A finite element evaluation of single-layer and multi-layer theories for the analysis of laminated plates

A layerwise polynomial expansion along the thickness direction for displacements is assumed to analyse the behaviour of an arbitrary laminated composite plate. In contrast with other proposed approaches and in order to take into account the transverse normal stress distribution, out-of-plane displacements are not assumed to be constant along the thickness. Based on the proposed kinematic assumptions the continuity of the interlaminar stress components at the interface can be also achieved. A finite element procedure is established and plate models are derived in which the stress field is obtained directly from the constitutive relations and not by the integration of the three-dimensional equilibrium equations. Comparisons among the numerical results obtained with the proposed layerwise models, single-layer models, the classical laminate theory and exact three-dimensional elasticity solutions are presented and briefly discussed.