Un element fini mixte tridimensionnel pour le cal cui des contraintes d 'interface
Keywords:
Heteregeneous materials, interfacial stresses, mixed finite-elements, mixed principle, three-dimensional analysisAbstract
In this paper we present an interfacial finite element designed for analysing planar interfaces in a three-dimensional approach. The element is derived from Hellinger-Reissner's mixed variational principle and takes into account the continuity of the displacement and of the transverse stress components through the interface. Stress analysis of a sandwich plate is made to assess the validity and the effectiveness of the element models, with comparisons to closed-form and numerical solutions.
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References
[AIV 84] AIVAZZADEH S., Elements finis d'interface. Application aux assemblages colles et
structures stratifiees, These de Docteur lngenieur de I'Universite de Technologie de
Compiegne, Specialite Mecanique appliquee a Ia Construction, 1984.
[ATE 98] ATE A., Elements finis mixtes tridimensionnels pour le calcul des champs de
contrainte dans les structures heterogenes, These de Doctoral de I'Universite de
Bourgogne, 1984.
[BAB 91] BABI M., Elements finis specialises pour I' analyse des interfaces, These de
Doctoral de I'Universite Claude Bernard, Lyon I, 1991.
[BAT 96] BATHE K.J., Finite element procedures, Prentice Hall Englewood Cliffs, New
Jersey, 1996.
[BAT 90] BATOZ J.L., DHATT G., Modelisation des structures par eltiments finis, vol.l et 2,
, Hermes, Paris.
[BAT 89] BATOZ J.L., LARDEUR P., «A discrete shear triangular nine degree of freedom
element for the analysis of thick to very thin plates >>, International journal for numerical
methods in engineering, 28, 1989.
[BIC 90] BICHARA M., Formulation d'elements finis d'interface. Application aux assemblages
colles, These de Doctoral de I'Universite Paris VI, 1990.
[BOU 92] BouzERD H., Elements finis mixtes pour interface coherente et fissuree, These de
Doctoral de I'Universite Claude Bernard, Lyon I, 1992.
[COO 72] CooK R.D., <
plates >>,International journal for numerical methods in engineering, John Wiley & Sons,
Ltd vol. 5, p. 277-288, 1972.
[ENG 87] ENGRAND D., << Effets locaux dans les structures composites>>, Calcul des
structures et intelligence artificielle, Edition Pluralis, vol. I, p. 3-6, 1987.
[HAB 90] HABIB M., AIVAZZADEH S., VERCHERY G., <
bonded composite tubes using axisymmetric interface finite elements >>, Computer aided
design in composite material technology, Computational mechanics publications,
Springier Verlag, p. 415-428, 1990.
[HAD 91] HADJ-RABAH Y., Etude par elements finis d'interface des effets debord et des
defauts dans les assemblages colles, These de Doctoral de I'Universite de Bourgogne,
[HUA 90] HUANG K., HoA S.V., SANKAR T.S., <
formulation for stress analysis of anisotropic laminate structures >>, Composite material
design analysis, Computational mechanics publications, Springier Verlag, p. 189-200,
[NEV 87] NEVERS T., << Singularites et delaminage dans les structures composites >>, Calcul
des structures et intelligence artificielle, Edition Plural is, vol. I, p. 23-37, 1987.
[NOO 83] NooR A.K., << Multi field (mixed and hybrid) finite element models, State of the art
surveys in finite element technology >>, American Society of Mechanical Engineers,
Chap. 5, p. 127-162, 1983.
[OLS 83] OLSON M.D., «Mixed finite element method in elasticity and elastic contact
problems >>, Hybrid and mixed finite elements methods, John Wiley and Sons, Chap. 2,
p. 19-48, 1983.
[PAG 89] PAGANO N.J., SONI S.R., << Interlaminar response of composite materials>>,
Composite materials series, Models for studying free-edge effects, vol. 5, 1989.
[PAG 70] PAGANO N.J. <
sandwich plates >>, Journal of composite materials, vol. 4, p. 20-34, 1970.
[PEN 90] PENADO F.E., DROPEK R. K., << Numerical design and analysis >>, Adhesives and
sealants, Engineered material handbook, Edition ASM International, vol. 3, p. 477-500,
[PHA 76] PHAM DANG T, Theories des plaques sandwiches elastiques anisotropes, These de
Docteur lngenieur de I'Universite de Technologie de Compiegne. Specialite Mecanique
appliquee a Ia Construction, 1976.
[REI 50] REISSNER E., <>, Journal of mathematics and
physics, vol. 3, p. 90-95, 1950.
[SPI 81] SPILKER R.L., <
analysis>>, International journal for numerical methods in engineering, John Wiley &
Sons Ltd, vol. 17, p. 53-69, 1981.
[SPI 82] SPILKER R.L., SPINGH S.P, <
displacement elements>>, International journal for numerical methods in engineering,
John Wiley & Sons, Ltd, vol. 18, p. 445-465, 1982.
[VAN 98) VANNUCCI P., AIVAZZADEH S., VERCHERY G., «A comparative analysis of some
theories and finite elements for sandwich plates and shells >>, Mechanics of sandwich
structures, Kluwer Academic Publishers, p. 43-52, 1998.
[VER 87] VERCHERY G., << Methodes numeriques de calcul des champs de contrainte dans Ies
materiaux heterogenes >>, Calcul des structures et intelligence artijicielle, Edition Pluralis,
vol. I, p. 7-21, 1987.
[ZIE 89) ZIENKIEWICZ, TAYLOR, The finite element method, vol. I, McGrawHill Book
Company, London 1989 (41
h edition).
