Transcript Ship Reliability Analysis

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
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A major concern: safety
 On a competitive market
 New ship concepts
 Cost / Weight reduction
 Considerations on sea safety are
increasing
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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
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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
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From global to local
50 000 dof
300 000 dof
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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
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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
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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
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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
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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
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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
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Gangway
12
Industrial Application:
reinforced opening
Limit stress
Scantling Load
 Maximum shear stress criterion
 Evolution of reliability with optimisation
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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
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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
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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
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High speed craft
Buckling
High speed vessel on large
wave crest
Significant bending
moment inducing buckling
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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)
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T
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Fatigue
Reliability analysis
Large number of welded
connections, where cracks
may initiate
Typical welded structural
detail, fatigue prone
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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)
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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
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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)   
ww
 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
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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
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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
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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
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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
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Thank you for your attention
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