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The purpose of this paper is to consider the static analysis of nanocomposite plates. Nanocomposites consist of a small amount of nanoscale reinforcements which can have an observable effect on the macroscale properties of the composites.

In the present study the reinforcements considered are non‐spherical, high aspect ratio fillers, in particular nanometer‐thin platelets (clays) and nanometer‐diameter cylinders (carbon nanotubes, CNTs). These plates are considered simply supported with a bi‐sinusoidal pressure applied at the top. These conditions allow the solving of the governing equations in a closed form. Four cases are investigated: a single layered plate with CNT reinforcements in elastomeric or thermoplastic polymers, a single layered plate with CNT reinforcements in a polymeric matrix embedding carbon fibers, a sandwich plate with external skins in aluminium alloy and an internal core in silicon foam filled with CNTs and a single layered plate with clay reinforcements in a polymeric matrix. A short review of the most important results in the literature is given to determine the elastic properties of the suggested nanocomposites which will be used in the proposed static analysis. The static response of the plates is obtained by using classical two‐dimensional models such as classical lamination theory (CLT) and first order shear deformation theory (FSDT), and an advanced mixed model based on the Carrera Unified Formulation (CUF) which makes use of a layer‐wise description for both displacement and transverse stress components.

The paper has two aims: to demonstrate that the use of classical theories, originally developed for traditional plates, is inappropriate to investigate the static response of nanocomposite plates and to quantify the beneficial effect of the nanoreinforcements in terms of static response (displacements and stresses).

In the literature these effects are usually given only in terms of elastic properties such as Young moduli, shear moduli and Poisson ratios, and not in terms of displacements and stresses.

Finite Elements FE based on the Reissner’s Mixed Variational Theorem RMVT, for the analysis of multilayered plates subjected to magneto‐electro‐elastic MEE fields, are developed in this work. Accurate description of the various field variables has been provided by employing a variable kinematic model which is based on the Carrera’s Unified Formulation CUF. Displacements, transverse shear/normal stresses, magnetic and electric potentials have been chosen as independent unknowns. Interlaminar continuity of mechanical variables is “a priori” guaranteed by the RMVT application. Layer‐wise plate elements with linear up to fourth order distribution in the thickness direction have been compared. FE governing equations, according to CUF, are presented in terms of fundamental nuclei whose form is not affected by kinematic assumptions. Results show the effectiveness of the proposed elements, the superiority of mixed FEs with respect to the classical ones, as well as their capability, by choosing appropriate kinematics, to accurately trace the static response of laminated plates subject to magneto‐electro‐elastic fields.

Finite elements for the analysis of multilayered plates subjected to magneto‐electro‐elastic fields are developed in this work. An accurate description of the various field variables has been provided by employing a variable kinematic model which is based on the Unified Formulation, UF. Displacements, magnetic and electric potential have been chosen as independent unknowns. Equivalent single layer and layer‐wise descriptions have been accounted for. Plate models with linear up to fourth‐order distribution in the thickness direction have been compared. The extension of the principle of virtual displacements to magneto‐electro‐elastic continua has been employed to derive finite elements governing equations. According to UF these equations are presented in terms of fundamental nuclei whose form is not affected by kinematic assumptions. Results show the effectiveness of the proposed elements as well as their capability, by choosing appropriate kinematics, to accurately trace the static response of laminated plates subject to magneto‐electro‐elastic fields.

The purpose of this paper is to present several two‐dimensional plate elements for the analysis of shear actuated laminate.

The limitations of the classical formulations based on the principle of virtual displacements in depicting the peculiar behavior of the transverse and normal stresses of multilayered structures have been easily overcome by using the mixed variational theorem proposed by Reissner (Reissner mixed variational theorem). In the framework of a unified formulation (UF), the assumptions of the unknowns is made through a common expansion leading both to global and layerwise description of the assumed unknowns. In addition, the possibility to choose the order of the expansion between one and four allows to be derived and compared 22 different plate models. The performances of the proposed elements have tested on application for whom an exact solution is available in open literature.

The obtained results complain quite well with the exact ones even if the need of advanced plate models come to evidence.

This paper describes how the capabilities of the UF to accurately analyze multilayered structures exploiting the shear mode actuation have been tested and states that in order to extend the capabilities of the UF, further efforts should be made toward the assumptions of discontinuous electric fields (potential and normal displacement). The paper confirms the need for advanced higher order plate models in modeling of adaptive laminate.

This paper aims to analyze the dynamics of the Spanish public debt–gross domestic product ratio during the period 1850–2020.

This study uses a recent procedure to test for recurrent explosive behavior (Phillips et al., 2011; Phillips et al., 2015a, 2015b) to identify episodes of explosive public debt dynamics and also the episodes of fiscal adjustments over this long period.

The identified episodes of explosive behavior of public debt coincided with fiscal stress events, whereas fiscal adjustments and changes in economic policies stabilized public finances after periods of explosive dynamics of public debt.

The longer than usual span of the data should allow the authors to obtain some more robust results than in most of previous analyses of long-run sustainability.