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Showing papers on "Plate theory published in 2018"


Journal ArticleDOI
TL;DR: In this paper, the buckling and free vibration behaviors of functionally graded (FG) porous nanocomposite plates reinforced with graphene platelets (GPLs) were investigated. And a comprehensive parametric investigation on the influences of the weight fraction and geometric parameters of GPL nanofiller and the porosity coefficient was conducted to identify the most effective way to achieve improved buckling.

299 citations


Journal ArticleDOI
Qingya Li1, Di Wu1, Xiaojun Chen1, Lei Liu1, Yuguo Yu1, Wei Gao1 
TL;DR: In this paper, the nonlinear vibration and the dynamic buckling of a graphene platelet reinforced sandwich functionally graded porous (GPL-SFGP) plate are thoroughly investigated and the effects of the Winkler-Pasternak elastic foundation, thermal environment and damping are incorporated.

212 citations


Journal ArticleDOI
TL;DR: In this article, the free vibration of functionally graded (FG) porous nanocomposite plates reinforced with a small amount of graphene platelets (GPLs) and supported by the two-parameter elastic foundations with different boundary conditions was investigated.

178 citations


Journal ArticleDOI
TL;DR: In this article, a general approach for the vibration analysis of a rotating cylindrical shell coupled with an annular plate is proposed, where the Sanders shell theory and Mindlin plate theory are employed to calculate the strain energy of the shell and plate, respectively.

164 citations


Journal ArticleDOI
TL;DR: In this paper, the size dependency in nonlinear large-amplitude vibrational response of functionally graded porous micro/nano-plates reinforced with graphene platelets (GPLs) was explored.

151 citations


Journal ArticleDOI
TL;DR: In this article, an analytical approach to investigate buckling and post-buckling behavior of FGM plate with porosities resting on elastic foundations and subjected to mechanical, thermal and thermomechanical loads is presented.

141 citations


Journal ArticleDOI
TL;DR: The free vibration analysis of a circular plate made up of a porous material integrated by piezoelectric actuator patches has been studied in this article, where the plate is assumed to be thin and its shear deformations have been neglected.
Abstract: The free vibration analysis of a circular plate made up of a porous material integrated by piezoelectric actuator patches has been studied. The plate is assumed to be thin and its shear deformations have been neglected. The porous material properties vary through the plate thickness according to some given functions. Using Hamilton's variational principle and the classical plate theory (CPT) the governing motion equations have been obtained. Simple and clamped supports have been considered for the boundary conditions. The differential quadrature method (DQM) has been used for the discretizations required for numerical analysis. The effect of some parameters such as thickness ratio, porosity, piezoelectric actuators, variation of piezoelectric actuators-to-porous plate thickness ratio, pores distribution and pores compressibility on the natural frequency, radial and circumferential stresses has been illustrated. The results have been compared with the similar ones in the literature.

139 citations


Journal ArticleDOI
TL;DR: In this paper, the static linear elasticity, natural frequency, and buckling behavior of functionally graded porous plates reinforced by graphene platelets (GPLs) were investigated within the Isogeometric Analysis framework.

131 citations


Journal ArticleDOI
TL;DR: In this article, the linear and nonlinear vibration behaviors of the smart piezoelectric composite plate reinforced by uniformly and non-uniformly dispersing graphene platelets (GPLs) were investigated.

121 citations


Journal ArticleDOI
TL;DR: In this paper, the pull-in characteristics of a microplate-based microelectromechanical system (MEMS) are investigated via a multi-degree freedom energy-based technique where the in-plane and out-of-plane motions are retained in the modelling and simulations.

120 citations


Journal ArticleDOI
Marco Amabili1
TL;DR: In this paper, a nonlinear damanaping of rectangular plates is derived assuming the material to be viscoelastic, and the constitutive relationship to be governed by the standard linear solid model.
Abstract: Even if still little known, the most significant nonlinear effect during nonlinear vibrations of continuous systems is the increase of damping with the vibration amplitude. The literature on nonlinear vibrations of beams, shells and plates is huge, but almost entirely dedicated to model the nonlinear stiffness and completely neglecting any damping nonlinearity. Experiments presented in this study show a damping increase of six times with the vibration amplitude. Based on this evidence, the nonlinear damanaping of rectangular plates is derived assuming the material to be viscoelastic, and the constitutive relationship to be governed by the standard linear solid model. The material model is then introduced into a geometrically nonlinear plate theory, carefully considering that the retardation time is a function of the vibration mode shape, exactly as its natural frequency. Then, the equations of motion describing the nonlinear vibrations of rectangular plates are derived by Lagrange equations. Numerical results, obtained by continuation and collocation method, are very successfully compared to experimental results on nonlinear vibrations of a rectangular stainless steel plate, validating the proposed approach. Geometric imperfections, in-plane inertia and multi-harmonic vibration response are included in the plate model.

Journal ArticleDOI
TL;DR: In this paper, a thermal postbuckling analysis for composite laminated plates reinforced with graphene sheets is performed, where all of the thermomechanical properties of the composite media are assumed to be temperature dependent.
Abstract: A thermal postbuckling analysis for composite laminated plates reinforced with graphene sheets is performed in this research. All of the thermomechanical properties of the composite media are assumed to be temperature dependent. Volume fraction of the graphene in each layer is assumed to be different which results in a piecewise functionally graded plate. Based on the third order shear deformation plate theory of Reddy, the total strain energy of the plate is obtained. Composite laminated plate is assumed to be under uniform temperature rise. Properties of the graphene reinforced composite media are estimated by means of a refined Haptin-Tsai approach which contains efficiency parameters to capture the size dependency of the constituents. Afterwards, a non-uniform rational B-spline (NURBS) based isogeometric finite element method is implemented to study the thermal postbuckling response of the graphene reinforced composite laminated plates. Thermally induced postbuckling curves of the composite plate reinforced by graphene are provided for different functionally graded patterns, aspect ratios, side to thickness ratios and boundary conditions. It is shown that, FG-X pattern of graphene reinforcement results in the highest critical buckling temperature and the lowest postbuckling deflection.

Journal ArticleDOI
TL;DR: In this paper, a non-uniform rational B-spline (NURBS) based finite element method is used to study the large amplitude free vibration response of the graphene reinforced composite plates in thermal environment.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a new shear deformation theory including the stretching effect for free vibration of the simply supported functionally graded plates, which accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded plate without using shear correction factors.

Journal ArticleDOI
TL;DR: In this article, the electro-thermo-mechanical vibrational behavior of functionally graded piezoelectric (FGP) plates with porosities is explored via a refined four-variable plate theory for the first time.
Abstract: In this article, electro-thermo-mechanical vibrational behavior of functionally graded piezoelectric (FGP) plates with porosities is explored via a refined four-variable plate theory for the first time. Uniform, linear and nonlinear temperature changes are considered in this study. Electro-elastic material properties of porous FGP plate vary across the thickness based on modified power-law model. The governing equations derived from Hamilton’s principle are solved analytically. The exactness of solution is confirmed by comparing obtained results with those provided in the literature. Influences of applied voltage, porosity distribution, thermal loadings, material gradation, plate geometrical parameters and boundary conditions on the vibrational behavior of FGP plates are discussed. These results can be applied for accurate design of smart structures made of functionally graded piezoelectric materials by considering porosity distribution.

Journal ArticleDOI
TL;DR: In this paper, a nonlinear, eccentric, low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate on elastic foundations in hygrothermal conditions using the finite element method is performed.
Abstract: In the present article, a nonlinear, eccentric, low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate on elastic foundations in hygrothermal conditions using the finite element method is performed. In this regard, the governing equations are derived based on higher-order shear deformation plate theory and von Karman geometrical nonlinearity. Three types of distributions of the temperature field and moisture concentrations, namely, uniformly, linearly, or nonlinearly through the thickness direction of the plates are considered. The effective material properties of the multiphase nanocomposite are calculated using fiber micromechanics and Halpin–Tsai equations in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the matrix. The contact force between the impactor and the plate is obtained with the aid of the modified nonlinear Hertzian contact law models. After examining the validity of the present work, the ...

Journal ArticleDOI
TL;DR: In this paper, four types of distributions of uni-axially aligned single-walled carbon nanotubes are considered to reinforce the plates, and analytical solutions determined from mathematical formulation based on hyperbolic shear deformation plate theory are presented.
Abstract: This work examines vibration and bending response of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation. Four types of distributions of uni-axially aligned single-walled carbon nanotubes are considered to reinforce the plates. Analytical solutions determined from mathematical formulation based on hyperbolic shear deformation plate theory are presented in this study. An accuracy of the proposed theory is validated numerically by comparing the obtained results with some available ones in the literature. Various considerable parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are considered in the present investigation. According to the numerical examples, it is revealed that the vertical displacement of the plates is found to diminish as the increase of foundation parameters; while, the natural frequency increase as the increment of the parameters for every type of plate.

Journal ArticleDOI
TL;DR: In this article, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation.
Abstract: In this paper, an efficient higher-order shear deformation theoryis presented to analyze thermomechanical bending of temperature-dependentfunctionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinearthermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived fromthe principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier\'s method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependentFG plates.

Journal ArticleDOI
TL;DR: In this paper, the size-dependent shear buckling of nanoplates embedded in Winkler-Pasternak foundation and hygrothermal environment was studied and the equations of motion were derived based on the mentioned theories in conjunction with the nonlocal strain gradient theory employing Hamilton's principle.
Abstract: The present paper is focused on the size-dependent shear buckling of nanoplates embedded in Winkler-Pasternak foundation and hygrothermal environment. Hence, the refined higher-order plate theories (Polynomial, Exponential, and Hyperbolic) needless of any shear correction factor are used in the formulations. The equations of motion are derived based on the mentioned theories in conjunction with the nonlocal strain gradient theory employing Hamilton's principle. The four unknown functions denoting the buckling load of plates are defined in a modal manner, and Navier solution method is used to find the shear buckling response. Results for the shear buckling and thermal buckling analysis of nanoplates are approved by existing literature to demonstrate the accuracy of present formulation and solution method. From our knowledge, it is the first time that the hygrothermal environment and also the nonlocal strain gradient theory are applied to study on shear buckling of nanoplates. Hence, the influence of nanoplate geometry, various hygrothermal conditions, elastic medium, nonlocal parameter and gradient parameter on the shear buckling load are obtained and discussed using different plate theories. The numerical results indicate that the shear buckling of nanoplate in the absence of strain gradient parameter is significantly affected by the temperature and moisture variations.

Journal ArticleDOI
TL;DR: In this paper, a novel simple shear deformation theory for buckling analysis of single layer graphene sheet is formulated using the nonlocal differential constitutive relations of Eringen.
Abstract: In this paper, a novel simple shear deformation theory for buckling analysis of single layer graphene sheet is formulated using the nonlocal differential constitutive relations of Eringen. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the rectangular nano-plate. The equations of motion of the nonlocal theories are derived and solved via Navier\'s procedure for all edges simply supported boundary conditions. The results are verified with the known results in the literature. The influences played by Effects of nonlocal parameter, length, thickness of the graphene sheets and shear deformation effect on the critical buckling load are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

Journal ArticleDOI
TL;DR: In this article, a new first-order shear deformation theory (OVFSDT) on the basis of the inplane stability of the piezo-magnetoelectric composite nanoplate (PMEN) has been developed, and its precision has been evaluated.
Abstract: In the present investigation, a new first-order shear deformation theory (OVFSDT) on the basis of the in-plane stability of the piezo-magnetoelectric composite nanoplate (PMEN) has been developed, and its precision has been evaluated. The OVFSDT has many advantages compared to the conventional first-order shear deformation theory (FSDT) such as needless of shear correction factors, containing less number of unknowns than the existing FSDT and strong similarities with the classical plate theory (CPT). The composite nanoplate consisted of BaTiO3-CoFe2O4 , a kind of material by which coupling between piezoelectric and piezomagnetic in nanosize was established. The plate is surrounded by a motionless and stationary matrix that is embedded in a hygrothermal surround in order to keep it more stable, and to take into consideration the influences of the moisture and temperature on the plate's mechanical behavior. The governing equilibrium equations for the smart composite plate have been formulated using the higher-order nonlocal strain gradient theory within which both stress nonlocality and second strain gradient size-dependent terms are taken into account by using three independent length scale parameters. The extracted equations are solved by utilizing the analytical approaches by which numerical results are obtained with various boundary conditions. In order to evaluate the proposed theory and methods of solution, the outcomes in terms of critical buckling loads are compared with those from several available well-known references. Finally, after determining the accuracy of the results of the new plate theory, several parameters are investigated to show the influences of material properties of the ceramic composite nanoplate on the critical buckling loads.

Journal ArticleDOI
TL;DR: In this article, the size-dependent vibration of nano-sized piezoelectric double-shell structures under simply supported boundary condition is presented, and the surface energy effect on the natural frequencies is discussed.
Abstract: Combining Goldenveizer-Novozhilov shell theory, thin plate theory and electro-elastic surface theory, the size-dependent vibration of nano-sized piezoelectric double-shell structures under simply supported boundary condition is presented, and the surface energy effect on the natural frequencies is discussed. The displacement components of the cylindrical nano-shells and annular nano-plates are expanded as the superposition of standard Fourier series based on Hamilton's principle. The total stresses with consideration of surface energy effect are derived, and the total energy function is obtained by using Rayleigh-Ritz energy method. The free vibration equation is solved, and the natural frequency is analyzed. In numerical examples, it is found that the surface elastic constant, piezoelectric constant and surface residual stress show different effects on the natural frequencies. The effect of surface piezoelectric constant is the maximum. The effect of dimensions of the double-shell under different surface material properties is also examined.

Journal ArticleDOI
TL;DR: In this article, the wave propagation in functionally graded (FG) nanoplates using a nonlocal strain gradient theory and four-variable refined plate theory considering the magnetic field was investigated.
Abstract: In this work, analytical solutions are presented for the wave propagation in functionally graded (FG) nanoplates using a nonlocal strain gradient theory and four-variable refined plate theory considering the magnetic field. The size effects are included using nonlocal strain gradient theory that has two length scale parameters, and the nanoplate is modeled as a plate using four-variable refined plate theory. From the knowledge of authors, it is the first time that the influences of magnetic field on the wave propagation in FG nanoplates are investigated based on present methodology.

Journal ArticleDOI
TL;DR: In this article, the buckling and postbuckling behavior of a sandwich plate with a homogeneous core and graphene-reinforced composite (GRC) face sheets resting on an elastic foundation in thermal environments were investigated.
Abstract: Present investigation deals with the buckling and postbuckling behavior of a sandwich plate with a homogeneous core and graphene-reinforced composite (GRC) face sheets resting on an elastic foundation in thermal environments. The material properties of GRC face sheets are assumed to be piece-wise functionally graded by changing the volume fraction of graphene in the thickness direction. The material properties of both the homogeneous core layer and the GRC face sheets are assumed to be temperature-dependent, and are estimated by the extended Halpin-Tsai micromechanical model. The higher order shear deformation plate theory and the von Karman-type kinematic nonlinearity are used to derive the governing equations which account for the plate-foundation interaction and the thermal effects. The buckling loads and the postbuckling equilibrium paths are obtained by using a two-step perturbation technique. The impacts of the distribution type of reinforcements, core-to-face sheet thickness ratio, plate aspect ratio, temperature variation, foundation stiffness and in-plane boundary conditions on the postbuckling behavior of sandwich plates with functionally graded GRC face sheets are studied in detail.

Journal ArticleDOI
TL;DR: In this paper, the free vibration behaviors of functionally graded (FG) plates considering in-plane material inhomogeneity were investigated using Isogeometric analysis (IGA) in conjunction with a refined plate theory.

Journal ArticleDOI
TL;DR: In this article, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment.
Abstract: In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton\'s principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.

Journal ArticleDOI
TL;DR: In this paper, the buckling behavior of composite skew plates reinforced with aligned single walled carbon nanotubes (CNTs) is investigated and two different types of shear loads are considered.

Journal ArticleDOI
TL;DR: In this article, the buckling of embedded orthotropic nanoplates such as graphene is investigated by employing a new refined plate theory and nonlocal small-scale effects, where the elastic foundation is modeled as two-parameter Pasternak foundation.
Abstract: This work presents the buckling investigation of embedded orthotropic nanoplates such as graphene by employing a new refined plate theory and nonlocal small-scale effects. The elastic foundation is modeled as two-parameter Pasternak foundation. The proposed two-variable refined plate theory takes account of transverse shear influences and parabolic variation of the transverse shear strains within the thickness of the plate by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. Nonlocal governing equations for the single layered graphene sheet are obtained from the principle of virtual displacements. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.

Journal ArticleDOI
TL;DR: In this article, a comprehensive numerical study is presented on the large-amplitude free vibration of sandwich annular plates integrated with functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets resting on elastic foundation.

Journal ArticleDOI
TL;DR: In this paper, the Ritz approximation is applied to models based both on the classical lamination theory and a more advanced variable-kinematic formulation, capable of dealing with several higher order plate theories within an unified framework.