Advanced models for nonlocal magneto-electro-elastic multilayered plates based on Reissner mixed variational theorem

Abstract

In the present work, nonlocal layer-wise models for the analysis of magneto-electro-elastic multilayered plates are formulated. An Eringen non-local continuum behaviour is assumed for the layers material; in particular, as usual in plate theories, partial in-plane nonlocality is assumed whereas local constitutive behaviour is considered in the thickness direction. The proposed plate theories are obtained via the Reissner Mixed Variational Theorem, assuming the generalized displacements and generalized out-of-plane stresses as primary variables, and expressing them as through-the-thickness expansions of suitably selected functions, considering the expansion order as a free parameter. In the framework of the Carrera Unified Formulation, this allows the systematic generation of advanced high order plate theories via a layer-based assembly algorithm of the so-called fundamental nuclei associated with the variables exapansion terms. The use of the layerwise approach and Reissner Mixed Variational Theorem allows for: i) the explicit fulfilment of the transverse generalized stress interface equilibrium, which is crucial for a correct description of the plate fields, ii) the straightforward analysis of plates with layers exhibiting different characteristic lengths in their nonlocal behaviour. A Navier solution for the developed models has been implemented and tested for the static bending and free vibrations analyses of rectangular simply-supported plates. The obtained representative results favourably compare against available three-dimensional analytic results and demonstrate the features of the proposed theories.