La maitrise des modeles en mecan1que des structures
Erreurs et ameliorations adaptatives
Keywords:
mechanics, a posteriori errors, adaptativity, model/test, correlation, ajustement technic, mesh, vibrationsAbstract
Today, the construction and numerical simulation of models is, more than ever, a major activity in the field of mechanics. A constant concern in both industrial and research environments has been the control of these models, which can, nowadays, reach very high levels of complexity. A new factor during the past fifteen years has been the development of truly quantative tools for testing the quality of a model either theoretically or with the help of experiments. The following two themes have been used to illustrate these new procedures : the adaptative control of finite element modeling (i.e. the control of the actual calculation), and the control and adjustment of models based on the results of experiments. After presenting the state of the art and the difficulties involved in research, we explain in tktail the approach developed at L.M.T. of Cachan, which is based on the concept of error in constitutive relations and associated techniques. Various examples illustrate the possibilities afforded by theu new tools.
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References
PARTIE 1
BABUSKA I., RHEINBOLDT W.C., << Error estimates for adaptive finite element
computation »,SIAM J. Numer. Anal., 15, n° 4, 1978, p. 736-754.
BABUSKA I.,<< Feedback, Adaptivity and a posteriori Estimates in F.E. >>, 1986, p. 3-23 in
Accuracy Estimates and Adaptative refinements in F.E. Computations, Edited by
BABUSKA I., ZIENKIEWICZ O.C., GAGO 1., DE A. OLIVEIRA E.R. 1986, John Wiley.
BussY P., Optimisation et fiabilite des calculs par elements finis en non linearite
geometrique, these de docteur-ingenieur, universite Paris 6, 1984.
COOREVITS P., LADEVEZE P., PELLE J.P., RoUGEOT Ph., << Some new applications of a
method for the control and optimization of FE computation >> in New Advances in
Computational Structural Mechanics, ed. LADEVEZE P. and ZIENKIEWICZ O.C.,
Elsevier.
GASTINE J.L., LADEVEZE P., MARIN Ph., PELLE J.P., << Accuracy and Optimal Meshes and
FE Computation for nearly Incompressible Materials », in Camp. Meth. in Appl.
Mech. and Engineering (sous presse), 1991.
COFFIGNAL G., Fiabilite et optimisation des calculs elastoplastiques par elements finis,
these d'etat, universite Paris 6, 1986.
CooREVITS P., LADEVEZE P., PELLE J.P., << Mesh adaptivity for large gradient problem >>,
(to appear).
GUEZEL D., Sur l'encadrement du taux de restitution d'energie, these de 3° cycle,
universite Paris 6, 1981.
KELLY D.W., GAGO J.R., ZIENKIEWICZ O.C., BABUSKA I., << A Posteriori Error Analysis
and Adaptative Processes in Finite Element Method. Part I : Error Analysis >>, Int. J.
Numer. Meth. Engng, 19, 1983, p. 1593-1619.
LADEVEZE P., Comparaison de modeles de milieux continus, these d'etat, universite
Paris 6, 1975.
LADEVEZE P., << Nouvelle procedure d'estimation d'erreur relative a Ia methode des
elements finis et applications ''· Proc. J. Elements Finis, 1977, Rennes.
LADEVEZE P., LEGUILLON D.,<< Error estimate procedure in the finite element method and
application >>, SIAM J. Numer. Anal., 20, n° 3, 1983, p. 485-509
LADEVEZE P., << Sur une famille d'algorithmes en mecanique des structures >>, C.R. Acad.
Sc.Paris, 300, serie II, 1985, p. 41-44.
LADEVEZE P., COFFIGNAL G., PELLE J.P., << Accuracy of Elastoplastic and Dynamic
Analysis >>, 1986, p. 181-203, in Accuracy Estimates and Adaptative Refinement in
Finite Element Computations, Edited by BABUSKA I., ZIENKIEWICZ O.C., GAGO J.,
DE A. OLIVEIRA E.R., (WILEY).
LADEVEZE P, PELLE J.P., << Accuracy in finite element computation for eigenfrequencies
», International Journal for Numerical Methods in Engineering, 29,
, p. 1929-1949.
LADEVEZE P., « Modelisation et calcul des structures : de nouveaux defis >>,La Recherche
Aerospatiale, n° 5, septembre-octobre 1990, p. 29-56.
LADEVEZE P., PELLE J.P., RoUGEOT Ph., << Error estimates and mesh optimization for
FE computation >>, Engineering Computations, 8, 1991, p. 69-80.
MILLER K., MILLER R., « Moving finite elements », Part I, SIAM J. Numer. Anal., 18,
, p. 1019-1032.
MILLER K, « Moving finite elements », Part II, SIAM J. Numer. Anal., 18, 1981,
p. 1033-1057.
PELLE J.P., Fiabilite et optimisation des calculs par elements finis des frequences
propres, these d'etat, universite Paris 6, 1985.
PELLE J.P., ROUGEOT Ph., << Controle de qualite en elements finis et maillages
optimises >>, publie dans Calcul des Structures et Intelligence Artificielle, tome II,
, p. 209-220, FoUET J.M., LADEVEZE P., ORA YON R., Editeurs PLURALIS.
PELLE J.-P., ROUGEOT Ph., « Maillage adaptatif pour les elements c!assiques >>, publie
dans Calcul des Structures et Intelligence Artificielle », tome III, 1989, FouET J .M.,
LADEVEZE P., ORA YON R., Editeurs PLURALIS
R OUGEOT P., Sur le controle de Ia qualite des maillages elements finis, these de
l'universite P. et M. Curie, Paris, 1989.
SZALBO B.A., << Estimation and Control of Error Based on p Convergence >>, in Accuracy
Estimates and Adaptives Refinements in F.E. Computations, Edited by BABUSKA I.,
ZIENKIEWICZ O.C., GAGO J., DE A. OUVIERA, E.R.,John WILEY, 1986, p. 61-77.
ZHONG HG, BECKER P, Solution Approximation Error Estimators for the FE Solution,
report SA-140-Aerospace Lab. of univ. Liege, 1990.
ZHONG H.G., Estimateurs d'erreur a posteriori et adaptation de maillages dans Ia methode
des elements finis, these de l'universite de Liege, 1991.
ZIENKIEWICZ O.C, GAGO J.R., KELLY D.W., <
Analysis », Computer and structures, 16, n° 14, 1983, p. 53-65.
ZIENKIEWICZ O.C, CRAIG A., « Adaptive Refinement, Error Estimates, Multigrid Solution
and Hierarchic Finite Element Method Concepts », in Accuracy Estimates and
Adaptives Refinements in F.E. Computations, Edited by BABUSKA 1., ZIENKIEWICZ
O.C., GAGO J., DE A. OLMERA E.R., John WILEY, 1986, p. 25-59.
ZIENKIEWICZ O.C., ZHU JZ, « A Simple Error Estimator and Adaptative Procedure for
Practical Engineering Analysis », Int. J. for Num. Meth. in Engng., 24, 1987,
p. 337-357.
PARTIE2
BARUCH M., << Optimal Correction for Mass Matrix and Stiffness Matrix using Measuring
Modes», A.I.A.A., 82-4265, 1982.
BERMAN A., FLANNELLY 0., << Theory of Incomplete Models of Dynamics Structures »,
A./A.A. Journal, 9/8, 1971, p. 1481-1487.
BERGER H., BARTHE L., ORA YON R., << Recalage d'un modele par elements finis a partir de
donnees experimentales du type vibratoire. Concept de localisation >>, R.T. DRET,
n° 713313 RY 070 R, mai 1987.
BLACKEL Y K., DoBBS M., << Modification and Refinement of Large Dynamic Structural
Models : Efficient Algorithms and Computer Applications », Proceedings /st. Int.
modal analysis conf., 1984, p. 598-602, Orlando.
CAESAR B., << Correlation and Update of Dynamic Mathematical Models », 4th F.E. world
congress, Interlaken, septembre 1984.
CHEN J.C., Kuo C.P., GARBA J.A., « Direct Structural Parameter Identification Testing >>,
A.I.A.A., 83-0812, 1983.
COLLINS J.D., HART G.C., HASSELMAN J.K., KENNEDY B., « Statical Identification of
Structures>>, A.IAA. journal, 1212, 1974, p. 185-190.
COTTIN N., FELGENHAUER H.P., NATICE H.G., « On the parameter identification of
elastomechanical systems using input and output residuals >>, /ngenieur Archiv. 54,
, p. 378-387, Spring-Verlag.
HE J., EWINS D.J., « Analytical Stiffness Matrix Correction using Measured Vibration
Modes>>, Int. Journ. Analytical & Experimental Modal Analysis,/, n° 3, July 1986.
HEYLEN W., VANHONECKER P., «An Automated Technique for Improving Model Matrices
by Means of Experimentally Obtained Dynamic Data >>, Proceedings of the Int. modal
analysis conference, Orlando, 1984.
LADEVEZE P., Recalage de modelisation des structures complexes, Note technique n° 33
014, Aerospatiale Les Mureaux, 1983.
LADEVEZE P., REYNIER M., « A localisation Method of Stiffness Errors for the
Adjustement of F.E. Models>>, Special issue J of Appl. Mech., ASME, Proceedings of
th ASME Mechanical Vibration and Noise Conference, 1989.
LADEVEZE P., REYNIER M., BERGER H., 0HAYON R. QUETIN F., BARTHEL.,« Methode de
recalage de modeles de structures en dynamique : les approches par reaction dynamique
et par Ia notion d'erreur en relation de comportement », La Recherche Aerospatiale,
n° 5, 1991, p. 9-20.
REYNIER M., Sur le controle de modelisations par elements finis : recalage a partir
d'essais dynamiques, these de l'universite Paris 6/ENS Cachan, 1990.
MAUNDER E., « Finite Element Modelling of Exeter Cathedral », Finite Element News, 6,
, p.14-18.
N A TKE H., « Updating Computational Models in the Frequency Domain Based on
Measured Data: a Survey>>, Probabilistic Engineering Mechanics, 3, n° 1, 1988.
NEDJAR D., Correction parametrique de modelisations par elements finis a partir de
resultats d'essais vibratoires, these de l'universite Paris 6/ENS Cachan, 1992.
SIDHU J., EWINS D.J., « Correlation of Finite Element and Modal Studies of a Practical
Structure >>, Proceedings 2nd /MAC, fevrier 1984, p. 756-762.
SOIZE C., « Modelisation probabilistique du flou structural en dynamique lineaire des
systemes mecaniques complexes - Elements theoriques >>, La Recherche Aerospatiale,
, 1986, p. 337-362.
WOZNIAK C.S., «Tolerance and Fuziness in Problems of Mechanics »,Arch. Mech., 35,
, p. 5-6.
ZHANG W., LALLEMENT G., FILLOD R., PIRANDAJ., « A Complete Procedure for the
Adjustement of Mathematical Model from the Identified Complex Modes», /MAC-5,
Imperial College, Londres, 1987, 6-9 Ap.
