ASRANet Colloquium 2002 Reliability analysis of Ship Structures Fatigue and Ultimate Strength Fabrice Jancart François Besnier PRINCIPIA MARINE

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

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

4 ASRANet Colloquium 2002 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

5 ASRANet Colloquium 2002 Load modelling  Numerical wave bending moment scatter according to the same hypothesis from T*m to T*m

6 ASRANet Colloquium 2002 From global to local dof dof

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

8 ASRANet Colloquium 2002 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 Wave scatter diagram for one block Example of block decomposition introduce scatter in prediction

9 ASRANet Colloquium 2002 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

10 ASRANet Colloquium 2002 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

11 ASRANet Colloquium 2002 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

12 ASRANet Colloquium 2002 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 Gangway Door F -F

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

14 ASRANet Colloquium 2002 Industrial Application reinforced opening  Optimisation:  Mass decreases by 10%  Reliability of initial and optimised designs  Stochastic loading, normal distribution  Failure function G =  lim -  FE   lim stochastic variable, normal distribution  Failure probability increases from to Optimisation without reliability constraints jeopardises safety

15 ASRANet Colloquium 2002 Industrial Application: High speed craft  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 Impact (slamming) sagging

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

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

18 ASRANet Colloquium 2002 High speed craft Buckling  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 M extr, with a Gumbel max probability density law depending on ship service time T   : load modelling effect due to FEM approximations, with a normal distribution uu T  (M extr ) Buckling reliability at mid-ship section Failure state function

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

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

21 ASRANet Colloquium 2002  Uncertainties on  Critical damage D c 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 Fatigue Reliability analysis  Fatigue reliability due to global wave loads  Failure state function

22 ASRANet Colloquium 2002 Fatigue Reliability analysis  More complex failure function: D c :critical damage, taken from Classification Society recommendation and defined by a lognormal law, K p associated to the S-N curve definition S m.N=K p, and defined by a lognormal law m parameter of the S-N curve w,  parameters of the Weibull distribution C 1 deterministic coefficient associated to the time at sea considered, C 2 deterministic coefficient used in the long term loading distribution K L associated to the local stress effect S is the stress variation during wave loading.  gamma function :

23 ASRANet Colloquium 2002  Buckling reliability for 1 year of exploitation  Fatigue reliability for 15 years of exploitation  - index PfPf Tps CPU FORM SORM 0, ,2% 18,7% 29 mn RSM_LIN RSM_AXIAL 0, / ,1% 0.17/ mn 72 mn  - index PfPf Tps CPU Rule (SN curve)2,052%- SORM RSM_LIN 1, ,3% 16.45% 26 mn 50 mn RSM_CCD1,0115,7%84 mn Fatigue and buckling Reliability analysis

24 ASRANet Colloquium 2002  Ultimate strength VariableVs Mean valueVs Std dev. Loading uu VariableVs Mean valueVs Std dev K (S-N curve) Sollicitation S Critical damage D c Fatigue Fatigue and buckling Elasticity

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

26 ASRANet Colloquium 2002  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 Conclusions  « Considering alea in the design process introduces an additional accuracy» Hasofer

27 ASRANet Colloquium 2002 Thank you for your attention