Formulation du modèle MiSP coque tridimensionnel dégénéré

Authors

  • Rezak Ayad Université de Reims Champagne-Ardenne Groupe de Mécanique Matériaux et Structures (GMMS) EA 2617, ESIEC, Esp Roland Garros BP 1029, F-51686 Reims
  • Jean-Louis Batoz InSIC, 27 rue d’Hellieule F-88100 Saint-Dié des Vosges
  • Gouri Dhatt Laboratoire Roberval, Université de Technologie de Compiègne UPRES A 6066, Centre de Recherche de Royallieu BP 20529, F-60205 Compiègne cedex

Keywords:

finite element, shell, mixed formulation, Reissner-Mindlin, in-plane fiber rotation

Abstract

This work deals with a mixed variational approach for the linear analysis of shells. MiSP model (Mixed Shear Projection) is based on the Hellinger-Reissner principle with a particular representation of the transverse shear strains. To improve the membrane behaviour of shells, a 3D representation of the “Fiber Rotation” concept is made and adapted to the formulation of the degenerated MiSP model. Two 4-node shell finite elements are developed: MiSP4-Q4 and MiSP4-FRQ. Several tests usually used to validate shell elements are presented. These show a quite good behaviour of these two elements.

Downloads

Download data is not yet available.

References

[AHM 70] AHMAD S., IRONS B.M. and ZIENKIEWICZ O.C., «Analysis of thick and thin shell

structures by curved finite elements», Int. Jou. Num. Meth. Eng., 2, 1970, p. 419-451.

[AYA 93] AYAD R., Eléments finis de plaque et coque en formulation mixte avec projection

en cisaillement, Thèse de doctorat, Université de Technologie de Compiègne, France,

[AYA 95] AYAD R., « Une nouvelle approche variationnelle mixte-hybride pour les coques

avec effet de cisaillement transversal et un nouveau concept de rotation autour de la

normale pour améliorer la membrane », Actes du 2e colloque national en calcul des

structures, 16-19 Mai 1995, Giens, France.

[AYA 98] AYAD R., DHATT G. et BATOZ J.L., “A new hybrid-mixed variational approach for

Reissner-Mindlin plates. The MiSP model”, Int. Jou. Num. Meth. Eng., Vol. 42, 1998,

p. 1 149-1 179.

[BAT 80] BATOZ J.L., BATHE K.J. and HO L.W., “A study of three-node triangular plate

bending elements”, Int. Jou. Num. Meth. Eng., Vol. 15, 1980, p. 1 771-1 812.

[BAT 82a] BATHE K.J., Finite element procedures in engineering analysis, Prentice-Hall,

[BAT 82b] BATOZ J.L. and BEN TAHAR M., “Evaluation of a new thin plate quadrilateral

element”, Int. Jou. Num. Meth. Eng., Vol. 18, N° 11, 1982 ,p. 1 655-1 678.

[BAT 83] BATHE K.J. and DVORKIN E., “Our discrete Kirchhoff and isoparametric shell

elements for non-linear analysis”, Comput. Struct., Vol. 16, N° 1-4, 1983, p. 89-98.

[BAT 86] BATHE K.J and DVORKIN E.N., “A formulation of general shell elements - the use

of mixed interpolation of tensorial components”, Int. Jou. Num. Meth. Eng., 22, 1986,

p. 697-722.

[BAT 91] BATOZ J.L. et TRIKI S., Développement d’un élément fini de poutre vrillée,

Rapport interne, UTC/LG2MS/MNM, octobre 1991.

[BAT 92] BATOZ J.L. et DHATT G., Modélisation des structures par éléments finis, Vol.3:

Coques, Eds Hermès, Paris 1992.

[BOI 91] BOISSE P., DANIEL J.L. and GELIN J.C., “A new class of three node and four node

shell elements for the finite/inelastic strain analysis. Applications in sheet metal

forming”, European Conference on New Advances in Comp. Structural Mech., Giens,

France, 1991, p. 529-537.

[CHA 87] CHATELAIN J., Analyse non linéaire des coques minces isotropes et composites par

éléments finis quadrilatéraux, Thèse de Doctorat, Université de Technologie de

Compiègne, 1987.

[COF 91] COFER W.F. and Will K.M., “A three dimensional shell solid transition element for

general nonlinear analysis”,Comput. Struct., Vol. 38, N°4, 1991, p. 449-462.

[COO 89] COOK R.D., MALKUS D.S and PLESHA M.E., Concepts and applications of finite

element analysis, 3rd Ed., J.Wiley 1989.

[CRI 86] CRISFIELD M., Finite elements and solution procedures for structural analysis, Vol.

: Linear analysis, Pineridge press, 1986.

[DVO 84] DVOINRK E.N. and Bathe K.J., “A continuum mechanics based four node shell

element for general non-linear analysis”, Eng. Comput., Vol. 1, 1984, p. 77-88.

[DVO 91] DVORKIN E.N., “The Ahmad-Irons-Zienkiewicz shell element, the MITC4 shell

element, the MITC8 shell element”, Lectures in Nonlinear Analysis of Shells by Finite

Elements, CISM Course, Udine, Italy, June 1991.

[FEZ 81] FEZANS G., Analyse linéaire et non linéaire géométrique des coques par éléments

finis isoparamétriques tridimensionnels dégénérés, Thèse de Doctorat, ENSAE Toulouse,

[FLU 60] FLUGGE W., Sresses in shells, Springer Verla, 1960.

[GRE 61] GREENE B.E., STROME R. and WEIKEL R.C., “Application of the stiffness method

to the analysis of shell structures”, In Proc. Aviation Conference of ASME, Los Angeles,

CA, March 1961.

[HUG 81] HUGHES T.J. and LIU W.K., “Nonlinear finite element analysis of shells:

Part I: Three dimensional shells”, Com. Meth. App. Mec. Eng., 26, 1981, p. 331-362.

Part II: Two dimensional shells”, Com. Meth. App. Mec. Eng., 27, 1981, p. 167-181.

[HUG 87] HUGHES T., The finite element method - Linear static and dynamic finit element

analysis, Prentice Hall, 1987.

[IRO 76] IRONS B., “The semi-loof shell elements”, In Finite Elements for Thin shells and

Curved Members, Eds. Ashwell et al., J. Wiley, 1976, p. 197-222.

[KAT 93] KATILI I., Formulation et évaluation de deux nouveaux éléments finis pour

l’analyse linéaire des plaques et coques de forme quelconque, Thèse de doctorat, UTC,

France, 1993.

[LAR 90] LARDEUR P., Développement et évaluation de deux nouveaux éléments finis de

plaques et coques composites avec influence du cisaillement transverse, Thèse de

Doctorat, UTC, 1990.

[LIN 69] LINDBERG G.M. , OLSON M.D. and COWPER G.R., “New development in the finite

element analysis of shells”, Q. Bull Div. Mech. Eng. and Nat. Aeronautical

Establishment, National Research council of Canada, Vol. 4, 1969.

[MAC 85] MAC NEAL R. and HARDER R.L., “A proposed standart set of problems to test

finite element accuracy”, Finite Element Analysis Design, Vol. 1, 1985, p. 3-20.

[MAU 73] MAU S.T., PIAN T. H. H. and TONG P., “Vibration analysis of laminated plates

and shells by a hybrid stress element”, AIAA Jou. ,11, 1973, p. 1 450-1 452.

[NAT 90] National Agengy for Finite Element Methods and Standards (NAFEMS), U.K.

“The Standard NAFEMS Benchmarks”. TNSB, Rev. 3, October 1990.

[PAR 91] PARISCH H., “An investigation of a finite rotation four node assumed strain shell

element”, Int. Jou. Num. Meth. Eng., Vol. 31, 1991, p. 127-150.

[POL 92] POL P., Modélisation du comportement élastoplastique de coques minces par

éléments finis, Thèse de Doctorat, Université de Technologie de Compiègne, 1992.

[RAM 86] RAMM E. and MATZENMILLER A., “Large deformation shell analysis based on the

degeneration concept”, In Finite Element Methods for Plate and Shell Structures, Vol. 1,

Hughes, Hinton, Eds, 1986, p. 365-393.

[RAM 91] RAMMERSTOFER F.G., “Composite and sandwich shells”, Lecture in Nonlinear

Analysis of Shells by Finite Elements, CISM Course, Udine, Italy, June 1991.

[SIM 89] SIMO J.C., FOX D.D. and RIFAI M.S., “Geometrically exact stress resultant shell

models: formulation and computational aspects of the nonlinear theory”, In Analytical

and Computational Models of Shells, (Noor, Belytschko and Simo Eds), CED-Vol. 3,

ASME, 1989, p. 161-190.

[SIM 90] SIMO J.C., FOX D.D. and RIFAI M.S., “On stress resultant geometrically exact shell

model - Part III: Computational aspects on the nonlinear theory”, Com. Meth. App. Mec.

Eng, Vol. 79, 1990, p. 21-70.

[SCO 69] SCORDELIS A.C. and LO K.S., “Computer analysis of cylindrical shells”, J. Amer.

Conc. Ins., Vol. 61, 1969, p. 539-561.

[STA 85] STANLEY G., Continuum-based shell elements, Ph.d. thesis, Applied Mechanics

Division. Stan ford University, CA, 1985.

[VLA 87] VLACHOUTSIS S., Eléments finis tridimensionnels dégénérés de coques avec

intégration explicite suivant l’épaisseur, Thèse de Doctorat, ENSAE, Toulouse, 1987.

[VLA 90] VLACHOUTSIS S., “Explicit integration for three dimensional degenerated shell

finite elements”, Int. Jou. Num. Meth. Eng., Vol. 29, 1990, p. 861-880.

[WIL 90] WILT T.E., SALEEB A.F. and ChANG T.Y., “A mixed element for laminated plates

and shells”, Comput. Struct., Vol. 37, 1990, p. 597-611.

[YAN 90] YANG H.T.Y, SAIGAL and LIAW, “Advances of thin shell finite elements and some

applications - version 1”, Comp.Struct., 35, 1990, p. 481-504.

[YOS 74] YOSHIDA Y., “A hybrid stress element for thin shell analysis”, In Proc.

International Conference on Finite Element Method in Engineering, 1974, p. 271-284.,

Univ. of N.S.W., Australia.

[ZIE 77] ZIENKIEWICZ O.C., The finite element method, 3rd Edition, McGraw-Hill, 1977.

[ZIE 91] ZIENKIEWICZ O.C and TAYLOR R., The finite element method, Volume 2: Plates,

shell,fluids and non-linear problems, 4th Ed., Mc Graw-Hill, London 1991.

Downloads

Published

2002-04-24

How to Cite

Ayad, R., Batoz, J.-L. ., & Dhatt, G. . (2002). Formulation du modèle MiSP coque tridimensionnel dégénéré. European Journal of Computational Mechanics, 11(6), 719–747. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/2543

Issue

Section

Original Article