A family of sinus finite elements for the analysis of rectangular laminated beams

In 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 avoiding 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 computed 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.