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

1. A Comparison of Numerical Methods to Predict the Progressive Collapse of Lightweight Aluminium Vessels Simon Benson, Jonathan Downes, Robert S. Dow Newcastle University, UK 11thInternational Conference on Fast Sea Transportation September 26-29, 2011

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

3. 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

4. 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?

5. 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

6. 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

7. 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

8. Nonlinear Finite Element Method • Example mesh controls • Plate Imperfection • Stiffener Imperfection • Column Imperfection

9. Interframe Progressive Collapse Method Define (midship) cross section • Assumptions: • Cross-section remains plane • Interframe buckling • Panel elements act independently Divide section into elements Define load shortening curve for each element Apply curvature increment Find equilibrium NA position Calculate incremental Bending Moment

10. Compartment Progressive Collapse Method Define (midship) cross section • 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 Divide section into elements Define load shortening curve for each element Apply curvature increment Find equilibrium NA position Calculate incremental Bending Moment

11. Case Study: Box Girder • 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

12. 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)

13. Case Study: Box Girder • Box Girder Analysis: • FEM • Interframe progressive collapse method (Pcoll-I) • Compartment progressive collapse method (Pcoll-O) • Example result: M1-T1

14. 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

15. Case Study: Aluminium Multihull

16. Case Study: Aluminium Multihull

17. Case Study: Aluminium Multihull • Sag Bending Moment • Interframe Results • Very close agreement between FEM and PColl

18. 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

19. Case Study: Aluminium Multihull

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