Systems Engineering Sensitivity analysis Structural reliability

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1 Systems Engineering Sensitivity analysis Structural reliability In order to evaluate the risk of a technological solution and to optimize costs in design or maintenance

2 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 persons Scientific team founder Maurice PENDOLA CEO Doctor & Engineer IFMA Reliability Expert Prof. Maurice LEMAIRE Délégué scientifique Engineer INSA Lyon IFMA Research Director 2

3 Localization Paris Clermont-Ferrand Bordeaux Seyne / Mer Headquartered Parc Technologique de la Pardieu 1 allée Alan Turing F AUBIERE Tél (00 33) Fax (00 33) Subsidiary! New Adress! Technopôle Var Matin From January 03, 2008 Route de la Seyne F OLLIOULES Centre d'affaires du Zenith Tél (00 33) rue de Sarlièvre Fax (00 33) F COURNON d'auvergne

4 Our vocation, Our ambition «Expert in probability applied to engineering, PHIMECA aims to become the international reference in this field» Maurice PENDOLA, CEO PHIMECA Some references De grandes sociétés nous font déjà confiance: National & International scientific references Des références scientifiques nationales et internationales: 4 2 European projects 4 ANR projects ImdR actor More than 100 communications/articles 4

5 Ours Knowhows Scientist & Industrial 5

6 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 6

7 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. 7

8 General sketch for uncertainty analysis A new approach to your problems 8

9 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) A dedicated tool: PHIMECA Software 9

10 PHIMECA Software Probability of failure Failure probability Reliability index Second order approximations (SORM) Most Probable Failure Point (U et X) loading, time Safety factors Parametric study Partial safety factors Importance factors Sensitivities and elasticities with respect to distribution parameters Distribution analysis 10

11 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 Assess the level of component's reliability Fractile? Characterization & ranking of the impact of uncertainties on the size of a component 11

12 Exhaust 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, including all kind of uncertainties that affect the thermomechanical fatigue behavior Objectives : quantification of the reliability; quantification of the parameters importance; distribution of the lifetime of the manifold. 12

13 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 Tmin and the maximal temperatures Tmax (approximately nodes) Thermo-mechanical (FE models) simulation of the behavior Probability of failure Evaluation of ε p at a given node P (G({X}) 0) = P (Nf ( ε p {X}) Nrequired 0) Random fatigue model 13

14 Application to the manifold (2/2) Reliability results: Failure probability: 2.3% (43 FE calls) Most important parameters: o Fatigue randomness ξ o Tmax Direction cosines 1,2 0,977 1,0 o Yield strength SE o Young modulus E 0,8 o Plastic coefficient C 0,6 0,4 0,2 0,025 0,075-0,001-0,002 0,011 0,033 0,007 0,021 0,087 0,0-0,023-0,084-0,2-0,153-0,4 ep1 ep2 ep3 ep4 ep5 ep6 T max T ral ue uc ud use unr 14 Random variables that will be used for SFEM approximation

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