1. AN AUTOMATED FINITE ELEMENT METHODOLOGY FOR
HULL GIRDER PROGRESSIVE COLLAPSE ANALYSIS
Simon Benson, Jonathan Downes and Robert S. Dow
School of Marine Science and Technology

2. 2
Contents
 Motivation
 Nonlinear Finite Element Method (NLFEM)
 Hull Girder Modelling Strategy
 Geometric Imperfections
 Case Study

3. 3
Motivation
 Office of Naval Research (ONR) project:
“Structural Performance of Lightweight Naval Vessels”
 Development and extension of hull girder progressive
collapse analysis methodologies:
 Ultimate Strength Analysis
 Limit State Design
 Optimisation
 Reliability
 Damage Strength
 Recoverability
 Methods:
 Simplified Progressive Collapse Method
 Nonlinear Finite Element Method

4. 4
Nonlinear Finite Element Method
 Allows prediction of buckling and
collapse characteristics of a
structure
 Capable of predicting hull girder
progressive collapse:
 Longitudinal bending (global load)
 A nonlinear phenomenon
 A function of the buckling strength of the
compressed portion of the hull girder
 Nonlinear solver approach:
 Abaqus CAE 6.9
 “Quasi-static” implicit arc length solver
OR
 Dynamic-explicit solver

5. 5
NLFEM Modelling Strategy
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From here……

6. 6
NLFEM Modelling Strategy
 The FEM modelling process:
 Geometry definition
 Assignment of properties (thickness, material)
 Definition boundary conditions
 Selection of solver
 Generation of suitable mesh
 Introduction of geometric imperfections and residual stresses
 Solving and post-processing
 What aspects are time intensive (for the analyst)?
 Which aspects are important for nonlinear analysis?

7. 7
NLFEM Modelling Strategy
 Characteristics of a NLFEM Hull Girder Model:
 Model length
 Longitudinal structural details
 Transverse structural details
 Geometric imperfections (plate/stiffener out-of-flatness)
 Residual stresses due to welding
 These characteristics affect the global longitudinal strength
 How do we represent these factors in the NLFEM model?

8. 8
NLFEM Modelling Strategy
Define Basis Model
Apply Boundary
Conditions
Mesh and Apply
Geometric Imperfections
Solve for Initial
Residual Stresses
Solve for Load
Condition
Post Process

9. 9
Geometric Imperfections
 Buckling strength of plates and
panels are affected by geometric
imperfections
 Representative imperfections must
be explicitly modelled in the FEM
mesh
 Plate Imperfection
 Stiffener Imperfection
 Column Imperfection
 Imperfection amplitude
 Methods for modelling
imperfections:
 Eigenmode Superposition
 Direct Translation of Nodes

10. 10
Modelling Method
The “building block” approach
 Define longitudinal scantlings as a
collection of individual components:
 Simple plates
 Single stiffeners
 Assign stress zones and other properties at
the component level
 Keep component identity throughout model
build process
 Allows the nodes within each component to
be controlled individually and collectively to
impart initial imperfections into the model

11. 11
Modelling Method
 Method Steps:
1. Write/generate input file
2. Build geometry from pre-defined
building blocks in ABAQUS
(python script)
3. Set parameters (BCs, solver, etc.)
4. Mesh geometry and write out
“perfect” Abaqus input file
5. Apply geometric imperfections to
model (python script)
6. Solve “imperfect” Abaqus input
file

12. 12
Case Study
 1/3 Scale Frigate Model
 Experimental Test in 1988
(Dow 1991)
 Scantlings known
 Sag bending moment
 Correlated with equivalent
progressive collapse method
(interframe)
 Girder is re-analysed in
numerous papers
 FEM Analyses:
 Interframe (½+1+½ bays –
buckling in central bay)
 Single compartment (including
bulkheads)

13. 13
Interframe Result
Bending Moment Curve
 ½+1+½ bay model
 Imperfection in central bay only
(average imperfections)
 Comparison:
 Experiment
 Smith Method
 Close correlation to experiment
result

14. 14
Interframe Result
Effect of Imperfection Amplitude
 Three levels of geometric
imperfection
 Slight
 Average
 Severe
 Imperfection amplitudes as defined by
Smith (1991)
 Higher imperfection amplitude =
reduction in strength and bending
stiffness
Smith (1991) – Steel Panels Paik (2008) – Aluminium Panels
Slight Average Severe Slight Average Severe
wopl 0.025 2t 0.1 2t 0.3 2t 0.018 2t 0.096 2t 0.252 2t
woc (= 0.2) 0.0008a 0.0020a
( =0.4) 0.00025a 0.0012a 0.0038a 0.0016a 0.0018a 0.0056a
( >= 0.6) 0.0015a 0.0046a
vos - - - 0.00019a 0.001a 0.0024a

15. 15
Compartment Results
 Compartment model
 Allows buckling over multiple frames
 Top deck fails with an overall collapse
mode across the test bays
 Ultimate strength of about 85% of the
experiment and interframe FEM result

16. 16
Compartment Results
 Comparable buckling pattern in the numerical solution
compared to experiment
 Why do we show differences?

17. 17
Compartment Results

18. 18
Conclusions
 We propose an automated FEM approach with capabilities for robust
modelling of a complex hull girder section for interframe or
compartment level progressive collapse analysis
 The methodology allows the imperfection characteristics of the
section to be accurately modelled in the FEM mesh
 The automated methodology has potential for improving NLFEM
integration in a ship design process:
 Simple data file
 Integration with other software (e.g. CAD, HECSALV)
 The data file is comparable to those used in equivalent simplified
progressive collapse methodologies
 The automation procedure significantly improves the usability of
NLFEM in practical design situations
 Reduces the model build time
 Robust and repeatable methodology for imperfections

19. Thank you
http://www.ncl.ac.uk/marine/
http://sibenson.wordpress.com