Mixed finite elements for nonlocal elastic multilayered composite plate refined theories

A novel mixed finite element formulation for the layerwise analysis of nonlocal multilayered composite plates is presented. The finite elements are formulated starting from the weak form of a set of governing equations for the laminate layers that were deduced via the Reissner Mixed Variational Theorem. The primary variables, namely displacements and out-of-plane stresses, are expressed at layer level as through-the-thickness expansions of suitable selected functions with coefficients approximated by the finite element scheme. The through-the-thickness expansion order is considered as a free parameter. This way, finite elements for different refined higher order plate theories can be systematically developed by assembling the layers contributions associated with the variable expansion terms. These contributions are called fundamental nuclei and their definition is formally unique whatever the considered expansion order. The obtained finite elements inherently ensure stresses and displacements continuity at the layer interfaces and they allow to associate different values of the nonlocal parameter to the laminate layers. Standard 9-node and 16-node isoparametric, quadrilateral finite elements have been implemented to verify the viability of the proposed formulation. The obtained results compare favourably with literature solutions and highlight the characteristics of the approach. Original results are proposed also to serve as benchmarking data.