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

Simon Benson, Jonathan Downes, Robert S. Dow
Newcastle University, UK

11th International Conference on Fast Sea Transportation

September 26-29, 2011

Contents
• Introduction
• Longitudinal Bending Strength Methods:
– Nonlinear Finite Element Method
– Interframe Progressive Collapse Method
– Compartment Progressive Collapse Method
• Case Study
• Conclusions

11th International Conference on Fast Sea Transportation 2

Introduction
• Research funded through the Office of Naval Research
• Increasing size of lightweight vessels constructed from
aluminium:
Image ref: www.austal.com

• 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


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
5083-H116 Plate Load Shortening Curves
Define (midship) HAZ Ratio (HR) = 8

cross section 1
0.9

Normalised Stress, s' = save / s0
0.8
0.7

Divide section 0.6
0.5
b=2

into elements 0.4
0.3
0.2
0.1
0
Define load shortening 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Normalised strain, e' = e ave / e 0
curve for each element

Apply curvature
increment • Assumptions:
– Cross-section remains plane
1.50

Bending Moment, Mx (N.mm) x 10-10
1.00

Find equilibrium NA – Interframe buckling 0.50

position hog

– Panel elements act independently 0.00

sag
-0.50 Progressive Collapse - 150mm hard corners

Abaqus 5bay model (50mm element size)
-1.00
Calculate incremental Abaqus 5bay model (25mm element size)

-1.50
Bending Moment -4.00 -3.00 -2.00
11th International Conference on Fast Sea Transportation -1.00 0.00 1.00 2.00 3.00 4.00
9
Curvature, C (1/mm) x 106

Compartment Progressive Collapse Method
Define (midship)
cross section
• Extends the approach used to define the element
behaviour
Divide section • Revised Assumptions:
into elements
– Cross section remains plane (as before)
– Compartment level elements
Define load shortening – Elements do not act independently
curve for each element – Interframe and overall buckling properties
combined
Apply curvature • Elements defined with a semi analytical orthotropic
plate method
increment

Find equilibrium NA
position

Calculate incremental
Bending Moment 11th International Conference on Fast Sea Transportation
10
10

Case Study: Box Girder
a b tp
Dataset ID
(mm) (mm) (mm)
• Twelve box girder variants: M1
M2
1200
1200
400
400
14.8
11.1
– Plate thickness M3
M4
1200
1200
400
400
8.9
7.4
– Frame size Dataset hw tw bf tf
ID (mm) (mm) (mm) (mm)
• FEM Analyses: T1
T2
180
360
10
10
0
0
0
0
– Plate-Stiffener Combination T3 360 10 100 15

– Multi-bay panel
– Box girder
• Semi-analytical panel analyses:
– Plate-Stiffener Combination
– Multi-bay panel
• Compartment Progressive Collapse Analysis


• Single Flange Panel Analyses:
– FEM
– Semi Analytical Method
• Influence of overall collapse mode
• Example result: M1-T2 (stocky frame) 1.0
1.0
• Example result: M1-T1 (slender frame) 0.9
0.9
0.8
0.8
0.7
0.7
0.6

s xave /s00
0.6

s xave/s
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2 PSC (FEM)
PSC (FEM)
0.1 Semi Analytical Method
Semi Analytical Method
0.1
FEM
FEM
0.0
0.0
0.0
0.0 0.5
0.5 1.0
1.0 1.5 1.5 2.0
2.0
e /e 0
e /e
0


3.00E+08

• Box Girder Analysis: 2.50E+08

Bending Moment (Nm)
– FEM 2.00E+08

– Interframe progressive 1.50E+08

collapse method (Pcoll-I) 1.00E+08
– Compartment progressive FEM: M1 long., T1 frames
FEM: M1 long., T2 frames
5.00E+07 PColl-I - M1
collapse method (Pcoll-O) PColl-O: M1 long., T1 frames
PColl-O: M1 long., T2 frames

• Example result: M1-T1
0.00E+00
0 0.0005 0.001
Curvature (1/mm)


2.00E+08
1.80E+08
• Box Girder Analysis: 1.60E+08

Bending Moment (Nm)
– FEM 1.40E+08
1.20E+08
– Interframe progressive 1.00E+08

collapse method (Pcoll-I) 8.00E+07
6.00E+07
– Compartment progressive 4.00E+07
collapse method (Pcoll-O) 2.00E+07 PColl-O: M3 long., T1 frames
PColl-O: M3 long., T2 frames

• Example result: M1 0.00E+00
0 0.0005 0.001
Curvature (1/mm)
• 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



19

20

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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