Reliability analysis of Ship Structures Fatigue and Ultimate Strength Fabrice Jancart François Besnier PRINCIPIA MARI - PowerPoint PPT Presentation

Reliability analysis of Ship StructuresFatigue and Ultimate StrengthFabrice Jancart François Besnier PRINCIPIA MARINE

fabrice.jancart@nantes.principia.fr

ASRANet Colloquium 2002

• Uncertainties identification
• Rule based design and rational design
• Industrial applications using PERMAS reliability capabilities
• Optimisation and reliability
• Fatigue
• Ultimate strength
• Conclusions

ASRANet Colloquium 2002

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

ASRANet Colloquium 2002

• 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

• Numerical wave bending moment scatter according to the same hypothesis

from 5.104 T*m to 12 104 T*m

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50 000 dof

300 000 dof

ASRANet Colloquium 2002

• Material properties scatter
• True or nominal values
• S-N curves approximated by

P(f)=50%



N

ASRANet Colloquium 2002

• 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

• 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

• 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

• 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

• 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

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• Maximum shear stress criterion
• Evolution of reliability with optimisation

Limit stress

Scantling Load

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• 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

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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

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

High speed vessel on large wave crest

Significant bending

moment inducing buckling

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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

Large number of welded connections, where cracks may initiate

Typical welded structural detail, fatigue prone

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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

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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

• 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 :

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• Buckling reliability for 1 year of exploitation

• Fatigue reliability for 15 years of exploitation

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• Ultimate strength

Fatigue

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Fatigue and service time

• Introduction of time-variant effects in the reliability approach :
• Fatigue strength evolution
• Effects of aging and corrosion

ASRANet Colloquium 2002

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

ASRANet Colloquium 2002