A refined sinus plate finite element for laminated and sandwich structures under mechanical and thermomechanical loads

This paper presents a C1 6-node triangular finite element for multilayered composite plates submitted to mechanical and thermomechanical loads. It is based on the sinus model with layer refinement and includes the transverse normal effect. This kinematics allows to exactly ensure both (i) the continuity conditions for displacements and transverse shear stresses at the interfaces between layers of a laminated structure, and (ii) the boundary conditions at the upper and lower surfaces of the plates. It is important to notice that the number of unknowns is independent of the number of layers. This finite element is able to model both thin and very thick plates without any pathologies of the classic plate finite elements (shear locking, spurious modes, etc.). It is built on the Argyris interpolation for bending and the Ganev interpolation for membrane displacements and transverse shear rotations. The representation of the transverse shear strains by cosine functions allows avoiding shear correction factors. In addition, the transverse normal stress can be accurately recovered from equilibrium equations at the post-processing level, using the high degree of interpolation polynomia. echanical and thermomechanical tests for thin and very thick plates are presented in order to evaluate the capability of this new finite element to give accurate results with respect to exact three-dimensional 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 shear stresses computed from the constitutive relation are well estimated with regards to other equivalent single layer or even with respect to layerwise models.