Présentation de l’enseignement spécialisé « éléments finis » – S3733-S3735 S. Basseville, G. Cailletaud, T. Coupez, F. Feyel, M. Kern Année 2005
Jour | 9 :00–10 :30 10 :45–12 :30 | 13 :45–15 :30 15 :45–17 :30
Lundi | Introduction Eléments finis | ... PC Présentation
21 nov | (GC, FF) en 1D (MK) | (MK) des projets (GC, MK)
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Mardi | Présentations Méthode des | ... suite Formulation
22 nov | des logiciels (GC, MK) Elt finis (MK) | (MK) matricielle (GC)
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Mercredi | Estimation Technologie des | Maillage Projet
23 nov | d’erreur a priori(MK) éléments finis (GC) | (FF) (tuteurs)
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Jeudi | Maillage, erreur a Formulations | Projet Projet
24 nov | posteriori (TC) mixtes (TC) | (tuteurs) (tuteurs)
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Vendredi | Résolution de Intégration | Projet Projet
25 nov | systèmes (FF) temporelle (SB) | (tuteurs) (tuteurs)
| |
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Introduction
• GC
? Points de repères historiques (FEM)
? Points de repère sur le marché actuel (FEA)
? Exemples d’applications
• FF
? Les physiques...
• 1950–1960, les pionniers ; l’impulsion vient de l’industrie aéronautique aux U.S.
• 1955 : Argyris, théorèmes de l’énergie [1], Turner et al, le triangle à trois nœuds [18], Clough, la dénomination d’«éléments finis» [6]
• 1960–1970 : début des développements systématiques, rapprochement entre les approches ingénieur et les formulations mathématiques
• Connection Boeing–Berkeley, Ecole européenne (Liège, Swansea), [9, 19]
• 1964 : Gallagher, première revue ([10])
• 1967 : Zienkiewicz et Cheung, premier livre pour les ingénieurs [19], extension au génie civil,
• Développement de nouveaux types d’éléments finis : intégration numé- rique, fonctions de forme, notamment par Irons et al [12], formulations mixtes (résumé dans [16]). . .
• 1970–1980 : consolidation des acquis, bonne compréhension des ressorts théoriques, début de l’exploitation commerciale. «Tri» parmi les nombreux développements de la précédente décade.
• Extension à d’autres domaines que la mécanique [14]
• Début du contrôle d’erreur, éléments de plaque et de coques performants,
• Tentatives de développement d’autres méthodes (équations intégrales,
devenues ensuite «éléments frontières» (BEM))
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• 1980–1990 : la maturité, divulgation de la méthode en dehors des laboratoires et des grands groupes industriels,
• Arrivée des stations, puis des PC ; interfaces utilisateurs efficaces
• Des livres de référence ; en français : [8] ; reflétant l’école américaine, côte Est : [2] ; côte Ouest : [11] ; une encyclopédie : [13]
• 1990–2000 : l’intégration dans le processus de fabrication, lien renforcé avec la CA0
• D’autres livres de référence, en français : [3, 5] ; ou non : [7], rappelant l’aspect «ingénieur» : [15] (MSC-Nastran)
• Le non-linéaire [17, 4], le dynamique (codes explicites pour le crash), l’arrivée de l’optimisation (conception paramétrique)
• Les méthodes alternatives (méthodes sans maillage par exemple)
• La maturité du calcul parallèle
• 2000– : le bizeness, rachats-regroupements
• Le multi–physique, la réalité virtuelle (lunettes, casques,. . .)
• Diminuer les coûts, augmenter la fiabilité (ISO9000)
Quelques exemples des codes de calcul par éléments finis Démarche commerciale
• Nastran, 3000 personnes ? 45000 licences
• Ansys, (fondé en 1970), 600 personnes, 8600 sites, 130000 licences académiques
• Abaqus, 300 personnes, racheté en 2005 par Dassault System (Catia)
• Algor, la conception paramétrique
• Samcef, 50 personnes, 1500 licences
• Radioss
• Pam-crashet al
• LS-Dyna, crash 11 sept 2002 +
• Fluent
• Forge2/Forge3 (CEMEF)
Autres démarches
• Modulef, FreeFEM++,FEAP
• Castem, Code_Aster
• Zebulon
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http://directory.google.com/Top/Science/Technology/Software_for_Engineering
http://directory.google.com/Top/Science/Technology/Software_for_Engineering/Finite_Element_Analysis/
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http://directory.google.com/Top/Science/Technology/Software_for_Engineering/Finite_Element_Analysis/
http://directory.google.com/Top/Science/Technology/Software_for_Engineering/Finite_Element_Analysis/
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Quelques exemples d’utilisation
• Automobile
• Aéronautique
• Electronique, produits grands public
• Industries mécaniques
• Médical
• Caoutchouc
FE market
Infos sur le marché
AUTOMOBILE
Abaqus et l’automobile
* Engine durability * Transmission performance * Seal integrity * Component design * Powertrain bending * Noise &
vibration * Gasket analysis * Thermal cycling * Sheet metal forming * Forging analysis * Mechanisms analysis * Assembly (bolt loading) (d’aprèshttp ://www.abaqus.com)
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AERONAUTIQUE
Crash-test d’un tronçon de Boeing 737 par la NASA
* Static, dynamic, and coupled acoustic-structural analysis of aircraft frames * Simulations of large deployable space structures such as solar sails, space radars, and reflector antennas * Simulating the performance of various aircraft components, such as bulkhead under pressurization, wing panel buckling, and crack propagation in the fuselage * Blade containment evaluations and bird strike simulations * Thermomechanical simulation of aircraft engines and rocket motors under different operating conditions * Verification of turbine blade designs * Simulation of various aircraft mechanisms such as landing gears, wing flaps, and cargo doors * Peen forming and creep age forming of large aircraft components such as wing skins * Design of explosion resistant components and ballistic damage resistant armors * Simulating the effects of underwater explosions on ships and submarines * Structural analysis of submarine frames to predict buckling modes * Attenuation of noise generated by underwater vehicles * Design and simulation of critical components, such as a nozzles, piezoelectric motors, self-lubricating hinges and various bearings * Nonlinear analysis and damage assessments of structural components * Optimization of structural design details considering compression buckling analysis * Crack propagation analysis in pressurized fuselage panels * Manufacturing applications such as forming analyses of rivets
ELECTRONIQUE, PRODUITS GRAND PUBLIC
Calcul thermique Calcul mécanique
http ://www.algor.com
* Drop testing of diverse products, such as consumer electronics and fluid-filled containers * Pressurization and top-loading of packaging containers * Development and manufacturing of new materials, such as paper and film * Product-human body interactions * Simulation of media transport * Design and validation of acoustic properties of audio equipment * Thermomechanical simulation of electronic products * Thermal analysis of chip packaging * Design of consumer appliances such as washers and dryers (d’aprèshttp ://www.abaqus.com)
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CONSTRUCTION MECANIQUE
Cuve de centrale nucléaire
* Dynamic and acoustic analysis of rotating machinery, such as pumps, motors, and compressors * Thermomechanical and fatigue analysis of power generation equipment, such as boilers, turbines, and heat exchangers * Design of reliable rollover and falling object protective systems (ROPS and FOPS)
* Simulated operation of tools such as drills, grinders, and jackhammers under impact and other severe loading conditions * Crash analysis of rolling stock, such as locomotives and wagons * Static and dynamic analysis of piping systems under various loads, such as thermal, pressure, seismic, and loads * Structural durability and fatigue analysis of farm and construction equipment * Life predictions of various mechanisms, such as transmissions and industrial brakes and clutches * Thermomechanical simulations of material processing operations, such as rolling, sintering, extrusion, casting, and drawing
* Manufacturing of thermoplastic and polymeric materials (d’aprèshttp ://www.abaqus.com)
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BIOMEDICAL
Finite element analysis for the design of Nitinol medical devices Nuno Rebelo (Hibbitt, Karlsson & Sorensen (West), Inc, Fremont, CA) and Michael Perry (PEMSTAR Pacific Consultants Mt. View, CA)
http ://www.pacificconsultants.com/Documents/feanitinol.pdf
* Manufacturing of different types of medical devices * Design of mechanical connectors commonly used in all types of medical devices * Extending patentability, enhancing patent protection, and obtaining regulatory (FDA and CE mark) approval * Design of dental implants and hip, knee, and other prosthetic implants * Wear and impact simulation to improve durability and reliability of implants * Heart valve design * Assessment and prediction of injuries * Design and deployment of vascular stents, catheters, minimally invasive surgical equipment, drug delivery systems etc. * Soft tissue and joint modeling * Simulating the physiological response of body systems (d’aprèshttp ://www.abaqus.com)
CAOUTCHOUC ET JOINTS
O.A. Olatunbosun, A.M. Burke, Univ. Birmingham, UK Tire Science and Technology Conference, Akron, Ohio, Avril 2000.
http ://tiresociety.org/pdf/booklet_combined00.pdf
* Bushings * Sealing systems * Engine mounts * Sporting goods * Vibration suppression systems * Thermomechanical analysis of rubber products * Tire modeling and performance simulation : o Tire inflation, foot print, rolling, braking, and cornering simulations under different road conditions o Impact analysis o Modeling belt stresses o Tread wear simulation o Coupled acoustic-structural tire analysis (d’aprèshttp ://www.abaqus.com)
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Calculs de magnétisme
Doc support EMAS
www.ansoft.com
ANSYS
• Ansys et le secteur aérospatial ◦Simulating Rocket Start Up◦ DesignSpace Lightens the Load for Aerospace Design◦Keeping 747s Flight-Worthy ◦Optimizing an Underwater Robot Arm◦ DesignSpace Minimizes Weight of Aircraft Cargo Door Support Structure ◦ Using FEA to Simulate a Space Mission
• Ansys et l’automobile◦Bowles Fluidics Corp - building a better windshield washer nozzle that dominates the auto industry ◦DuPont - ANSYS software helps DuPont eliminate rattle from Porsche Boxster manifold ◦Eaton Corp - steering to big gains, paradigm shifts by optimizing designs ◦ Fisher Electric Motor Technology Inc - designing an electric motor for a pickup truck◦ Hendrickson Trailer Suspension Systems - over-the-road semi trailers ride better with analysis redesign of suspension system◦Larry Hedrick Motorsports - design optimization in the fast lane with DesignSpace from ANSYS, Inc.◦Lola Cars, Ltd - using ANSYS structural analysis to speed race car development ◦ LuK - engineers use ANSYS design analysis and optimization software to conduct fatigue tests to guarantee component safety◦LuK - reducing costs of ensuring excellent clutch performance through the use of simulation◦MAN AG - boosting bus body structural integrity through optimization and verification ◦ Melroe Co - optimizing Bobcat equipment with finite element analysis software from ANSYS, Inc.
• Ansys et le biomédical ◦ BLOODSIM - European consortium develops blood simulation tool to fight heart disease◦ Crystal Medical Technology - building a better artificial tooth◦ DEKA Research & Development Corp - developing an improved version of a medical stent design◦DePuy Inc - finding ways to decrease stress between the upper and lower articulating surfaces of an artificial knee joint◦ Kings University and Others - ANSYS Saves U.K. and U.S. Researchers Time and Money Constructing Patient-Specific Brain Models◦ Mitroflow International - improving the performance and longevity of implanted heart valves◦Technical University of Hamburg-Harburg - German University Avoids Costly Testing with ANSYS
• Ansys et l’électronique◦Compaq Computer Corporation - helping to solve solder problems in Compaq’s next-generation AlphaServer
◦Genus Ion Technology Division - implanting a speed-up in ion machines◦Genus Ion Technology Division -using ANSYS for virtual prototyping◦Motorola - using the viscoplastic analysis capabilities of ANSYS to optimize the manufacture of hybrid power modules◦ Motorola - helping Motorola solve resonance problems with ANSYS analysis, experimental verification◦ Symbol Technologies, Inc - leveraging concurrent engineering in developing scanners◦Symbol Technologies, Inc - developing a computer rugged enough to survive a six foot drop onto concrete◦Turk Elektrik Endustrisi - redesigning a washing machine motor for Siemens AG
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Encore quelques liens
NB cours + elements + finis = 383000 (94100 réponses en 2004) finite + element + course = 4680000 (1080000 réponses en 2004)
• Un cours à l’UCL (Belgique)
• Un cours à Marseille
• Les cours de Carlos Felippa (Boulder) :
◦ Introduction ◦ Non linear ◦ Advanced
• Les plus gros calculs du monde (10 milliards d’équations)
Références
[1] J.H. Argyris and S. Kelsey. Energy theorem and structural analysis. Aircraft Engrg., 26-27, 1954-1955.
[2] K.J. Bathe. Finite element procedures in engineering analysis. Prentice Hall, Inc., 1982.
[3] J.L. Batoz and G. Dhatt. Modélisation des structures par éléments finis, I—III. Hermès, 1991.
[4] T. Belytschko, W.K. Liu, and Brian Moran. Nonlinear Finite Elements for Continua and Structures. Wiley, 2000.
[5] P.G. Ciarlet and J.L. Lions. Handbook of Numerical Analysis : Finite Element Methods (Part 1), Numerical Methods for Solids (Part 2).
North Holland, 1995.
[6] R.W. Clough. The finite element method in plane stress analysis. In Proc 2nd ASCE Conf. on Electronic Computation, pages 345–378, Pittsburg, 1960.
[7] M.A. Crisfield. Nonlinear Finite Element Analysis of Solids and Structures. Wiley, 1991.
[8] G. Dhatt and G. Touzot. Une présentation de la méthode des éléments finis. Maloine, 1981.
[9] B.M. Fraejis de Veubeke. Upper and lower bounds in matrix structural analysis, in stress analysis, o.c. zienkiewicz and g. hollister ed., wiley, pp.145–197,1965. Int. J. Numer. Meth. Engng, 52 :287–342, 1965–2001.
[10] R.H. Gallaguer. A correlation study of methods of matrix structural analysis. Pergamon, 1964.
[11] T.J.R. Hughes. The finite element method : Linear static and dynamic finite element analysis. Prentice–Hall Inc., 1987.
[12] B. Irons and S. Ahmad. Techniques of finite elements. Ellis–Horwood, 1980.
[13] H. Kardestuncer, editor. Finite Element Handbook. Mc Graw Hill, 1987.
[14] H.C. Martin and G.F. Carey. Introduction to finite element analysis. McGraw–Hill, 1973.
[15] R. Mc Neal. Finite Element : their design and performance. Marcel Dekker, 1993.
[16] T.H.H. Pian. Some notes on the early history of hybrid stress finite element method. Int. J. Numer. Meth. Engng, 47 :419–425, 2000.
[17] J.C. Simo and T.R.J. Hughes. Computational Inelasticity. Springer Verlag, 1997.
[18] M.J. Turner, R.W. Clough, H.C. Martin, and L.J. Topp. Stiffness and deflection analysis of complex structures. J. Aero. Sci., 23 :805–824, 1956.
[19] O.C. Zienkiewicz and Y.K. Cheung. The finite element method in Engineering Science. McGraw–Hill, 1967.
