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Nonlinear bending of functionally graded metal/graphene (FGMG) sandwich rectangular plate with metal foam core resting on nonlinear elastic foundations is elucidated in this article. A new shear deformation plate theory is presented to formulate the displacement field. The nonlinear partial differential equations considering the small size effect are established via the principle of virtual work. The nonlinearity is considered by using Von Karman's strain-displacement relations. While, the size effect is captured by employing the modified couple stress theory. The upper and lower layers are made of aluminum as a matrix that reinforced with graphene platelets (GPLs). The GPLs are functionally graded through the thickness of the face layers according to a new cosine rule. Moreover, the metal foam core is also made of aluminum containing porosities that uniformly distributed or functionally graded through the core thickness. The governing equations are solved based on the Galerkin and Newton's methods. The obtained results are examined by introducing some comparison examples. In addition, several parametric examples are discussed including the effects of the porosity type, GPLs distribution type, core-to-face thickness, elastic foundation stiffness, side-to-thickness ratio, plate aspect ratio and material length scale parameter on the nonlinear deflection and stresses of FGMG sandwich plate with metal foam core. [ABSTRACT FROM AUTHOR]

This work reports the investigations of the electric potential impacts on the mechanical buckling of the piezoelectric nanocomposite doubly curved shallow shells reinforced by functionally gradient graphene platelets (FGGPLs). A four-variable shear deformation shell theory is utilized to describe the components of displacement. The present nanocomposite shells are presumed to be rested on an elastic foundation and subject to electric potential and in-plane compressive loads. These shells are composed of several bonded layers. Each layer is composed of piezoelectric materials strengthened by uniformly distributed GPLs. The Halpin–Tsai model is employed to calculate the Young's modulus of each layer, whereas Poisson's ratio, mass density, and piezoelectric coefficients are evaluated based on the mixture rule. The graphene components are graded from one layer to another according to four different piecewise laws. The stability differential equations are deduced based on the principle of virtual work. To test the validity of this work, the current mechanical buckling load is analogized with that available in the literature. Several parametric investigations have been performed to demonstrate the effects of the shell geometry elastic foundation stiffness, GPL volume fraction, and external electric voltage on the mechanical buckling load of the GPLs/piezoelectric nanocomposite doubly curved shallow shells. It is found that the buckling load of GPLs/piezoelectric nanocomposite doubly curved shallow shells without elastic foundations is reduced by increasing the external electric voltage. Moreover, by increasing the elastic foundation stiffness, the shell strength is enhanced, leading to an increase in the critical buckling load. [ABSTRACT FROM AUTHOR]

This paper aims to study the hygrothermal buckling of smart graphene/piezoelectric circular nanoplates lying on an elastic medium and subjected to an external electric field. The circular nanoplates are made of piezoelectric polymer reinforced with graphene platelets that are uniformly distributed through the thickness of the nanoplate. The material properties of the nanocomposite plate are determined based on the modified Halpin-Tsai model. To capture the nanoscale effects, the nonlocal strain gradient theory is applied. Moreover, the principle of virtual work is employed to establish the nonlinear stability equations in the framework of classical theory. The differential quadrature method is utilized to solve the governing equations. Among the important aims of the paper is to study the influences of various parameters such as graphene weight fraction, elastic foundation parameters, external applied electric field, humid conditions, and boundary conditions on the thermal buckling of the smart nanocomposite circular nanoplates. It is found that the increase in graphene components and elastic foundation stiffness enhances the strength of the plates; therefore, the buckling temperature will increase. [ABSTRACT FROM AUTHOR]

Based on the differential quadrature method (DQM), the bending of sandwich-curved beams with graphene platelets/aluminum (GPLs/Al) nanocomposite face sheets and aluminum honeycomb core is investigated using a new shear and normal deformations curved beam theory. The present new model is resting on elastic foundation and subjected to a circumferential magnetic field, thermal load, and humid conditions. The face sheets are made of several bonded composite layers with randomly oriented and uniformly distributed graphene platelets in each layer. The mechanical and hygrothermal properties of the faces are assumed to be functionally graded (FG) using a piece-wise law by varying the weight fraction of the GPLs in the face thickness direction. Four governing differential equations are derived based on a novel four-variable curved beam theory taking into account the thickness stretching effect. The governing equations are solved for various boundary conditions on the basis of the DQM. The displacements presented by the DQM are compared with those obtained by Navier solution. Impacts of various parameters such as geometric shape parameters, magnetic parameter, temperature, moisture, elastic foundation parameters, core thickness, boundary conditions, and graphene weight fraction on the displacements and stresses of the functionally graded graphene/aluminum sandwich-curved beams are illustrated. [ABSTRACT FROM AUTHOR]

In this paper, the effects of hygrothermal conditions on various behaviors, such as bending, free vibration, mechanical and thermal buckling, of exponentially graded microplates lying on two-parameter elastic foundations are investigated. The trigonometric four-variable plate theory incorporated to the modified couple stress theory (MCST) is employed to derive the equations of motion. The present MCST contains an internal material length scale parameter, thus it can capture the size effect. The microplate is assumed to be subjected to a temperature rise and moisture concentration which are varied linearly through the thickness of the plate. Based on an exponential law, the material properties of the microplate are graded only in z direction. The equations of motion are solved analytically to obtain the displacements, stresses, eigenfrequencies and critical buckling load and temperature of the microplates. The present results are validated by comparing them with those previously published. The numerical examples reveal that considering the size effect and/or the elastic foundations leads to an increment in plate stiffness and thereby leads to a decrement in the deflection and an increment in eigenfrequency and buckling loads. It is also shown that the size effect is negligible for the thicker plate. [ABSTRACT FROM AUTHOR]

The modified couple stress theory (MCST) is utilized to investigate the bending of viscoelastic nanobeams laying on visco-Pasternak elastic foundations based on a new shear and normal deformations beam theory. This model consists of the material length scale coefficient that captures the size impact on small-scale beams. The simply supported beam is made of viscoelastic material, subjected to time harmonic transverse load. The nanobeam is presumed to be laying on double layers of foundations. The first layer is modeled as Kelvin–Voigt viscoelastic model and the second is taken as a shear layer. Based on the proposed beam theory and MCST, the differential motion equations are deduced using Hamilton's principle. To check the validity of the obtained formulations, the predicted results are compared with those available in the open literature. In addition, the influences of various parameters such as the material length scale parameter, length-to-depth ratio, viscoelastic damping structure, the stiffness and damping coefficients of the viscoelastic substrate, and shear and normal strains on the deflection and stresses are illustrated. [ABSTRACT FROM AUTHOR]

The present work is concerned with the bending analysis of viscoelastic sandwich microplates with carbon nanotubes (CNTs)-reinforced face sheets under the effects of a 2D magnetic field as well as hygrothermal conditions. The core layer is assumed to be a fully homogeneous viscoelastic material, whereas the face sheets are made of a polymer matrix stiffened by uniformly distributed or functionally graded (FG) CNTs. The applied magnetic field results in a body force (Lorentz force) that is applied to each particle of the plate. In order to take into account the size effect, the modified couple stress theory is employed containing only one length scale parameter. The viscoelastic sandwich microplate is assumed to be resting on two layers of the foundations. The first is modeled as the viscoelastic Kelvin–Voigt model. However, the second represents the elastic Pasternak shear layer. Based on the sinusoidal four-variable plate theory, four governing equations are obtained involving Lorentz force and foundation interaction. An analytical solution for the obtained equations is presented to get the displacements and stresses of the reinforced sandwich plates. The present solution is examined by introducing comparison examples. Influences of the geometric parameters, material length scale parameter, magnetic field parameter, damping parameters, temperature rise, moisture concentration, and foundation coefficients on the bending of the FG-CNTs-reinforced viscoelastic sandwich microplates are discussed. [ABSTRACT FROM AUTHOR]

AbstractThe purpose of this study is to analyze the influence of geometric parameters and material properties on the free and forced vibration of bi-directional functionally graded sandwich (2D-FGSW) plates lying on an elastic foundation (EF) using an effective finite element method (FEM) based on the trigonometric shear deformation theory (TrSDT). The mechanical properties of 2D-FGSW are variable in both the x- and z-directions. The EF includes the springer stiffness k1 and the shear layer stiffness k2. Moreover, the impacts of structural damping and periodic loading on the behavior of 2D-FGSW plates are considered. Element matrices are created using a four-node quadrilateral plate element (Q4) with eight degrees of freedom per node. The effectiveness and accuracy of the current formulation are confirmed by contrasting the acquired results with those of earlier works. Then, many studies are carried out to illustrate how input parameters might affect the vibration characteristics of 2D-FGSW plates lying on EF. In addition, the eigenfrequencies of different types of 2D-FGSW plates with a center hole are investigated. [ABSTRACT FROM AUTHOR]

This study is devoted to illustrate the mechanical buckling and free vibration analyses of double-porous functionally graded (FG) nanoplates embedded in an elastic foundation. A new quasi-3D refined plate theory is presented to model the displacement field. This theory contains only five unknown functions and considers the shear strain as well as thickness stretching. Based on the modified Mooney-type exponential relation, a new exponential law is presented to govern the materials variation and porosities distribution through the thickness of the nanoplates. The two porous nanoplates are bonded together by a set of parallel elastic springs and surrounded by Pasternak medium. The nonlocal strain gradient theory containing the nonlocal parameter and gradient coefficient is utilized to study the size-dependent effects. Based on Hamilton's principle, the equations of motion are drawn including the material parameters, elastic foundation reaction and biaxial compressive forces. An analytical approach for simply-supported and clamped bilayer porous FG nanoplates is implemented. The obtained results are compared with those available in the literature. Additional numerical calculations are introduced to show the influences of the material length scale parameters, inhomogeneity parameter, porosity factor and other parameters on the critical buckling and frequencies of the double-porous FG nanoplates. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, the sinusoidal shear deformation plate theory (SDPT) is reformulated using the nonlocal differential constitutive relations of Eringen to analyze the bending and vibration of the nanoplates, such as single-layered graphene sheets, resting on two-parameter elastic foundations. The present SDPT is compared with other plate theories. The nanoplates are assumed to be subjected to mechanical and thermal loads. The equations of motion of the nonlocal model are derived including the plate foundation interaction and thermal effects. The governing equations are solved analytically for various boundary conditions. Nonlocal theory is employed to bring out the effect of the nonlocal parameter on the bending and natural frequencies of the nanoplates. The influences of nonlocal parameter, side-to-thickness ratio and elastic foundation moduli on the displacements and vibration frequencies are investigated. [Copyright &y& Elsevier]

Abstract: In this paper, the analyses of dynamic deflection and stresses in functionally graded (FG) plates resting on two-parameter elastic foundations, according to Pasternakʼs model, are investigated. The present FG plate is subjected to time harmonic thermal load. Material properties of the plate are assumed to be graded in the thickness direction, from the upper surface which is ceramic-rich to the lower one which is metal-rich, according to a simple exponential law distribution in terms of the volume fractions of the constituents. The governing equations of the dynamic response of a non-homogeneous composite plate are deduced by using various shear deformation theories as well as the classical one. The influences of the time parameter, power-law index, side-to-thickness ratio and the foundation parameters on the dynamic bending are illustrated. [Copyright &y& Elsevier]

Abstract: This paper deals with the vibration and buckling behavior of exponentially graded material (EGM) sandwich plate resting on elastic foundations under various boundary conditions. New functions for midplane displacements are suggested to satisfy the different boundary conditions. The elastic foundation is modeled as Pasternak’s type which can be either isotropic or orthotropic and as a special case it converges to Winkler’s foundation if the shear layer is neglected. The present EGM sandwich plate is assumed to be made of a fully ceramic core layer sandwiched by metal/ceramic EGM coat. The governing equations of the dynamic response of non-homogeneous composite plates are deduced by using various shear deformation plate theories. Numerical results for the natural frequencies and critical buckling loads of several types of symmetric EGM sandwich plates are presented. The validity of the present solution is demonstrated by comparison with solutions available in the literature. The influences of the inhomogeneity parameter, aspect ratio, thickness ratio and the foundation parameters on the natural frequencies and critical buckling loads are investigated. [Copyright &y& Elsevier]

Transient size-dependent mechanical and thermal buckling analyses of sandwich microplates with viscoelastic core and single-walled carbon nanotubes (CNTs)-reinforced face sheets are introduced in this paper. The CNTs are uniformly distributed or functionally graded (FG) through the thickness of the face layers. The viscoelastic sandwich microplate is resting on three-parameter viscoelastic foundations that modeled according to the viscoelastic Kelvin-Voigt model with a shear layer. Effects of a 2D magnetic field as well as hygrothermal conditions on the present analyses are studied. The modified couple stress model containing one material length scale parameter is employed to capture the small scale effect. A body force (Lorentz force) is deduced from Maxwell's magnetic equations, that is applied to each particle of the structure. The higher-order shear deformation plate theory with four unknowns is utilized to describe the displacement field. The stability equations are obtained using the principle of virtual displacement. By applying Navier method, the stability equations are solved to obtain the mechanical and thermal buckling of viscoelastic sandwich microplates. Various numerical examples are presented including the effects of the length scale parameter, moisture concentration, magnetic field parameter and other parameters on the buckling of the viscoelastic FGCNTs-reinforced sandwich microplates. [ABSTRACT FROM AUTHOR]