a comparison of numerical methods to predict the progressive collapse of lightweight aluminium...
TRANSCRIPT
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
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Contents
• Introduction• Longitudinal Bending Strength Methods:
– Nonlinear Finite Element Method– Interframe Progressive Collapse Method– Compartment Progressive Collapse Method
• Case Study• Conclusions
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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
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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?
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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
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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
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Nonlinear Finite Element Method
• 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
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Nonlinear Finite Element Method
• Example mesh controls
– Plate Imperfection
– Stiffener Imperfection
– Column Imperfection
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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
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• 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
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• 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
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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
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Case Study: Box Girder
• 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
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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
Case Study: Box Girder
• Box Girder Analysis:– FEM– Interframe progressive
collapse method (Pcoll-I)– Compartment progressive
collapse method (Pcoll-O)
• Example result: M1• Example result: M3
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Case Study: Aluminium Multihull
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Case Study: Aluminium Multihull
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Case Study: Aluminium Multihull
• Sag Bending Moment• Interframe Results• Very close agreement between
FEM and PColl
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Case Study: Aluminium Multihull
• 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
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Case Study: Aluminium Multihull
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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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