Analysis of laminated composites and sandwich structures by variable-kinematic MITC9 plate elements

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.