Réduction de modèles 18 mai 2006ENSAM - Réduction de modèles pour des applications en temps réel F. Druesne, J-L Dulong, P. Villon, A. Ouahsine Laboratoire.

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Rduction de modles 18 mai 2006ENSAM - Rduction de modles pour des applications en temps rel F. Druesne, J-L Dulong, P. Villon, A. Ouahsine Laboratoire Roberval UTC Compigne Slide 2 Rduction de modles 18 mai 2006ENSAM - Contexte industriel : Savoir-faire & besoin Approche : Apprentissage Temps rel Mthode a posteriori Mthode a priori Application sur une durit automobile Slide 3 Rduction de modles 18 mai 2006ENSAM - Context Virtual prototype Decision aid for project review 3D immersive visualization of a product Tool for mechanical design Simulation of manual operations on rigid parts ( assembly simulation ) as early as design phase Automotive industry & aeronautics With haptic feedback Tool for operators training PSA EADS 3 Slide 4 Rduction de modles 18 mai 2006ENSAM - Example : Access to a motor unit by pushing an hose back Tool for operators training Tool for mechanical design Simulation of manual operations on flexible parts Virtual prototype Context Automotive industry 4 Problematic: Part deformation in real time, if non linearity Slide 5 Rduction de modles 18 mai 2006ENSAM - Contexte industriel : Savoir-faire & besoin Approche : Apprentissage Temps rel Mthode a posteriori Mthode a priori Application sur une durit automobile Slide 6 Rduction de modles 18 mai 2006ENSAM - Approach Real time Virtual model 1000 Hz 30 Hz Haptic device Learning CAD model FEM code Response surface Calculation campaign Finite Element Model Reduced response surface Model reduction How to build it ? 6 Slide 7 Rduction de modles 18 mai 2006ENSAM - Contexte industriel : Savoir-faire & besoin Approche : Apprentissage Temps rel Mthode a posteriori Mthode a priori Application sur une durit automobile Slide 8 Rduction de modles 18 mai 2006ENSAM - Problem geometry Slender structure in rubber embedded at one extremity handled at the other Mechanical model meshed with H8 finite elements n = 3408 degrees of freedom Finite deformation Hyperelastic material (neo-hookean) Quasi-static problem FEAP code Load cases S = 100 load cases following a regular grid Test structure 8 Slide 9 Rduction de modles 18 mai 2006ENSAM - Quasi-static campaign by solving u (t s ) on each point t s of the load cases grid Newton-Raphson scheme on u (size n) : A posteriori methodology n = 3408 S = 100 9 Slide 10 Rduction de modles 18 mai 2006ENSAM - Model reduction by the Karhunen-Loeve Expansion (KLE) 1,2 1.Centered displacements by subtracting the average 2.Covariance matrix 3.Eigenvectors of and selection of the m first (highest eigenvalues) A posteriori methodology 1 Krysl, Lall, Marsden 2000 2 Barbi, James 2005 10 Slide 11 Rduction de modles 18 mai 2006ENSAM - Model reduction by the Karhunen-Loeve Expansion (KLE) 4.Approached displacement n = 3408 S = 100 m ~ 20 A posteriori methodology 11 Slide 12 Rduction de modles 18 mai 2006ENSAM - average initial A posteriori methodology 12 Slide 13 Rduction de modles 18 mai 2006ENSAM - Error induced by the KLE A posteriori methodology 13 Slide 14 Rduction de modles 18 mai 2006ENSAM - Contexte industriel : Savoir-faire & besoin Approche : Apprentissage Temps rel Mthode a posteriori Mthode a priori Application sur une durit automobile Slide 15 Rduction de modles 18 mai 2006ENSAM - Quasi-static campaign by solving a (t s ) on each point t s of the loading cases grid Newton-Raphson scheme on a (size m) : A priori methodology Convergence on a, with fixed Cost of (size m x m) is low But a can converge, even if is large ! is too poor to describe solution have to be enriched 15 Slide 16 Rduction de modles 18 mai 2006ENSAM - A priori methodology Adaptative strategy by R-enrichment orthonormalize Algorithm : enrichment loop iterative loop (Newton Raphson) until convergence on a until convergence on R else enrichment Reduction by KLE if size( ) becomes too large 1 1 Ryckelynck 2005 16 Slide 17 Rduction de modles 18 mai 2006ENSAM - A priori methodology 17 load cases base size base size m Slide 18 Rduction de modles 18 mai 2006ENSAM - A priori methodology 18 base size m load cases Slide 19 Rduction de modles 18 mai 2006ENSAM - A priori vs A posteriori 19 1.6 1.8 Slide 20 Rduction de modles 18 mai 2006ENSAM - 20 A priori vs A posteriori 2.2 2.6 Slide 21 Rduction de modles 18 mai 2006ENSAM - average initial average initial a posteriori a priori without reduction 21 A priori vs A posteriori Slide 22 Rduction de modles 18 mai 2006ENSAM - Contexte industriel : Savoir-faire & besoin Approche : Apprentissage Temps rel Mthode a posteriori Mthode a priori Application sur une durit automobile Slide 23 Rduction de modles 18 mai 2006ENSAM - Application Problem geometry Automotive hose in rubber embedded at its 2 extremities handled in a point Mechanical model meshed with H8 finite elements n = 18720 degrees of freedom Large deformation Hyperelastic material (neo-hookean) Quasi-static problem FEAP code Load cases S = 100 load cases following a regular grid 23 Slide 24 Rduction de modles 18 mai 2006ENSAM - Application : results Error induced by the a posteriori KLE 24 Slide 25 Rduction de modles 18 mai 2006ENSAM - Slide 26 Rduction de modles 18 mai 2006ENSAM - Application : results 25 Slide 27 Rduction de modles 18 mai 2006ENSAM - Interpolation on data from training phase Slide 28 Rduction de modles 18 mai 2006ENSAM - Conclusion Feasibility of large deformation in real time, with non linear hyperelastic material. New tool for mechanical design. The classical a posteriori methodology is possible but slower than the a priori one. Perspectives Hyperreduction methodology (Ryckelynck 2005). Introduce material history in the reduced surface response. Introduce boundary conditions non linearity. 27

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