In this paper, classical as well as various refined plate finite elements for the analysis of laminates and sandwich structures are discussed. The attention is particularly focussed on a new variable-kinematic plate element. According to the proposed modelling approach, the plate kinematics can vary through the thickness within the same finite element. Therefore, refined approximations and layer-wise descriptions of the primary mechanical variables can be adopted in selected portions of the structures that require a more accurate analysis. The variable-kinematic model is implemented in the framework of the Carrera unified formulation, which is a hierarchical approach allowing for the straightforward implementation of the theories of structures. In particular, Legendre-like polynomial expansions are adopted to approximate the through-the-thickness unknowns and develop equivalent single layer, layer-wise, as well as variable-kinematic theories. In this paper, the principle of virtual displacements is used to derive the governing equations of the generic plate theory and a mixed interpolation of tensorial components technique is employed to avoid locking phenomena. Various problems are addressed in order to validate and assess the proposed formulation, including multi-layer plates and sandwich structures subjected to different loadings and boundary conditions. The results are compared with those from the elasticity theory given in the literature and from layer-wise solutions. The discussion clearly underlines the enhanced capabilities of the proposed variable-kinematic mixed interpolation of tensorial component plate elements, which allows, if used properly, to obtain formally correct solutions in critical areas of the structure with a considerable reduction of the computational costs with respect to more complex, full layer-wise models. This aspect results particularly advantageous in problems where localized phenomena within complex structures play a major role.
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