Showing papers on "Plate theory published in 2017"

Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments

Abstract: Modeling and analysis of the postbuckling behavior of graphene-reinforced composite (GRC) laminated plates are presented in this paper. The GRC plates are in a thermal environment, subjected to uniaxial compression and resting on an elastic foundation. The temperature-dependent material properties of functionally graded graphene-reinforced composites (FG-GRCs) are assumed to be graded in the plate thickness direction with a piece-wise type, and are estimated through a micromechanical model. The postbuckling problem of FG-GRC laminated plates is modeled using a higher order shear deformation plate theory and the plate-foundation interaction and thermal effects are taken into consideration. A two-step perturbation technique is employed to determine the buckling loads and the postbuckling equilibrium paths. The compressive buckling and postbuckling behavior of perfect and imperfect, geometrically mid-plane symmetric FG-GRC laminated plates under different sets of thermal environmental conditions is obtained and is also compared with the behavior of uniformly distributed GRC laminated plates. The results show that the buckling loads as well as the postbuckling strength of the GRC laminated plates may be enhanced through piece-wise functionally graded distribution of graphene.

Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: An analytical approach

Abstract: In this paper, the free vibration analysis of rectangular plates composed of functionally graded materials with porosities is investigated based on a simple first-order shear deformation plate theory. The network of pores in assumed to be empty or filled by low pressure air and the material properties of the plate varies through the thickness. Using Hamilton's principle and utilizing the variational method, the governing equations of motion of FG plates with porosities are derived. Considering two boundary layer functions, the governing equations of the system are rewritten and decoupled. Finally, two decoupled equations are solved analytically for Levy-type boundary conditions so as to obtain the eigenfrequencies of the plate. The effects of porosity parameter, power law index, thickness-side ratio, aspect ratio, porosity distribution and boundary conditions on natural frequencies of the plate are investigated in detail.

Thermal buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations

Abstract: This paper presents the modeling and analysis for the thermal postbuckling of graphene-reinforced composite laminated plates resting on an elastic foundation and subjected to in-plane temperature variation A micromechanical model is used to estimate the temperature-dependent material properties of the graphene-reinforced composites (GRCs) Piece-wise functionally graded (FG) GRC layers along the thickness direction of a plate is considered in this study Employing the higher order shear deformation plate theory, the governing equations for FG-GRC plates are derived and the effects of plate-foundation interaction and temperature variation are included in the modeling A two-step perturbation technique is applied to obtain the buckling temperature and the thermal postbuckling load-deflection curves for perfect and imperfect FG-GRC laminated plates The results show that the buckling temperature as well as thermal postbuckling strength of the plates can be increased as a result of the functionally graded graphene reinforcement for the plates

Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory

Abstract: Modern structures and components may require advanced materials whose properties vary continuously not only in one specified direction, but also different other directions. In particular, the bi-directional functionally graded materials (2D-FGMs) introduced are expected to have more effective properties, consequently eliminating commonly awkward problems such as local stress concentrations and delamination. In this paper, buckling and bending behaviors of 2D-FGM plates, which are of great importance in the design and development of engineering applications, are numerically analyzed by a finite element model. The plate kinematics are described using a new third-order shear deformation plate theory (TSDT), without the need for special treatment of shear-locking effect and shear correction factors. The present TSDT theory based on rigorous kinematic of displacements, which is shown to be dominated over other preceding theories, is derived from an elasticity formulation, rather by the hypothesis of displacements. The materials are assumed to be graded in two directions and their effective properties are computed through the rule of mixture. The accuracy of the proposed approach assessed on numerical results is confirmed by comparing the obtained results with respect to reference published solutions. The effects of some numerical aspect ratios such as volume fraction, boundary conditions, thickness to length ratio, etc. on static deflections and critical buckling are numerically studied. The investigation of results confirms that such aforementioned aspect ratios have significant effects on the mechanical behaviors of plates.

A new and simple HSDT for thermal stability analysis of FG sandwich plates

Abstract: The novelty of this work is the use of a new displacement field that includes undetermined integral terms for analyzing thermal buckling response of functionally graded (FG) sandwich plates. The proposed kinematic uses only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional higher shear deformation theories (HSDTs). The theory considers a trigonometric variation of transverse shear stress and verifies the traction free boundary conditions without employing the shear correction factors. Material properties of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law variation in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are assumed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is employed to derive the governing equations as an eigenvalue problem. The validation of the present work is checked by comparing the obtained results the available ones in the literature. The influences of aspect and thickness ratios, material index, loading type, and sandwich plate type on the critical buckling are all discussed.

Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory

Abstract: In this work, free vibration analysis of size-dependent functionally graded (FG) nanoplates resting on two-parameter elastic foundation is investigated based on a novel nonlocal refined trigonometric shear deformation theory for the first time. This theory includes undetermined integral variables and contains only four unknowns, with is even less than the conventional first shear deformation theory (FSDT). Mori–Tanaka model is employed to describe gradually distribution of material properties along the plate thickness. Size-dependency of nanosize FG plate is captured via the nonlocal elasticity theory of Eringen. By implementing Hamilton\'s principle the equations of motion are obtained for a refined four-variable shear deformation plate theory and then solved analytically. To show the accuracy of the present theory, our research results in specific cases are compared with available results in the literature and a good agreement will be demonstrated. Finally, the influence of various parameters such as nonlocal parameter, power law indexes, elastic foundation parameters, aspect ratio, and the thickness ratio on the non-dimensional frequency of rectangular FG nanoscale plates are presented and discussed in detail.

A simple FSDT-based meshfree method for analysis of functionally graded plates

Abstract: Modeling of mechanical behavior of plates has been accomplished in the past decades, with different numerical strategies including the finite element and meshfree methods, and with a range of plate theories including the first-order shear deformation theory (FSDT). In this paper, we propose an efficient numerical meshfree approach to analyze static bending and free vibration of functionally graded (FG) plates. The kinematics of plates is based on a novel simple FSDT, termed as S-FSDT, which is an effective four-variable refined plate theory. The S-FSDT requires C 1 -continuity that is satisfied with the basis functions based on moving Kriging interpolation. Some major features of the approach can be summarized: (a) it is less computationally expensive due to having fewer unknowns; (b) it is naturally free from shear-locking; (c) it captures the physics of shear-deformation effect present in the conventional FSDT; (d) the essential boundary conditions can straightforwardly be treated, the same as the FEM; and (e) it can deal with both thin and thick plates. All these features will be demonstrated through numerical examples, which are to confirm the accuracy and effectiveness of the proposed method. Additionally, a discussion on other possible choices of correlation functions used in the model is given.

A New Quasi 3D Nonlocal Plate Theory for Vibration and Buckling of FGM Nanoplates

Abstract: This paper presents the analyses of free vibration and buckling of functionally graded (FG) nanoplates in thermal environment by using a new quasi-3D nonlocal hyperbolic plate theory in which both shear and normal strains are included. The nonlocal equations of motion for the present problem are derived from Hamilton’s principle. For simply-supported boundary conditions, Navier’s approach is utilized to solve the motion equations. Eringen’s nonlocal theory is employed to capture the effect of the nonlocal parameter on natural frequency and buckling of the FGM nanoplates. Numerical results of the present formulation are compared with those predicted by other theories available in the open literature to explain the accuracy of the suggested theory that contains the shear deformation and thickness stretching. Other numerical examples are also presented to show the influences of the nonlocal coefficient, power law index and geometrical parameters on the vibration and buckling load of FGM nanoplates.

Buckling of FG-CNT-reinforced composite plates subjected to parabolic loading

Abstract: It is known that the distribution of stresses in a rectangular plate is the same as the applied stresses on the boundaries when the loading is uniform or linearly varying. For other types of compressive loads, for instance parabolic compressive loading, the distribution of stresses in the plate is different from the applied loads at the boundaries of the plate. For such conditions, to obtain the buckling loads of the plate, an accurate prebuckling analysis should be performed. The present research aims to obtain the buckling loads and buckling pattern of composite plates reinforced with carbon nanotubes with uniform or functionally graded distribution across the plate thickness. The properties of the composite media are obtained based on a modified rule of mixtures approach with the introduction of efficiency parameters. First-order shear deformation plate theory is used to approximate the plate kinematics. The plate is subjected to uniaxial compressive loads which vary as parabolic functions across the width of the plate. At first, using the Ritz method and Airy stress function formulation, the distribution of stress resultants in the plate domain is obtained as a two-dimensional elasticity formulation. Afterwards, by means of the Chebyshev polynomials as the basic functions of the Ritz solution method, an eigenvalue problem is established to obtain the buckling load and buckling shape of the plate. Comparison studies are provided to assure the accuracy of the presented formulation for isotropic homogeneous and cross-ply laminated plates. Afterwards, parametric studies are performed for composite plates reinforced with carbon nanotubes.

Nonlinear dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shear deformable plates with temperature-dependent material properties and surrounded on elastic foundations

Abstract: Based on Reddy’s third-order shear deformation plate theory, the nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates on elastic foundations subjected to dynamic loads and temperature are presented. The plates are reinforced by single-walled carbon nanotubes which vary according to the linear functions of the plate thickness. The plate’s effective material properties are assumed to depend on temperature and estimated through the rule of mixture. By applying the Airy stress function, Galerkin method and fourth-order Runge–Kutta method, nonlinear dynamic response and natural frequency for imperfect FG-CNTRC plates are determined. In numerical results, the influences of geometrical parameters, elastic foundations, initial imperfection, dynamic loads, temperature increment, and nanotube volume fraction on the nonlinear vibration of FG-CNTRC plates are investigated. The obtained results are validated by comparing with those of ...

Nonlocal vibrations and stabilities in parametric resonance of axially moving viscoelastic piezoelectric nanoplate subjected to thermo-electro-mechanical forces

Abstract: This work is motivated by the self-powered component of biomedical nano-robotic device which is expected to move in arterial blood vessels. The transverse vibrations and steady-state responses of axially moving viscoelastic piezoelectric two-dimensional nanostructures are investigated based on the nonlocal viscoelasticity thin plate theory. The constitutive relations of viscoelastic piezoelectric nanoplate containing the thermal effect are performed and the governing partial differential equations of the problem model are derived using the Hamilton's principle. The natural frequencies are numerically determined via the Galerkin method, the complex mode method, as well as the finite element method for comparison. Moreover, the theoretical calculations are compared with those in previous literature to verify effects in nonlocal nanoscale framework and average speed on natural frequency. Afterwards, the instable behaviors of axially non-uniformly moving viscoelastic piezoelectric nanoplate characterized as a sine variation about the constant average speed are addressed using the method of multiple scales. The analyses are mainly focused on the boundaries of instable regions in combination parametric resonance and principal parametric resonance. The non-dimensional numerical results imply the existences of nonlocal nanoscale parameter and average speed contribute to reduce the rigidity, and further produce the coupled vibrations and flutter instabilities for complex frequencies. Additionally, the instable regions of combination and principal parametric resonances decrease with increases in the biaxial compression, change of temperature, positive electric voltage and viscoelastic coefficient. The dynamic responses of axially moving viscoelastic piezoelectric nanoplate under the coupling of thermo-electro-mechanical multi-fields are expected to play significant roles in designing biomedical nano-robots.

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Abstract: Here, free vibration analysis of functionally graded piezoelectric (FGP) plates with porosities is carried out based on refined four-unknown plate theory. The present plate theory captures shear deformation impacts needless of shear correction factor. A modified power-law model is adopted to describe the graded material properties of a functionally graded piezoelectric plate. Implementing an analytical approach, which satisfies different boundary conditions, governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in the literature. The impacts of applied voltage, porosity distribution, material graduation, plate geometrical parameters, and boundary conditions on vibration of porous FGP plate are discussed.

Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers

Abstract: Thermo-electro-mechanical transient analysis of a sandwich nanoplate is studied in this paper. The sandwich nanoplate consists of a Kelvin–Voigt viscoelastic nanoplate and two integrated piezoelectric face sheets resting on a visco-Pasternak foundation. The sandwich nanoplate is subjected to thermal and mechanical loads, and the piezoelectric face sheets are subjected to an applied electric potential. Two-variable sinusoidal shear deformation plate theory is used for the description of the displacement components. The governing equations of motion are derived using Hamilton’s principle by calculation of strain and kinetic energies and energy due to external forces. The natural frequencies of the sandwich nanoplate are calculated in terms of three parameters of foundation, structural viscoelastic damping parameter and excitation frequency. Also, bending results of the problem in terms of the parameters of the temperature loadings are presented.

Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations

Abstract: This paper proposes a four-variable shear deformation refined plate theory for free vibration analysis of embedded smart plates made of porous magneto-electro-elastic functionally graded (MEE-FG) materials Magneto-electro-elastic properties of FG plate are supposed to vary through the thickness direction and are estimated through the modified power-law rule in which the porosities with even and uneven type are approximated The governing differential equations and boundary conditions of embedded porous FG plate under magneto-electrical field are derived through Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factors An analytical solution procedure is used to achieve the natural frequencies of embedded porous FG plate supposed to magneto-electrical field with various boundary condition Influences of several important parameters such as material graduation exponent, porosity volume fraction, magnetic potential, electric voltage, various boundary conditions, elastic foundation parameters and plate side-to-thickness ratio on natural frequencies of embedded porous MEE-FG plate are investigated and discussed in detail It is concluded that these parameters play significant roles on the dynamic behavior of porous MEE-FG plates resting on elastic foundation Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases