Analyses elements finis adaptatives pour les structures tridimensionnelles en elasticite
Keywords:
three-dimensional mesh, adaptivity, error in constitutive relation, finite element computationAbstract
The design of three-dimensional structures requires finite element computations, whose cost in human and computational time becomes prohibitive when a reasonable criterion of quality is imposed. Methods of control of the discretization errors and optimization of the parameters of the analysis enable the application of finite element analysis ; yet, the main difficulty in 3D is the adaptivity of the meshes. The purpose of this paper is to present and compare several methods in order to address this difficulty.
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References
[BAB 78] BABUSKA 1., RHEINBOLDT W.C., "Error estimate for adaptive finite computation",
SIAM J. Num. Anal., Vol. 15, W4, pp. 736-754, 1978.
[BAE 87] BAEHMAN P.L., SHEPARD M.S., "Automatic three-dimensional mesh generation by
finite octree technique", Engng. Computers, Vol. 5, pp. 235-247, 1987.
[BEC 94] BECKERS P., "Adaptation de maillages membranes, plaques et volumes", Journee
d'etude C.S.M.A. (L.M.T. & I.N.R.I.A.), 1994.
[CIA 78] CIARLET P., "The finite element method for elliptic problem", North Holland, 1978.
[COF 87] COFFIGNAL G., "Optimisation et fiabilite des calculs elements finis en
elastoplasticite", These de doctorat d'etat, Universite Pierre et Marie Curie, 1987.
[COO 93] CooREVITS P., PELLE J.-P., "Post-processor for adaptive mesh of problems with
steep gradient areas, Advances in Factories of the Future", CIM and Robotics, Elsevier,
M. Cotsaftis and F. Vernadat Eds, pp. 157-166, 1993.
[COO 94a] COOREVITS P., LADEVEZE P., PELLE J.P., "Mesh optimization for problems with
steep gradients", Engineering Computations, Vol. 11, pp. 129-144, 1994.
[COO 94b] COOREVITS P., PELLE J.-P., ROUGEOT P., "Sur l'adaptativite des maillages a base
de quadrilateres. Application a l'automatisation de calculs par elements finis en elasticite
D", Revue europeenne des elements finis, Vol. 3, pp. 379-409, 1994.
[COO 95a] COOREVITS P., LADEVEZE P., PELLE J.-P., "An automatic procedure for finite
element analysis in 2D elasticity", Comp. Meth. in Appl. Mech. and Engng, Vol. 121,
pp. 91-120, 1995.
[COO 95b] COOREVITS P., DUMEAU J.P., NOR S., PELLE J.P., "Adaptivity of three-dimensional
meshes for the design of propellers", Actes du 4eme Colloque sur la Conception
Mecanique integree, PRIMECA, pp. 65-70, La Plagne, France, 1995.
[DUM 95] DUMEAU J.P., "Controle et adaptation des maillages 3D : application a
l'automatisation des calculs", These de !'Ecole Normale Superieure de Cachan, 1995.
[GAG 83] GAGO J.P., KELLY D.W., ZIENKIEWICZ O.C., BABUSKA 1., "A posteriori error
analysis and adaptive processes in the finite element method : part II - Adaptive mesh
refinement", Int. Jour. Num. Meth. Engng., Vol. 19, pp. 1621-1656, 1983.
[GAS 92] GASTINE J.L., LADEVEZE P., MARIN P., PELLE J.-P., "Accuracy and Optimal
Meshes in Finite Element Computation for nearly incompressible Materials", Comp.
Meth. inAppl. Mech. and Engng, Vol. 94, pp. 303-315, 1992.
[GEO 93] GEORGES P.L., "Automatic mesh generation :application to finite elemnt methods",
Collection RMA, Ed. Masson, 1993.
[IDE 86] IDEAS, "Manuel d'utilisation, Version Vl.i", 1986.
[KEL 83] KELLY D.W., GAGO J.P., ZIENKIEWICZ O.C., 8ABUSKA 1., "A posteriori error
analysis and adaptive processes in the finite element method: part I- Error analysis", Int.
Jour. Num. Meth. Engng., Voll9, pp. 1593-1619, 1983.
[LAD 77] LADEVEZE P., "Nouvelles procedures d'estimations d'erreur relative a Ia methode
des elements finis et applications", Proc. Joumees Elements Finis, Rennes, 1977.
[LAD 83] LADEVEZE P., LEGUILLON D., "Error estimate procedure in the finite element
method and applications", SIAM J. Num. Anal., Vol. 20, no 3, pp. 485-509, 1983.
[LAD 86] LADEVEZE P., COFFIGNAL G., PELLE J.P., "Accuracy of elastoplastic and dynamic
analysis, Accuracy estimates and adaptative refinements in Finite Element computations",
Babuska, Gago, Oliveira, Zienkiewicz Editors, J. Wiley, Chapter 11, pp. 181-203, 1986.
[LAD 91] LADEVEZE P., PELLE J.P., RoUGEOT P., "Error estimation and mesh optimization
for classical Finite Elements", Engng. Computation, Vol. 8, pp. 69-80, 1991.
[LAD 92] LADEVEZE P., "La maltrise des modeles en mecanique des structures", Revue
Europeenne des elements finis, Vol. 1, pp. 9-30, 1992.
[NOE 94] NOEL F., LEON J.C., TROMPETIE P., "An auto-adaptive surface meshing software
for a CAD environment", Proc. of the Second Int. Conf. on Computational Structures
Technology, Athenes, pp. 205-213, 1994.
[NOE 95] NOEL F., LEON J.C. , TROMPETIE P., "A new approach to free form surface mesh
control in a CAD environment", Int. J. for Num. Meth. in Engng., Vol. 38, pp. 3121-3142,
[OHT 92] OHTSUBO H., KITAMURA M., "Element by element a posteriori error estimation of
the finite element analysis for three dimensionnal elastic problems", Int. J. Num. Meth. in
Engng., Vol. 29, pp. 223-244, 1992.
[RAS 95] RASSINEUX A., "Maillage automatique tridimensionnel par une methode frontale
pour Ia methode des elements finis", These de l'Universite Nancy-I, 1995.
[STR 76] STRANG G., Fix G., "An analysis of finite element", Prentice-Hall, 1976.
[ZIE 87] ZIENKIEWICZ O.C., ZHu J.Z., "A simple error estimator and adaptive procedure for
practical engineering analysis", Int. J. Num. Meth. Engng., Vol. 24, pp. 337-357, 1987.
[ZIE 89] ZIENKIEWICZ O.C, ZHU J .. Z., GONG N.G, "Effective and practical h-p version
adaptive analysis procedures for the finite element method", Int. Jour. Num. Meth.
Engng., Vol. 28, pp. 879-891, 1989.
[ZIE 92] ZIENKIEWICZ O.C, ZHU J.Z., "The superconvergent patch recovery and a posteriori
error estimates: part I- The recovery technique", Int. Jour. Num. Meth. Engng., Vol 33,
pp. 1331-1364, 1992.
