Reliability analysis of Ship Structures Fatigue and Ultimate Strength Fabrice Jancart François Besnier PRINCIPIA MARIN

1. Reliability analysis of Ship StructuresFatigue and Ultimate StrengthFabrice Jancart François Besnier PRINCIPIA MARINE fabrice.jancart@nantes.principia.fr ASRANet Colloquium 2002

2. Summary • Uncertainties identification • Rule based design and rational design • Industrial applications using PERMAS reliability capabilities • Optimisation and reliability • Fatigue • Ultimate strength • Conclusions ASRANet Colloquium 2002

3. A major concern: safety • On a competitive market • New ship concepts • Cost / Weight reduction • Considerations on sea safety are increasing ASRANet Colloquium 2002

4. Designing in an uncertain world: from models… • Modelling uncertainties: due to imperfect knowledge of phenomena and idealization and simplification in analysis procedure • Loading • Hydrodynamic forces (physical and mathematical models) • Damage evaluation • Structural response • Finite element model • Approximations, simplifications • From global to local: • Uncertainties on fabrication effects • Fabrication tolerance, residual stresses • “ Natural” uncertainties ASRANet Colloquium 2002

5. Load modelling • Numerical wave bending moment scatter according to the same hypothesis from 5.104 T*m to 12 104 T*m ASRANet Colloquium 2002

6. From global to local 50 000 dof 300 000 dof ASRANet Colloquium 2002

7. Designing in an uncertain world:From material stochastic properties • Material properties scatter • True or nominal values • S-N curves approximated by P(f)=50%  N ASRANet Colloquium 2002

8. Designing in an uncertain world:From “natural” stochastic properties • Natural uncertainties: due to statistical nature of ship mission • Environmental loading • Short term sea states • Long term sea states distribution • Missions and routes Example of block decomposition introduce scatter in prediction Wave scatter diagram for one block ASRANet Colloquium 2002

9. Rule based design:method and limits • Rule based approach with • Historical hidden safety margins • Calibrated by experience on large conventional ships • Incompatible with innovative ship or structural concepts • Cannot be applied on structural optimisation process • Incompatible with uncertainties on the complex ship environment and structural behavior • Difficulty to determine the safety margins and their evolution • Conflicting with first principal or rational design • Need to update the safety partial coefficients with first principles ASRANet Colloquium 2002

10. Reliability approach:risk quantification • Stochastic definition of the problem: • Closer to reality • Computes the probability that solicitations L exceed strength of the structure R Deterministic Probabilistic ASRANet Colloquium 2002

11. Use of PERMAS reliability capabilities • Work mainly done during EC supported ASRA Esprit project • Objective : Optimisation under reliability constraints with Permas software • Numerical calculation of failure probability • Comparison of various methods: • FORM/SORM gradient based methods • Response surface methods (RSM) • Crude and adaptive Monte Carlo • Stochastic calibration of partial safety factors • Sequences of reliability - optimisation – reliability ASRANet Colloquium 2002

12. Industrial Application: reinforced opening • Optimisation of reinforced passengers ship doors • Many occurrences of this costly detail • Submitted to alternate shear forces • Reinforced for fatigue criteria F Door Gangway -F ASRANet Colloquium 2002

13. Industrial Application: reinforced opening • Maximum shear stress criterion • Evolution of reliability with optimisation Limit stress Scantling Load ASRANet Colloquium 2002

14. Industrial Application reinforced opening • Optimisation: • Mass decreases by 10% • Reliability of initial and optimised designs • Stochastic loading, normal distribution • Failure function G = slim - sFE • slim stochastic variable, normal distribution • Failure probability increases from 1.7 10-5to 2.8 10-3 Optimisation without reliability constraints jeopardises safety ASRANet Colloquium 2002

15. Industrial Application: High speed craft Impact (slamming) sagging • Exploitation of high speed crafts (fast mono hulls) reveals: • Fatigue problems under alternate bending and repeated slamming • Ultimate strength problems (local and deck buckling ) First principle design reliability based approach compared to traditional (rule based) approach ASRANet Colloquium 2002

16. Industrial Application: High speed craft • Loading uncertainties (models and stochastic nature) • Structural strength uncertainties • Fatigue limit • Ultimate buckling stress • Missions, routes and service life • Heavy weather countermeasures Fatigue failure & buckling collapse Confirmed to be very critical design criteria and subjected to significant uncertainties ASRANet Colloquium 2002

17. High speed craftBuckling High speed vessel on large wave crest Significant bending moment inducing buckling ASRANet Colloquium 2002

18. High speed craftBuckling u  (Mextr) T • Buckling reliability at mid-ship section • Failure state function • Uncertainties on • Ultimate buckling stress u due to scatter on in-yard fabrication tolerances, built in stresses, described by a log-normal distribution • Extreme value of wave bending moment Mextr,with a Gumbel max probability density law depending on ship service time T • : load modelling effect due to FEM approximations, with a normal distribution ASRANet Colloquium 2002

19. FatigueReliability analysis Large number of welded connections, where cracks may initiate Typical welded structural detail, fatigue prone ASRANet Colloquium 2002

20. FatigueReliability analysis 2 1 Historic S K (S-N curve) Loading N T S Local mesh for stress extrapolation (hot spot) Detail loaded by displacements of global model ASRANet Colloquium 2002

21. FatigueReliability analysis • Fatigue reliability due to global wave loads • Failure state function • Uncertainties on • Critical damage Dc with a log-normal distribution • S-N curve (K) due to variable fabrication conditions described by a log-normal distribution • Load modelling S • due to hydrodynamic numerical and navigation condition hypothesis • due to effort in avoiding numerical singularities with the extrapolation near the weld • described by log-normal distributions • C(T): function of service time T ASRANet Colloquium 2002

22. FatigueReliability analysis • More complex failure function: Dc: critical damage, taken from Classification Society recommendation and defined by a lognormal law, Kp associated to the S-N curve definition Sm.N=Kp,and defined by a lognormal law m parameter of the S-N curve w ,  parameters of the Weibull distribution C1 deterministic coefficient associated to the time at sea considered, C2 deterministic coefficient used in the long term loading distribution KL associated to the local stress effect S is the stress variation during wave loading.  gamma function : ASRANet Colloquium 2002

23. Fatigue and bucklingReliability analysis • Buckling reliability for 1 year of exploitation • Fatigue reliability for 15 years of exploitation ASRANet Colloquium 2002

24. Fatigue and buckling Elasticity • Ultimate strength Fatigue ASRANet Colloquium 2002

25. Fatigue and service time • Introduction of time-variant effects in the reliability approach : • Fatigue strength evolution • Effects of aging and corrosion ASRANet Colloquium 2002

26. Conclusions • « Considering alea in the design process introduces an additional accuracy» Hasofer • Rule based design is not always conservative • Reliability approach can lead to an optimised and robust design. • Simulation methods (Monte Carlo) are too costly for industrial applications. • Use of an existing tool coupling structural and reliability calculations • Gradient based and RSM methods efficient • Application on innovative ship structural concepts ASRANet Colloquium 2002

27. Thank you for your attention ASRANet Colloquium 2002