Analyse non lineaire geometrique de plaques multicouches
Un nouvel eU~ment fini C1
Keywords:
multilayered plates, refined model, C1 finite element, transverse normal stress, linear and non-linear testsAbstract
In this paper, we focus our attention on geometrically non linear behaviour of multilayered plates. For this purpose, a high order plate model is used which exactly ensure both the continuity conditions for displacements and transverse shear stresses at the interfaces between layers of a laminated structure, and the boundary conditions at the upper and lower surfaces of the plate. Based on this kinematics, a six node C1 triangular finite element is developed, using a conforming finite element method and a displacement approach. The Argy'T'is interpolation is used for transverse displacement and the Ganev interpolation is used for membrane displacements and transverse shear rotations. A set of linear and non-linear tests is presented in order to show the efficiency of this finite element.
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References
[ ARG 68] ARGYRIS J., FRIED I. et ScHARPF D., " The TUBA family of plate
elements for the matrix displacement method ". Aero. J. Royal Aeronaut.
Soc., vol. 72, p. 701-709, 1968.
[AUR 99] AURICCHIO F. et SACCO E., "A mixed-enhanced finite element for
the analysis of laminated composite plates ". Int. Jour. Num. Meth. Eng.,
vol. 44, p. 1481-1504, 1999.
[BEA 93] BEAKOU A. et TOURATIER M., " A rectangular finite element for
analysing composite multilayered shallow shells in statics, vibration and
buckling". Int. Jour. Num. Meth. Eng., val. 36, p. 627-653, 1993.
[BER 96] BERNADOU M., Finite Element Methods for Thin Shell Problems.
John Wiley et Sons, 1996.
[CAR 96] CARRERA E., " C0 Reissner-Mindlin multilayered plate elements
including zig-zag and interlaminar stress continuity ". Int. Jour. Num.
Meth. Eng., val. 39, p. 1797-1820, 1996.
[DUN 85] DUNAVANT D., " Hight degree efficient symmetrical gaussian
quadrature rules for the triangle". Int. Jour. Num. Meth. Eng., vol. 21, p.
-1148, 1985.
[GAN 80] GANEY H. et DIMITROV T., "Calculation of arch dams as a shell
using IBM-370 Computer and curved finite elements". In Theory of shells,
p. 691-696. North-Holland, Amsterdam, 1980.
[NOO 94] NOOR A., BURTON W. et PETERS J., "Hierarchical adaptative
modeling of structural sandwiches and multilayered composite panels ".
Appl. Num. Math., val. 14, p. 69-90, 1994.
[NOO 96] NOOR A., BURTON W. et BERT C., " Computational models for
sandwich panels and shells". App. Mech. Rev., val. 49, n° 3, p. 155-199,
[PAG 70] PAGANO N., "Exact solutions for rectangular bidirectional composites
and sandwich plates ". J. Camp. Materials, val. 4, p. 20-34, 1970.
[POL 94] POLIT 0., TOURATIER M. et LORY P., "A new eight-node quadrilateral
shear-bending plate finite element ". Int. Jour. Num. Meth. Eng.,
vol. 37, p. 387-411, 1994.
[RED 89] REDDY J., " On refined computational models of composite laminates
". Int. Jour. Num. Meth. Eng., vol. 27, p. 361-382, 1989.
[RED 97] REDDY J ., Mechanics of laminated composite plates - Theory and
analysis. CRC Press Inc., 1997.
[SCI 95] SCIUVA M. D., " A third order triangular multilayered plate finite
element with continuous interlaminar stresses ". Int. Jour. Num. Meth.
Eng., val. 38, p. 1-26, 1995.
[SRI 70] SRINIVAS S. et RAO A., "Bending, vibration and buckling of simply
supported thick orthotropic rectangular plates and laminates ". Int. J.
Solids Struc., vol. 6, p. 1463-1481, 1970.
[TOU 91] TOURATIER M., "An efficient standard plate theory". Int. J. Eng.
Sci., vol. 29, p. 901-916, 1991.
