A new eight-node quadrilateral shear-bending Reissner-Mindlin plate finite element for the very thin and thick plates without locking and spurious zero-encrgy modes is presented. The element has very good convergence characteristics both for thin and thick plates, is hardly insensitive to mesh distortions, and passes the patch tests. The formulation of the element is derived from a displacement variational principle and some general criteria to compute inconsistent transverse shear strains. These criteria have been applied with success to four-and eight-node quadrilateral plate finite elements and could be applied to construct triangular elements. The eight-node quadrilateral shear-bending plate finite element proposed has been found to be very dficient.

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International audienceA two-phase approach is proposed to model the rheology of polymer glass-fiber compounds such as SMC or GMT during processing. The anisotropic behavior of the composite, which is related to the microstructure of the fiber network, is reduced to the simple case of transverse isotropy. The rheology of the two media, e.g. the matrix and the fiber network, as well as their interaction follow non-linear viscous behaviors. The equations of this model are simplified to the case of the compression of SMC, giving the formulation of a shell model whose equations are written into a finite element code. Simple simulation examples thus show the strong influence of material and process parameters on the phenomenon of phase separation.Un formalisme biphasique est proposé pour modéliser la rhéologie des composites fibres de verre-matrice polymère de type SMC ou GMT au cours de leur mise en forme. L'anisotropie liée à la morphologie du réseau de fibres est simplifiée au cas de l'orthotropie de révolution. Le comportement visqueux non linéaire régit la rhéologie des deux milieux considérés (matrice et réseau de fibres) ainsi que leur interaction. Les équations de ce modèle sont simplifiées et adaptées au cas du procédé de compression des SMC ; ceci aboutit à la formulation d'un modèle coque, dont les équations sont introduites dans un code éléments finis. Des exemples simples de simulations permettent alors de souligner l'importance des paramètres « matériau » et « procédé » sur le phénomène de redistribution de phases