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

ASRANet Colloquium 2002

Reliability analysis of Ship Reliability analysis of Ship StructuresStructures

Fatigue and Ultimate StrengthFatigue and Ultimate Strength

Fabrice JancartFabrice Jancart François Besnier François Besnier

PRINCIPIA MARINEPRINCIPIA [email protected]

ASRANet Colloquium 2002 2

SummarySummary

Uncertainties identification Rule based design and rational design Industrial applications using PERMAS reliability

capabilities Optimisation and reliability Fatigue Ultimate strength

Conclusions


A major concern: safetyA major concern: safety

On a competitive market New ship concepts Cost / Weight reduction Considerations on sea safety

are increasing


Designing in an uncertain world:Designing in an uncertain world: from models… 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 modelApproximations, simplifications

From global to local:

Uncertainties on fabrication effects Fabrication tolerance, residual stresses

“ Natural” uncertainties


Load modellingLoad modelling

Numerical wave bending moment scatter according to the same hypothesis

from 5.104 T*m to 12 104 T*m

MODIFIED HULL, 0 knots

-1,40E+05

-1,20E+05

-1,00E+05

-8,00E+04

-6,00E+04

-4,00E+04

-2,00E+04

0,00E+00

2,00E+04

-100 -80 -60 -40 -20 0 20 40 60 80 100

X (m)

Wav

e be

ndin

g m

omen

t (t.m

)

L1

L1(bis)

L2

L3

L4

L5

L6

L7

L8


From global to localFrom global to local

300 000 dof

50 000 dof


Designing in an uncertain world:Designing in an uncertain world:From material stochastic propertiesFrom material stochastic properties

Material properties scatter True or nominal values S-N curves approximated by )(log.)(log)(log 101010 mCN

N

P(f)=50%


Designing in an uncertain world:Designing in an uncertain world:From “natural” stochastic propertiesFrom “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

4-6

10-12

16-18

0

50

100

150

200

250

Occu

rence

Scatter Diagram

Wave scatter diagram for one block

Example of block decomposition

introduce scatter in prediction


Rule based design:Rule based design:method and limitsmethod 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


Reliability approach:Reliability approach:risk quantificationrisk quantification

Stochastic definition of the problem: Closer to reality

Computes the probability that solicitations L exceed strength of the structure R

LR

R

LR

LR

ettff PLRP arg,)(

Deterministic

Probabilistic


Use of PERMAS Use of PERMAS reliability capabilitiesreliability 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


Industrial Application: Industrial Application: reinforced openingreinforced 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


Industrial Application: Industrial Application: reinforced openingreinforced opening

Maximum shear stress criterion Evolution of reliability with optimisation

Limit stress Scantling Load


Industrial Application Industrial Application reinforced openingreinforced 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


Industrial Application: Industrial Application: High speed craft 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


Industrial Application: Industrial Application: High speed craft High speed craft

Fatigue failure & buckling collapse

Confirmed to be very critical design criteriaand 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


High speed craftHigh speed craftBucklingBuckling

High speed vessel on large wave crest

Significant bending moment inducing buckling


High speed craftHigh speed craftBucklingBuckling

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

)M(G extru

u

T

(Mextr)

Buckling reliability at mid-ship section

Failure state function


Typical welded structural detail, fatigue prone

Large number of welded connections, where cracks may initiate

FatigueFatigueReliability analysisReliability analysis


Local mesh for stress extrapolation (hot spot)

2 1S

LoadingN

K (S-N curve)

T

Historic S


Detail loaded by displacements of global model


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 distributionsC(T): function of service time T


Fatigue reliability due to global wave loads Failure state function

mc S

K

)T(CDG



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 :

mmL

m

pc SKC

m

K

CDG ..).(.

21 1

dteSS ta

0

1

w

S

w

S

wSf exp)(

1


Buckling reliability for 1 year of exploitation

Fatigue reliability for 15 years of exploitation

- index Pf Tps CPU

FORMSORM

0,9470.89

17,2%18,7%

29 mn29 mn

RSM_LINRSM_AXIAL

0,950.95/0.89

17,1%0.17/0.187

60 mn72 mn

- index Pf Tps CPU

Rule (SN curve) 2,05 2% -

SORMRSM_LIN

1,020.976

15,3%16.45%

26 mn50 mn

RSM_CCD 1,01 15,7% 84 mn

Fatigue and bucklingFatigue and bucklingReliability analysisReliability analysis


Ultimate strength

Variable Vs Mean value Vs Std dev.

Loading -5.88 -0.24

u 9 0.69

Variable Vs Mean value Vs Std dev

K (S-N curve)Sollicitation S

1.753.29

-0.47-0.58

Critical damage Dc

1.525 -0.24

Fatigue

Fatigue and buckling Fatigue and buckling ElasticityElasticity


Fatigue and service time

Introduction of time-variant effects in the reliability approach :

Fatigue strength evolutionEffects of aging and corrosion


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

ConclusionsConclusions

« Considering alea in the design process introduces an additional accuracy» Hasofer


Thank you for your attention

Documents

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