New hierarchical robust three-node finite element for thin to thick laminate plates

This paper presents the development of a new hierarchical triangular Finite Element (FE) for the linear elastic static analysis of composite plates. The proposed element uses C 0 interpolation with three nodes for the approximation of the geometry, which is a very useful and simple description for automatic meshing software, and is robust with respect to the numerical pathologies of classical FE approximations. The displacement field across the thickness is described with an Equivalent Single Layer (ESL) approach of order one, using bottom and top displacements in the three directions. The transverse normal stress is accounted for, thus allowing the incorporation of three-dimensional constitutive law and extending the range of applicability to very thick structures as well as to thermo-mechanical analyses. To this aim, the approximation order of the transverse displacement is increased, adding a third unknown, avoiding Poisson locking. To be efficient in the field of composite modelling, Sinus functions and Zig-Zag terms are also added for the two in-plane displacements. It results in a family of FE encompassing 7-, 9-, or 11-parameters. The elements’ robustness is first demonstrated on some standard plate tests. Subsequently, the results of displacements and stress computed here are compared with those of exact three-dimensional solutions for the plates undergoing mechanical/thermal loads. All results show that the intended FE has very favourable convergence properties, is free of locking problems, is independent of mesh geometry, and provides accurate results for both displacements and stresses.