Showing papers on "Plate theory published in 2020"
TL;DR: In this article, the free vibration and buckling responses of functionally graded nanoplates with magneto-electro-elastic coupling are studied for the first time using a nonlocal modified sinusoidal shear deformation plate theory including the thickness stretching effect.
Abstract: In this study, the free vibration and buckling responses of functionally graded nanoplates with magneto-electro-elastic coupling are studied for the first time using a nonlocal modified sinusoidal shear deformation plate theory including the thickness stretching effect. The constitutive relations for these kind of structures are defined. The equations of motion for rectangular sandwich plates in macro and nano scale are derived using a modified dynamic version of Hamilton's principle including a contribution of the electric and magnetic fields. The closed-form analytical solution to simply supported plates is obtained using Navier solution technique. A power-law distribution and a half cosine variation are used to model the variation of materials properties and electric/magnetic potentials, respectively. The analytical solutions are verified with well-known solutions in the literature. A parametric study was conducted to show the effect of nonlocal parameter, power-law index, predefined electric and magnetic fields, axial compressive and tensile forces, the aspect ratio of plates, and volume ratio of functionally graded and piezomagnetic layers on mechanical behaviors of nanoplates. Obtained numerical results can be used as benchmark values for validation of correctness of diverse analytical and numerical methods applied for design and analysis of composite nanoelectromechanical systems.
140 citations
TL;DR: In this article, a quasi-3D hyperbolic shear deformation theory is proposed to analyze the statics and free vibration of functionally graded porous plates resting on elastic foundations, and the equations of motion are derived from the Hamilton principle.
Abstract: This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to
discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal
deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and
efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.
134 citations
TL;DR: In this paper, a fundamental study on the buckling temperature and postbuckling analysis of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) disk covered with a piezoelectric actuator and surrounded by the nonlinear elastic foundation is presented.
Abstract: This is a fundamental study on the buckling temperature and post-buckling analysis of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) disk covered with a piezoelectric actuator and surrounded by the nonlinear elastic foundation. The matrix material is reinforced with graphene nanoplatelets (GPLs) at the nanoscale. The displacement–strain of thermal post-buckling of the FG-GPLRC disk via third-order shear deformation theory and using Von Karman nonlinear plate theory is obtained. The equations of the model are derived from Hamilton’s principle and solved by the generalized differential quadrature method. The direct iterative approach is presented for solving the set of equations that includes highly nonlinear parameters. Finally, the results show that the radius ratio of outer to the inner (Ro/Ri), the geometrical parameter of GPLs, nonlinear elastic foundation, externally applied voltage, and piezoelectric thickness play an essential impact on the thermal post-buckling response of the piezoelectrically FG-GPLRC disk surrounded by the nonlinear elastic foundation. Another important consequence is that, when the effect of the elastic foundation is considered, there is a sinusoidal effect from the Ro/Ri parameter on the thermal post-buckling of the disk and this matter is true for both boundary conditions.
129 citations
TL;DR: In this article, the wave propagation in functionally graded metal foam plates reinforced with graphene platelets (GPLs) is studied, where various types of porosity and GPL distribution are taken in account.
113 citations
106 citations
TL;DR: In this paper, a dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory is presented, in which the unknowns number is reduced.
Abstract: The current work, present dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory. The present analytical model is simplified which the unknowns number are reduced. The zero-shear stresses at the free surfaces of the FG-sandwich plate are ensured without introducing any correction factors. The four equations of motion are determined via Hamilton\' principle and solved by Galerkin\'s approach for FG-sandwich plate with three kinds of the support. The proposed analytical model is verified by comparing the results with those obtained by other theories existing in the literature. The parametric studies are presented to detect the various parameters influencing the fundamental frequencies of the symmetric and non-symmetric FG-sandwich plate with various boundary conditions.
104 citations
TL;DR: The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor.
Abstract: This work presents an efficient and original high-order shear and normal deformation theory for the static and free vibration analysis of functionally graded plates. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
100 citations
TL;DR: In this paper, size-dependent deflection analysis of FG graphene nanoplatelets (GNPs) reinforced composite micro-plates with porosity subjected to transverse load is studied. But the analysis is limited to the case of GNPs.
96 citations
TL;DR: In this paper, a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions.
Abstract: In this study a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions. The key feature of this theoretical formulation is that, in addition to considering shear deformation effect, it has only three unknowns in the displacement field as in the case of the classical plate theory (CPT), contrary to five as in the first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Material characteristics of the sandwich plate faces are considered to vary within the thickness direction via an exponential law distribution as a function of the volume fractions of the constituents. Equations of motion are obtained by employing Hamilton\'s principle. Numerical results for buckling and free vibration analysis of exponentially graded sandwich plates under various boundary conditions are obtained and discussed. Verification studies confirmed that the present three -unknown shear deformation theory is comparable with higher-order shear deformation theories which contain a greater number of unknowns.
88 citations
TL;DR: In this article, the influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original high order shear theory.
Abstract: The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich
plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton\'s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT).
Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin\'s approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
87 citations
TL;DR: In this article, an analysis on thermal buckling of composite laminated annular sector plates reinforced with the graphene platelets is examined in the presence of randomly oriented and uniformly distributed fillers in each ply of the composite media.
Abstract: An analysis on thermal buckling of composite laminated annular sector plates reinforced with the graphene platelets is examined in this research. It is assumed that the graphene platelets fillers are randomly oriented and uniformly distributed in each ply of the composite media. Effective elasticity modulus of the nanocomposite media is extracted utilizing the modified Halpin-Tsai procedure which takes into account the size effects of the graphene fillers. Using the von Karman type of geometrical nonlinearity and first order shear deformation plate theory, the governing equilibrium equations for the buckling of nanocomposite plates in sector shape under uniform temperature rise are established. Stability equations are obtained using the adjacent equilibrium criterion and solved by means of the generalized differential quadrature method. Numerical examples are given to study the effects of boundary conditions, weight fraction of the graphene platelets, and distribution pattern of the graphene platelets on critical temperature and the fundamental buckled shapes. Results represent that, with introduction of a small amount of graphene platelets into the isotropic matrix of the composite media, the critical buckling temperature of the plate may be enhanced.
TL;DR: In this article, the flexural analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal loading using a refined plate theory with four variables is presented. But the boundary conditions on the top and bottom surfaces of the plate are satisfied; hence the use of the transverse shear correction factors is avoided.
Abstract: This article deals with the flexural analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal loading using a refined plate theory with four variables. In this theory, the undetermined integral terms are used and the number of variables is reduced to four, instead of five or more in other higher-order theories. The boundary conditions on the top and the bottom surfaces of the plate are satisfied; hence the use of the transverse shear correction factors is avoided. The principle of virtual work is used to obtain governing equations and boundary conditions. Navier solution for simply supported plates is used to derive analytical solutions. For the validation of the present theory, numerical results for displacements and stresses are compared with those of classical, first-order, higher-order and trigonometric shear theories reported in the literature.
TL;DR: In this article, the static and free vibration responses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using an efficient polygonal finite element method (PFEM).
Abstract: In this study, we numerically investigate static and free vibration responses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using an efficient polygonal finite element method (PFEM). While the bending strain field is approximated through quadratic serendipity shape functions, the shear strain field is calculated by employing Wachspress basis functions. In order to eliminate the shear locking phenomenon, Timoshenko's beam theory is utilized to determine assumed strain fields on each side of polygonal domain. The present formulation possesses various outstanding features: (a) is valid for triangular, quadrilateral and polygonal elements; (b) can conveniently implement various different plate theories via choosing appropriate transverse shear function; (c) eliminates the shear locking phenomenon; (d) does not increase degrees of freedom (DOFs) per polygonal element despite employing the quadratic serendipity shape functions and (e) obtains more accurate and stable results than those of other PFEMs. Various dispersions of internal pores as well as GPLs into metal matrix through the thickness of plate are examined. The effective material properties varying across the plate's thickness can be estimated by Halpin-Tsai model for Young's modulus and the rule of a mixture for Poisson's ratio and mass density. The effect of several important parameters such as porosity coefficient, weight fraction and dimensions of GPLs, distribution of porosity and GPLs into metal matrix are thoroughly investigated via various numerical examples.
TL;DR: In this paper, an exact analytical solution based on first order shear deformation plate theory was used for the solution of stability and vibration problems, and the virtual displacement principle was utilized to derive governing differential equations.
TL;DR: In this article, the Gurtin-Murdoch surface theory of elasticity is applied to the higher-order shear deformation plate theory within the framework of the oblique coordinate system.
Abstract: The prime objective of the present investigation is to predict the shear buckling characteristics of skew nanoplates made of a functionally graded material (FGM) in the presence of surface stress effect. For this purpose, the Gurtin-Murdoch surface theory of elasticity is applied to the higher-order shear deformation plate theory within the framework of the oblique coordinate system. Different types of the homogenization scheme including Reuss model, Voigt model, Mori-Tanaka model, and Hashin-Shtrikman bounds model are taken into consideration in order to extract the effective mechanical properties of FGM skew nanoplates. The Ritz method using Gram-Schmidt shape functions is utilized to obtain the surface elastic-based shear buckling loads of FGM skew nanoplates. It is indicated that by increasing the value of the index associated with the material property gradient, the significance of the surface stress type of size effect on the shear buckling behavior of a FGM skew nanoplate improves. Moreover, by changing the boundary conditions from simply supported ones to clamped ones, the influence of the skew angle on the surface elastic-based shear buckling load of a FGM skew nanoplate increases. Also, it is illustrated that by increasing the width to thickness ratio of a skew nanoplate, the free surface area increases which results in to enhance the effect of surface residual stress on its shear buckling characteristics.
TL;DR: In this paper, the authors present an analytical modeling framework and its analysis for thin piezoelectric metamaterial plates to enable and predict low-frequency bandgap formation in finite structural configurations with specified boundary conditions.
TL;DR: In this paper, the authors developed a pair of two-scale plate models relying on the anisotropic form of Mindlin's strain gradient thermoelasticity theory for three-dimensional cellular plate-like structures with a triangular microarchitecture.
Abstract: For three-dimensional cellular plate-like structures with a triangular (extruded lattice) microarchitecture, the article develops a pair of two-scale plate models relying on the anisotropic form of Mindlin’s strain gradient thermoelasticity theory. Accordingly, a computational homogenization method is proposed for determining the constitutive parameters of the related higher-order constitutive tensors. First, a Reissner–Mindlin plate model is derived by dimension reduction from a general framework of three-dimensional orthotropic strain gradient thermoelasticity and written as a variational formulation. An isogeometric conforming Galerkin method is formulated accordingly. Second, the plate model is modified in order to reduce the number of the constitutive strain gradient parameters. These steps are then repeated by following the kinematical assumptions of the Kirchhoff plate theory. Third, in order to see the cellular microarchitecture as a homogeneous three-dimensional material with classical modulae of transversal isotropy, classical computational homogenization is accomplished for determining the corresponding material parameters. Fourth, in order to see the cellular structures as two-dimensional plates, a non-classical homogenization procedure is proposed for the identification of the strain gradient modulae of the plate models. Finally, a set of numerical examples illustrates the reliability and efficiency of the resulting plate models in homogenizing cellular plate-like structures into strain gradient plate models capturing the bending size effects induced by the microarchitecture.
TL;DR: In this article, the size effects on the shear buckling behaviors of skew nanoplates made of functionally graded materials (FGMs) are presented, and various homogeniza-tion schemes including the Reuss model, the Voigt model, and the Mori-Tanaka model are used.
Abstract: The size effects on the shear buckling behaviors of skew nanoplates made of functionally graded materials (FGMs) are presented. The material properties are supposed to be changed uniformly from the ceramic phase to the metal one along the plate thickness. To estimate the associated effective material properties, various homogeniza-tion schemes including the Reuss model, the Voigt model, the Mori-Tanaka model, and the Hashin-Shtrikman bound model are used. The nonlocal elasticity theory together with the oblique coordinate system is applied to the higher-order shear deformation plate theory to develop a size-dependent plate model for the shear buckling analysis of FGM skew nanoplates. The Ritz method using Gram-Schmidt shape functions is used to solve the size-dependent problem. It is found that the significance of the nonlocality in the reduction of the shear buckling load of an FGM skew nanoplate increases for a higher value of the material property gradient index. Also, by increasing the skew angle, the critical shear buckling load of an FGM skew nanoplate enhances. This pattern becomes a bit less significant for a higher value of the material property gradient index. Furthermore, among various homogenization models, the Voigt and Reuss models in order estimate the overestimated and underestimated shear buckling loads, and the difference between them reduces by increasing the aspect ratio of the skew nanoplate.
TL;DR: In this paper, a three-variable high-order shear deformation plate theory (THSDT) was proposed for free vibration, buckling and instability analysis of functionally graded porous (FGP) plates reinforced by graphene platelets (GPLs).
TL;DR: In this article, a size-dependent meshfree model using the higher-order shear deformation plate theory in conjunction with the nonlocal Eringen elasticity theory for bending and free vibration analyses of functionally graded carbon nanotube-reinforced composite (FG CNTRC) nanoplates is presented.
Abstract: In this paper, a size-dependent meshfree model using the higher-order shear deformation plate theory in conjunction with the nonlocal Eringen elasticity theory for bending and free vibration analyses of functionally graded carbon nanotube-reinforced composite (FG CNTRC) nanoplates is presented. Configurations of carbon nanotubes (CNTs) are carried out for the uniform and functionally graded distributions via the plate thickness. Effective material properties are computed by the extended rule of mixture. The differential equation form of nonlocal elasticity theory is utilized to take account of size-dependent effects. Based on the principle of virtual work, discretized governing equations for nanoplates are obtained. Thereafter, the displacement and natural frequency of the FG CNTRC nanoplates are determined by a moving Kriging meshfree method. Essential boundary conditions are directly enforced at nodes the same with the finite element method because the moving Kriging shape function satisfies the Kronecker delta function property. Numerical results prove that the present model is simple, stable and well accurate prediction for nanostructures. Moreover, the stiffness-softening mechanisms are found when using the nonlocal elasticity theory leading to a rise of deflection and a decrease of natural frequency of FG CNTRC nanoplates.
TL;DR: In this article, the effect of primary and secondary resonances in nonlinear forced vibration of piezoelectric/functionally graded (FG) porous nanocomposite subjected to a moving load and external electric voltage was investigated.
Abstract: Since micro/nano-electromechanical devices made of nanocomposites are strongly influenced by external excitations, this paper intends to comprehensively investigate the effect of the primary and secondary resonances in performance of nano-electromechanical systems (NEMS). This model also helps to analyze nonlinear vibration behaviors of the recently built single-layered graphene sheet (SLGS) and multi-layered graphene sheet (MLGS) nanomechanical resonators. The aim of this work is to derive the effect of primary and secondary resonances in nonlinear forced vibration of piezoelectric/functionally graded (FG) porous nanocomposite subjected to a moving load and external electric voltage. At first, an FG porous core nanoplate glued with two piezoelectric layers is modeled. Then, the modeled nanocomposite is rested on a visco-Pasternak foundation. In the next step, Mindlin and Kirchhoff plate theories and Hamilton’s principle are separately employed to derive governing equation of motion. Galerkin technique and multiple time scales method are used, respectively, to solve the equation. Furthermore, primary and secondary resonances are analyzed and modulation equation of piezoelectric/FG porous nanocomposite for both of them is obtained. Finally, modulation equation under sub-harmonic and super-harmonic stimulations is studied and graphs are derived. Results show that there is a periodic relation between amplitude response and velocity of moving load. Also, even in the absence of electric voltage, the piezoelectric effect of the material can reduce the nonlinear vibration.
TL;DR: In this article, a small-scale nonlinear solution is established using the Von-Karman hypothesis and the modified couple stress theory (MCST) to obtain the deflection of the plate, the Reddy higher-order plate theory coupled with isogeometric analysis (IGA).
Abstract: The static bending behavior of porous functionally graded (PFG) micro-plate under the geometrically nonlinear analysis is studied in this article. A small-scale nonlinear solution is established using the Von-Karman hypothesis and the modified couple stress theory (MCST). To obtain the deflection of the plate, the Reddy higher-order plate theory coupled with isogeometric analysis (IGA) is utilized. The distribution of porosities is assumed to be even and uneven across the plate’s thickness and the effective material properties of porous functionally graded micro-plate are calculated using the refined rule-of-mixture hypothesis. The influence of power index, porosity parameter and material length scale parameter on the nonlinear behaviors of static bending of porous FGM micro-plates are also investigated using several numerical examples.
TL;DR: In this article, the authors employed the modified strain gradient theory (MSGT) in conjunction with the refined shear deformation plate theory to explore the buckling behavior of simply supported and clamped OSC.
TL;DR: In this article, thermal vibration analysis of a graphene oxide powder-reinforced (GOPR) embedded plate is carried out once the plate is exposed to different types of thermal loading.
Abstract: In this research, thermal vibration analysis of a graphene oxide powder-reinforced (GOPR) nanocomposite embedded plate is carried out once the plate is exposed to different types of thermal loading. The plate is reinforced with various functionally graded (FG) distributions through the thickness, namely uniform, X, V, and O in a comparative way to find out the most efficient model of GOPs’ distribution for the purpose of improving vibrational behaviors of the structure. Also, the Halpin–Tsai micromechanical model is employed to describe the material properties of an FG nanocomposite plate. The shear deformation effects are taken into account using a refined higher order shear deformation plate theory. Moreover, the governing equations of the structure have been derived using Hamilton’s principle and then solved analytically for a simply supported GOPR nanocomposite plate. Besides, detailed parametric studies are procured to show the influences of different variants on the natural frequency of the nanocomposite plates. Presented results reveal that the frequency responses of the nanocomposite plates in a thermal environment dramatically depend on the distribution pattern of the GOPs.
TL;DR: In this paper, the saturation and the jumping phenomena between the torsional vibration mode and the bending vibration mode are investigated for a rotating cantilever plate under the subsonic air flow force.
TL;DR: In this article, the vibration of a porous rectangular plate which is located between two piezo-electromagnetic layers based on two variables sinusoidal shear deformation plate theory and accord...
Abstract: In the present research vibration of a porous rectangular plate which is located between two piezo-electromagnetic layers based on two variables sinusoidal shear deformation plate theory and accord...
TL;DR: In this paper, a semi-analytical approach to investigate wave propagation characteristics in functionally graded graphene reinforced piezoelectric composite plates is presented, and the results show great potential of graphene reinforcements in design of smart composite structures and application for structural health monitoring.
TL;DR: In this article, the authors investigated the enhanced thermo-mechanical static and dynamic behaviors for the functionally graded graphene nanoplatelet reinforced aluminium-based (GRA) composite plate.
TL;DR: In this paper, a comprehensive numerical finite element implementation of the nonlocal strain gradient theory applied to thin laminated composite nanoplates using Kirchhoff theory is presented, where Hermite interpolation functions are used to approximate membrane and bending degrees of freedom according to the conforming and nonconforming approaches.
TL;DR: In this article, a semi-analytical approach integrated with Monte Carlo simulation for stochastic buckling analyses of porous functionally graded plates arising due to the inevitable source-uncertainties of geometrical configurations and material properties is introduced.