Report

Reliability analysis of Ship Structures Fatigue and Ultimate Strength Fabrice Jancart François Besnier PRINCIPIA MARINE [email protected] ASRANet Colloquium 2002 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 2 A major concern: safety On a competitive market New ship concepts Cost / Weight reduction Considerations on sea safety are increasing ASRANet Colloquium 2002 3 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 4 Load modelling MODIFIED HULL, 0 knots 2,00E+04 0,00E+00 -100 -80 -60 -40 -20 0 20 40 60 80 100 Wave bending moment (t.m) -2,00E+04 L1 -4,00E+04 L1(bis) L2 L3 -6,00E+04 L4 L5 L6 -8,00E+04 L7 L8 -1,00E+05 -1,20E+05 -1,40E+05 X (m) Numerical wave bending moment scatter according to the same hypothesis from 5.104 T*m to 12 104 T*m ASRANet Colloquium 2002 5 From global to local 50 000 dof 300 000 dof ASRANet Colloquium 2002 6 Designing in an uncertain world: From material stochastic properties Material properties scatter True or nominal values S-N curves approximated by log10 ( N ) log10 (C) m. log10 ( ) P(f)=50% N ASRANet Colloquium 2002 7 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 Scatter Diagram 250 100 m( 150 s) Occurence 200 dT 50 Signi 0 ficativ 1 e Heig 2 ht... Pe rio 0 16-18 Example of block decomposition 10-12 4-6 introduce scatter in prediction 3 Wave scatter diagram for one block ASRANet Colloquium 2002 8 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 9 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 LD LR R L R RD RR R LL R Pf ( R L) Pf ,t arget Probabilistic ASRANet Colloquium 2002 10 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 11 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 -F ASRANet Colloquium 2002 Gangway 12 Industrial Application: reinforced opening Limit stress Scantling Load Maximum shear stress criterion Evolution of reliability with optimisation ASRANet Colloquium 2002 13 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 1.7 10-5 to 2.8 10-3 Optimisation without reliability constraints jeopardises safety ASRANet Colloquium 2002 14 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 ) Impact (slamming) sagging First principle design reliability based approach compared to traditional (rule based) approach ASRANet Colloquium 2002 15 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 ASRANet Colloquium 2002 16 High speed craft Buckling High speed vessel on large wave crest Significant bending moment inducing buckling ASRANet Colloquium 2002 17 High speed craft Buckling Buckling reliability at mid-ship section Failure state function G u (Mextr ) 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 u (Mextr) ASRANet Colloquium 2002 T 18 Fatigue Reliability analysis Large number of welded connections, where cracks may initiate Typical welded structural detail, fatigue prone ASRANet Colloquium 2002 19 Fatigue Reliability analysis Historic S K (S-N curve) Loading N T S Detail loaded by displacements of global model 2 1 Local mesh for stress extrapolation (hot spot) ASRANet Colloquium 2002 20 Fatigue Reliability analysis Fatigue reliability due to global wave loads Failure state function Uncertainties on C( T ) m G Dc S K 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 21 Fatigue Reliability analysis m More complex failure function: C1 m G Dc .( 1).C 2 . K Lm . S m Kp 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 S f (S) ww 1 S e xp w 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 : S a 1 t S e dt 0 ASRANet Colloquium 2002 22 Fatigue and buckling Reliability analysis Buckling reliability for 1 year of exploitation FORM SORM RSM_LIN RSM_AXIAL - index Pf Tps CPU 0,947 0.89 17,2% 18,7% 29 mn 29 mn 0,95 0.95/0.89 17,1% 0.17/0.187 60 mn 72 mn Fatigue reliability for 15 years of exploitation - index Pf Tps CPU Rule (SN curve) 2,05 2% - SORM RSM_LIN 1,02 0.976 15,3% 16.45% 26 mn 50 mn RSM_CCD 1,01 15,7% 84 mn ASRANet Colloquium 2002 23 Fatigue and buckling Elasticity Ultimate strength Variable Vs Mean value Vs Std dev. Loading -5.88 -0.24 9 0.69 u Fatigue Variable Vs Mean value Vs Std dev K (S-N curve) Sollicitation S 1.75 3.29 -0.47 -0.58 Critical damage Dc 1.525 -0.24 ASRANet Colloquium 2002 24 Fatigue and service time Introduction of time-variant effects in the reliability approach : Fatigue strength evolution Effects of aging and corrosion ASRANet Colloquium 2002 25 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 26 Thank you for your attention ASRANet Colloquium 2002 27