numerical Methods to Predict the Progressive Collapse of Lightweight Aluminium...

A Comparison of Numerical Methods to Predict the Progressive Collapse of Lightweight

Aluminium Vessels

Simon Benson, Jonathan Downes, Robert S. DowNewcastle University, UK

11th International Conference on Fast Sea Transportation

September 26-29, 2011

11th International Conference on Fast Sea Transportation 2

Contents

• Introduction• Longitudinal Bending Strength Methods:

– Nonlinear Finite Element Method– Interframe Progressive Collapse Method– Compartment Progressive Collapse Method

• Case Study• Conclusions


Introduction

• Research funded through the Office of Naval Research• Increasing size of lightweight vessels constructed from

aluminium:

• Requirement for special purpose tools to quantify primary hull structural performance in intact and damage conditions,

• Methods must account for:– “Novel” lightweight structures (trimaran, catamaran, monohull)– Unconventional materials and construction (aluminium, composites)– Deep ocean operability

Image ref: www.austal.com


Hull Girder Strength Methods

• Established hull girder progressive collapse methods have been developed primarily for STEEL ships.

• Two general approaches:– Simplified analytical methods (e.g. progressive collapse):

• Fast and efficient• Simplifying assumptions• Implicit characterisation of material and geometric imperfections

– Nonlinear finite element methods (FEM):• Computationally expensive• Requires explicit characterisation of all material and geometric properties in the FE

model

• How do we adapt these approaches to high speed craft?


Hull Girder Strength Methods

• Nonlinear FEM:– Relatively complex setup and analysis– Predicts overall and interframe collapse modes– Readily adaptable to novel structures

• Progressive Collapse Method:– Relatively simple setup and analysis– Requires element load-end shortening curves– Assumes interframe failure

• “Extended” Progressive Collapse Method:– Relatively simple setup and analysis– Requires element and large panel load-end shortening curves– Capacity for interframe and multi-bay failure– Improved capabilities for lightweight structures


Nonlinear Finite Element Method

• Established general purpose pre/post processors and solvers: – ABAQUS

• Where is the analysis time spent?– Pre-processing– Solver– Post-processing

• Complex material and geometric properties:– Heat Affected Zone– Residual Stress– Geometric Imperfections

• A robust modelling approach is required



• Building Block Approach:– FEM model created using

input data-file– Complex structure built from

simple plate and stiffener components

– Cartesian translation– Keep control of imperfection

and residual stresses in each component

– Imperfections modelled using node translation with Fourier series

– HAZ and residual stresses



• Example mesh controls

– Plate Imperfection

– Stiffener Imperfection

– Column Imperfection


Interframe Progressive Collapse Method

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

-4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00

Bend

ing

Mom

ent,

Mx

(N.m

m) x

10-1

0

Curvature, C (1/mm) x 106

Progressive Collapse - 150mm hard corners

Abaqus 5bay model (50mm element size)

Abaqus 5bay model (25mm element size)

hog

sag

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Nor

mal

ised

Str

ess,

s' =

sav

e/ s 0

Normalised strain, e' = eave / e0

5083-H116 Plate Load Shortening CurvesHAZ Ratio (HR) = 8

b=2.5

Define (midship) cross section

Divide section into elements

Define load shortening curve for each element

Apply curvature increment

Find equilibrium NA position

Calculate incremental Bending Moment

• Assumptions:– Cross-section remains plane– Interframe buckling– Panel elements act independently


• Extends the approach used to define the element behaviour

• Revised Assumptions:– Cross section remains plane (as before)– Compartment level elements– Elements do not act independently– Interframe and overall buckling properties combined

• Elements defined with a semi analytical orthotropic plate method

Compartment Progressive Collapse MethodDefine (midship)

cross section

Divide section into elements

Define load shortening curve for each element

Apply curvature increment

Find equilibrium NA position

Calculate incremental Bending Moment


• Twelve box girder variants:– Plate thickness– Frame size

• FEM Analyses:– Plate-Stiffener Combination– Multi-bay panel– Box girder

• Semi-analytical panel analyses:– Plate-Stiffener Combination– Multi-bay panel

• Compartment Progressive Collapse Analysis

Case Study: Box GirderDataset ID

a(mm)

b(mm)

tp

(mm)M1 1200 400 14.8M2 1200 400 11.1M3 1200 400 8.9M4 1200 400 7.4

Dataset ID

hw(mm)

tw(mm)

bf(mm)

tf(mm)

T1 180 10 0 0T2 360 10 0 0T3 360 10 100 15


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0s

xave

/s0

e /e0

PSC (FEM)Semi Analytical MethodFEM

Case Study: Box Girder

• Single Flange Panel Analyses:– FEM– Semi Analytical Method

• Influence of overall collapse mode• Example result: M1-T2 (stocky frame)• Example result: M1-T1 (slender frame)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0s

xave

/s0

e /e0

PSC (FEM)Semi Analytical MethodFEM



• Box Girder Analysis:– FEM– Interframe progressive

collapse method (Pcoll-I)– Compartment progressive

collapse method (Pcoll-O)

• Example result: M1-T1 0.00E+00

5.00E+07

1.00E+08

1.50E+08

2.00E+08

2.50E+08

3.00E+08

0 0.0005 0.001

Bend

ing M

omen

t (N

m)

Curvature (1/mm)

FEM: M1 long., T1 framesFEM: M1 long., T2 framesPColl-I - M1PColl-O: M1 long., T1 framesPColl-O: M1 long., T2 frames


0.00E+00

2.00E+07

4.00E+07

6.00E+07

8.00E+07

1.00E+08

1.20E+08

1.40E+08

1.60E+08

1.80E+08

2.00E+08

0 0.0005 0.001

Bend

ing M

omen

t (N

m)

Curvature (1/mm)

FEM: M3 long., T1 frames

FEM: M3 long., T2 frames

PColl-O: M3 long., T1 frames

PColl-O: M3 long., T2 frames


• Box Girder Analysis:– FEM– Interframe progressive

collapse method (Pcoll-I)– Compartment progressive

collapse method (Pcoll-O)

• Example result: M1• Example result: M3


Case Study: Aluminium Multihull



• Sag Bending Moment• Interframe Results• Very close agreement between

FEM and PColl



• 7 bay results:– reduction in ultimate strength– Buckling of top deck prior to ultimate strength

point– Buckling of second deck at ultimate strength

point– Close agreement between FEM and PColl

• Top Deck Load Shortening Curve:– Accounts for different longitudinal stiffener sizes


Conclusions

• Extended progressive collapse method:– Capable of predicting interframe and compartment level collapse

modes for lightweight ship structures

• Validated with simple box girder and catamaran• Further work has been identified including:

– Investigate the suitability of the present method to predict biaxial bending moment response with overall collapse modes

– Investigate the effects of different unsupported deck widths and lengths

– Investigate the effects of transverse loads, such as may be caused by prying moment in a catamaran

– Apply the methods to realistic ship structures

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A Comparison of Numerical Methods to Predict the Progressive Collapse of Lightweight Aluminium...

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