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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.

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.

The purpose of this paper is to investigate the linear and non-linear free vibration of a functionally graded material (FGM) rotating cantilever plate in the thermal environment. The study employs the development of a non-linear mathematical model using the higher order shear deformation theory in which the traction free condition is applied to derive the simplified displacement model with seven field variables instead of nine.

A mathematical model is developed based on the higher order shear deformation theory using von-Karman type non-linearity. The rotating plate domain has been discretized into C0 eight-noded quadratic serendipity elements with node wise 7 degrees of freedom. The material properties are considered temperature dependent and graded along the thickness direction obeying a simple power law distribution in terms of the volume fraction of constituents, based on Voigt’s micromechanical method. The governing equations are derived using Hamilton’s principle and are solved using the direct iterative method.

The importance of the present mathematical model developed for numerical analysis has been stated through the comparison studies. The results provide an insight into the vibration response of FGM rotating plate under thermal environment. The influence of various parameters like setting angle, volume fraction index, hub radius, rotation speed parameter, aspect ratio, side-thickness ratio and temperature gradient on linear and non-linear frequency parameters is discussed in detail.

A non-linear mathematical model is newly developed based on C0 continuity for the functionally graded rotating plate considering the 1D Fourier equation of heat conduction. The present findings can be utilized for the design of rotating plates made up of a FGM in the thermal environment under real-life situations.

The purpose of this paper is to attempt the buckling analysis of a laminated composite skew plate using the C₀ finite element (FE) model based on higher-order shear deformation theory (HSDT) in conjunction with minimax probability machine regression (MPMR) and multivariate adaptive regression spline (MARS).

HSDT considers the third-order variation of in-plane displacements which eliminates the use of shear correction factor owing to realistic parabolic transverse shear stresses across the thickness coordinate. At the top and bottom of the plate, zero transverse shear stress condition is imposed. C₀ FE model based on HSDT is developed and coded in formula translation (FORTRAN). FE model is validated and found efficient to create new results. MPMR and MARS models are coded in MATLAB. Using skew angle (α), stacking sequence (Ai) and buckling strength (Y) as input parameters, a regression problem is formulated using MPMR and MARS to predict the buckling strength of laminated composite skew plates.

The results of the MPMR and MARS models are in good agreement with the FE model result. MPMR is a better tool than MARS to analyze the buckling problem.

The present work considers the linear behavior of the laminated composite skew plate.

To the authors’ best of knowledge, there is no work in the literature on the buckling analysis of a laminated composite skew plate using C₀ FE formulation based on third-order shear deformation theory in conjunction with MPMR and MARS. These machine-learning techniques increase efficiency, reduce the computational time and reduce the cost of analysis. Further, an equation is generated with the MARS model via which the buckling strength of the laminated composite skew plate can be predicted with ease and simplicity.

The present findings report a significant influence of disc profile and thickness on the order of excitation leading to critical speed condition. Certain transverse modes of vibration of the disc have been obtained to be more susceptible to get excited while recording the lowest critical speeds.

Numerical simulation using finite-element method has been adopted due to the complicated geometry, complex loadings and intricate analytical formulation. A comprehensive analysis of exclusive as well as combination of thermal and centrifugal loads has been taken up to determine the intensity and characteristics of the individual/combined effects.

The typical gas turbine disc profile has been analyzed to predict the critical speed under the factual working condition of an aero-engine. FEM analysis of uniform and variable thickness discs have been carried out under stationary, rotating and rotating-thermal considerations while emphasizing the effect of disc profile and thickness. Centrifugal stresses developed due to rotational effect result in unceasing stiffening of the discs with higher stiffening for a greater number of nodal diameters. On the other hand, a role reversal of thermal effect from stiffening to softening is figured out with increasing numbers of nodal diameters. However, the discs are subjected to an overall stiffening effect on account of the combined centrifugal and thermal loading, with the effect decreasing with an increase in disc thickness. Under the combined loading, the order of excitation leading to critical speed condition is dependent on disc profile and thickness. Moreover, the vibrational modes (0,1) and (0,2) are identified as more prominent adverse modes corresponding to lowest critical speeds.

The present findings are expected to serve as guidelines during the design phase of gas turbine discs of aeroengine applications.

The present work deliberates on the simulation and analysis of gas turbine disc specific to aeroengine application. The real-life disc geometry has been analyzed with due consideration of major factual operating conditions to identify the critical speed. The identification of various critical speed using numerical analysis can help to reduce the number of experimental tests required for certification.

This article focuses on the low-velocity impact (LVI) output of carbon nanotubes (CNTs)’ reinforcement circular plates, considering agglomeration size effect and clumping of CNTs’ inner side of the agglomerations.

A representative volume element (RVE) is used to determine the nanocomposite properties reinforced with agglomerated CNTs with random orientation. First-order shear deformation theory (FSDT) is used to obtain the motion equations of LVI analysis. These equations are handled by developing a Ritz method and Lagrangian mechanics. To extract the mass and stiffness matrices, terms with second and higher degrees are ignored.

Formulation validation is performed by providing various examples, including comparisons with other research and ABAQUS FE code. The effects of agglomeration size, clumping of CNTs’ inner side of the agglomerations, CNT volume fraction and impact location on the responses of impact load, projectile displacement and plate deflection are analytically studied. These achievements illuminate how the influence of agglomeration size is very small on the impact response. Also, the influence of clumping of CNTs’ inner side of the agglomerations is significant, and as it increases, the displacement values and impact time increase, and the impact force decreases.

In this article, to avoid additional calculations, the parameters of the mass matrix and the stiffness coefficients are linearized to obtain the equations of motion of the impact on the circular plate.

The purpose of this paper is to determine the temperature distribution of a thin rectangular plate made of thermosensitive functionally graded (FG) material. By finding out thermal deflection and stress resultants, the thermal stresses have been obtained and analyzed.

Initially, the rectangular plate is kept at the surrounding temperature. The upper, lower and two parallel sides (y=0, b and z=0, c) are thermally insulated, while other parallel sides (x=0, a) are given convective-type heating, that is, the rate of change of the temperature of the rectangular plate is proportional to the difference between its own temperature and the surrounding temperature. The non-linear heat conduction equation has been converted to linear form by introducing Kirchhoff’s variable transformation and the resultant heat conduction equation is solved by integral transform technique with hyperbolic varying point heat source.

A mathematical model is prepared for FG ceramic–metal-based material, in which alumina is selected as the ceramic and nickel as the metal. The thermal deflection and thermal stresses have been obtained for the homogeneous and nonhomogeneous materials. The results are illustrated numerically and depicted graphically for comparison. During this study, one observed that variations are seen in the stresses, due to the variation in the inhomogeneity parameters.

The paper is constructed purely on theoretical mathematical modeling by considering various parameters and functions.

This type of theoretical analysis may be useful in high-temperature environments like nuclear components, spacecraft structural members, thermal barrier coatings, etc., as the effect of temperature and evaluation of temperature-dependent and nonhomogeneous material properties plays a vital role for accurate and reliable structural analysis.

In this paper, the authors have used thermal deflection and resultant stresses to determine the thermal stresses of a thin rectangular plate with temperature- and spatial variable-dependent material properties which is a new and novel contribution to the field.

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.

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.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.