A Comparison of Various Two-Dimensional Assumptions in Finite Element Analysis of Multilayered Plates

This work deals with a refined Finite Element (FE) analysis of multilayered plates. Various two-dimensional axiomatic assumptions in the thickness direction are illustrated and discussed by considering: 1-Taylor type expansion; 2-combinations of Legendre polynomials; 3-Lagrange polynomials. Both cases of an equivalent single layer description (the whole plate is seen as an equivalent single layer) and a layer-wise description (each layer is seen as an independent plate) have been implemented. The order N of the thickness expansions is a free parameter of the present formulation. A large variety of plate theories are therefore obtained. Related standard serendipity-type quadrilateral FEs are considered in this paper. FE matrices are written in a concise form by referring to the Carrera Unified Formulation and in terms of a few fundamental nuclei, whose form does not depend on the through-the-thickness polynomial assumption, order N, variable description or element number of nodes. The advantages and disadvantages of the various FEs are discussed by considering static and dynamic problems related to significant multilayered plate problems.