Systems Engineering Sensitivity analysis Structural reliability

Systems Engineering

Sensitivity analysis

Structural reliability

In order to evaluate the risk of a technological solution and to

optimize costs in design or maintenance

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General presentation

General presentation

Public company with 110 k€ of funds

Location : Clermont-Ferrand - France

Prize winner in 2001 and 2003 for its innovative developments

Company created in 2001

22 persons

Scientific team founder

Prof. Maurice LEMAIRE

Délégué scientifique

Engineer INSA Lyon

IFMA Research Director

Maurice PENDOLA

CEO

Doctor & Engineer IFMA

Reliability Expert

3 Paris Clermont-Ferrand Bordeaux Seyne / Mer Paris Clermont-Ferrand Bordeaux Seyne / Mer

Parc Technologique de la Pardieu 1 allée Alan Turing

F-63170 AUBIERE Tél (00 33) 4 73 28 93 66 Fax (00 33) 4 73 28 95 76 aubiè[email protected]

Subsidiary Technopôle Var Matin

Route de la Seyne F-83191 OLLIOULES Tél (00 33) 4 94 62 51 95 Fax (00 33) 4 94 62 59 47 [email protected]

Localization

! New Adress ! From January 03, 2008

Centre d'affaires du Zenith 34 rue de Sarlièvre F-63200 COURNON d'Auvergne

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Our vocation, Our ambition

«  Expert in probability applied to engineering, PHIMECA aims to

become the international reference in this field»

Maurice PENDOLA, CEO PHIMECA

De grandes sociétés nous font déjà confiance:

Des références scientifiques nationales et internationales:

2 European projects

4 ANR projects

ImdR actor

More than 100 communications/articles

Some references

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Ours Knowhows

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Modelling & Engineering systems

From drafting to complete design, PHIMECA offers adapted solutions

Expertise:

CAD modelling

Structural analyses by finite element (elasticity, plasticity, fracture, fatigue, stability, thermal and dynamic)

Design according to codes of practices Integrity justification

Durability estimation Drafting

Tools:

CAD : SolidWorks 2007, CATIA V5, I-deas

Simulations : ANSYS V11, ABAQUS, NASTRAN NX Clusters

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Dedicated Software solutions

Software development of high-tech tools

From simple Graphical User Interface (GUI) to high performance solvers, our computer science department research and develop yours tools.

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General sketch for uncertainty analysis

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Reliability by PHIMECA Engineering

Interest of this approach

Control of possible outcomes for a given design Prediction of success and safety margins

Taking into account of the randomness on the input parameters Quantification and hierarchization of input parameters (driving a probable failure)

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PHIMECA Software

loading, time

Probability

of failure Failure probability_{Reliability index}

Second order approximations (SORM) Most Probable Failure Point (U et X) Parametric study

Safety factors Safety

factors Partial safety factors

Importance factors

Sensitivities and elasticities with respect to distribution parameters

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Sensitivity analysis / Reliability analysis

Sensitivity analysis / Reliability analysis

Sensibility analysis =>

probability distribution of an output

What’s the shape of the distribution ? What’s the influence of input variables ?

Numerical methods:

- Response surfaces (polynomial chaos) - FORM, ...

Reliability analysis =>

probability to exceed a treeshold for a failure event

Fractile ?

Assess the level of component's reliability Characterization & ranking of the impact of uncertainties on the size of a component

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Exhaust manifold

Objectives :

• quantification of the reliability;

• quantification of the parameters importance;

• distribution of the lifetime of the manifold.



Manufacturing processes

and

diversity of the customers

introduce great variability in

design parameter values and then influence the

failure risk

of the exhaust manifold



Develop a

complete probabilistic framework

in

fatigue design

of an exhaust manifold,

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Application to the manifold (1/2)



Probabilistic parameters

•

Geometry

: 6 thicknesses overall the manifold

•

Material

: Young’s modulus

E

, yield strength

S

_E

, hardening coefficients

C ,D

(dependent from temperature)

•

Fatigue randomness

expressed by

ξ

(independent from temperature)

•

Loadings

: minimal

T

_min

and the maximal temperatures

T

_max

Thermo-mechanical (FE models)

simulation of the behavior

Probability of failure

P (G({X}) ≤ 0) = P (N_f (∆ε_p {X})− N_required ≤ 0)

Evaluation of ∆

ε

_p

at a

given node

Random fatigue model

(approximately 200000 nodes)

Thermo-mechanical (FE models)

simulation of the behavior

Probability of failure

P (G({X}) ≤ 0) = P (N_f (∆ε_p {X})− N_required ≤ 0)

Thermo-mechanical (FE models)

simulation of the behavior

Probability of failure

P (G({X}) ≤ 0) = P (N_f (∆ε_p {X})− N_required ≤ 0)

Evaluation of ∆

ε

_p

at a

given node

Random fatigue model

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Application to the manifold (2/2)



Reliability results:

-0,023 0,025 0,075 _{-0,001 -0,002 0,011 0,007} -0,084 0,033 _0,021 0,087 0,977 -0,153 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2

ep1 ep2 ep3 ep4 ep5 ep6 T max T ral uE uC uD uSE uNr

Direction cosines

• Failure probability: 2.3% (43 FE calls)

•

Most important parameters:

_{o Fatigue randomness}

_ξ

o

T

_max

o Yield strength

S

_E

o Young modulus

E

o Plastic coefficient

C



Reliability results:

-0,023 0,025 0,075 _{-0,001 -0,002 0,011 0,007} -0,084 0,033 _0,021 0,087 0,977 -0,153 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2

ep1 ep2 ep3 ep4 ep5 ep6 T max T ral uE uC uD uSE uNr

Direction cosines

-0,023 0,025 0,075 _{-0,001 -0,002 0,011 0,007} -0,084 0,033 _0,021 0,087 0,977 -0,153 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2

ep1 ep2 ep3 ep4 ep5 ep6 T max T ral uE uC uD uSE uNr

Direction cosines

• Failure probability: 2.3% (43 FE calls)

•

Most important parameters:

_{o Fatigue randomness}

_ξ

o

T

_max

o Yield strength

S

_E

o Young modulus

E

o Plastic coefficient

C

Random variables that will be used for

SFEM approximation

Random variables that will be used for

SFEM approximation