Advanced models for smart multilayered plates based on Reissner Mixed Variational Theorem

Abstract

In the present work, families of equivalent singe layer and layer-wise models for the static and free vibrations analysis of magneto-electro-elastic multilayered plates are developed. The models are defined in the framework of a unified formulation, which offers a systematic approach for generating refined plate theories through suitable expansions of the through-the-thickness components of the relevant fields, considering the expansion order as a free parameter. The key features of the developed formulation are: a) the condensation of the electric and magnetic description into the mechanical representation, based on the quasi-static electric-magnetic approximation, which allows to reduce the computation of the analysis for both layer-wise and equivalent single layer models; b) the employment of the Reissner Mixed Variational Theorem, in which the displacements and transverse stress components are used as primary variables, thus allowing the explicit fulfilment of the transverse stress interface equilibrium. The proposed methodology is assessed by generating different layer-wise and equivalent single layer models for the analysis of thick magneto-electro-elastic plates and comparing their solution against available three-dimensional analytic results.