High-order triangular sandwich plate finite element for linear and non-linear analyses

Abstract

The objective of this paper is to present a new C 1 six-node triangular finite element for geometrically linear and non-linear elastic multilayered composite plates. This finite element must be able to model both thin and moderately thick plates without any pathologies of the classic plate finite elements (shear locking, spurious modes, …). It is based on a new kind of kinematics proposed by Touratier [1], and built on the Argyris interpolation for bending and the Ganev interpolation for membrane displacements and transverse shear rotations. This kinematics allows to 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 plates. The representation of the transverse shear strains by cosine functions allows avoiding shear correction factors. In addition, transverse normal stress can be deduced with good precision from equilibrium equations at the post-processing level, using the high degree of interpolation polynomia. The element performances are evaluated on some standard plate tests and also in comparison with exact three-dimensional solutions for multilayered plates in linear and non-linear (moderately large deflection) statics, dynamics and for buckling. Comparisons with other plate models using the present finite element approximation and an eight-node C 0 finite element based on the Reissner–Mindlin model are also given. All results indicate that the present element has very fast convergence properties and also gives very accurate results for displacements and stresses.