International audienceIn the framework of a sinus models family, a new three-noded mechanical beam finite element is designed for the analysis of laminated beams. It is based on a sinus distribution with layer refinement. The transverse shear strain is obtained by using a cosine function avoid-ing the use of shear correction factors. This kinematic accounts for the interlaminar continuity conditions on the interfaces between the layers, and the boundary conditions on the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent from the number of layers.Both static and vibration mechanical tests for thin and thick beams are presented in order to evaluate the capability of this new finite element to give accurate results with respect to elasticity or finite element reference solutions. Both convergence velocity and accuracy are discussed and this new finite element yields very satisfactory results at a low computational cost. In particular, the transverse stress com-puted from constitutive relation is well estimated with regards to classical equivalent single layer models. Moreover, this family of sinus model is very efficient owing to the low number of unknowns

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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.

International audienceThis paper deals with the influence of the use of the Murakami’s zig-zag function in the sine model for the analysis of laminated beams. The adding of this function introduces a discontinuity of the first derivative of the in-plane displacement with only one more unknown. The kinematics is based on a sine distribution and the transverse displacement remains constant through the thickness. The transverse shear strain is obtained using a cosine function avoiding the use of shear correction factors. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent of the number of layers. The purpose is to develop a finite element approach with a low computational cost and without numerical pathology.This study aims at determining the influence of an additional zig-zag function in the Sine model for sta-tic and vibration analysis. In this way, mechanical tests for thin/thick laminated and sandwich beams are presented in order to evaluate the capability of this finite element. The results are compared with elas-ticity or finite element reference solutions in statics and vibration. Both convergence velocity and accu-racy are discussed. This finite element yields satisfactory results at a low computational cost