Use of Lagrange polynomials to build refined theories for laminated beams, plates and shells

This paper proposes an equivalent single-layer approach for modeling laminated structures, where the number layers to be considered as a single one is chosen a priori by the user. Lagrange points are set to locate and, eventually, join equivalent single-layer and layer-wise tenchiques by imposing displacement continuity in the thickness direction. The Finite Element (FE) method is applied to provide numerical solutions whereas the Carrera Unified Formulation (CUF) is used to generate the related stiffness matrices in a compact and straightforward way. The approach is employed using one-dimensional beam and two-dimensional plate and shell models and several case studies, taken from well-known examples in the literature, are analyzed. Results clearly show the advantages and superiority of the present approach to completely capture the displacements and the distribution of the axial stress components, whereas local values of the shear stresses can be obtained by opportunely chosing the Lagrange points pattern opportunely.