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 Contents Motivation Nonlinear Finite Element Method (NLFEM) Hull Girder Modelling Strategy Geometric Imperfections Case Study
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 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
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 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 NLFEM Modelling Strategy Define Basis Model Apply Boundary Conditions Mesh and ApplyGeometric Imperfections Solve for Initial Residual Stresses Solve for Load Condition Post Process
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 Modelling MethodThe “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 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 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 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 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 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 Compartment Results Comparable buckling pattern in the numerical solution compared to experiment Why do we show differences?
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
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