Showing papers on "Plate theory published in 2014"

An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates

Abstract: In this paper, an efficient and simple higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton’s principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with 3-dimensional and quasi-3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

New Quasi-3D Hyperbolic Shear Deformation Theory for the Static and Free Vibration Analysis of Functionally Graded Plates

Abstract: In this paper, a new quasi-three-dimensional (3D) hyperbolic shear deformation theory for the bending and free vibration analysis of functionally graded plates is developed. By dividing the transverse displacement into bending, shear, and thickness stretching parts, 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 five, as against six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory.

Analysis of functionally graded sandwich plates using a new first-order shear deformation theory

Abstract: In this paper, a new first-order shear deformation theory is presented for functionally graded sandwich plates composed of functionally graded face sheets and an isotropic homogeneous core. By making a further assumption to the existing first-order shear deformation theory, the number of unknowns and governing equations of the present theory is reduced, thereby making it simple to use. In addition, the use of shear correction factor is no longer necessary in the present theory since the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. Equations of motion are derived from Hamilton's principle. Analytical solutions for bending, buckling and free vibration analysis of rectangular plates under various boundary conditions are presented. Verification studies show that the present first-order shear deformation theory is not only more accurate than the conventional one, but also comparable with higher-order shear deformation theories which have a greater number of unknowns.

Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory

Abstract: In this paper, the free vibration of magnetoelectro-elastic (MEE) nanoplates is investigated based on the nonlocal theory and Kirchhoff plate theory. The MEE nanoplate is assumed as all edges simply supported rectangular plate subjected to the biaxial force, external electric potential, external magnetic potential, and temperature rise. By using the Hamilton's principle, the governing equations and boundary conditions are derived and then solved analytically to obtain the natural frequencies of MEE nanoplates. A parametric study is presented to examine the effect of the nonlocal parameter, thermo-magneto-electro-mechanical loadings and aspect ratio on the vibration characteristics of MEE nanoplates. It is found that the natural frequency is quite sensitive to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the thermal loading.

Isogeometric analysis of functionally graded plates using a refined plate theory

Abstract: We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of functionally graded material (FGM) plates. A new inverse tangent distributed function through the plate thickness is proposed. The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions namely B-splines or non-uniform rational B-splines (NURBS) which reach easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field with four degrees of freedom per each control point allowing an efficient solution process.

Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection

Abstract: This paper deals with non-linear dynamic stability of initially imperfect piezoelectric functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates under a combined thermal and electrical loadings and interaction of parametric and external resonance. The excitation, which derives from harmonically varying actuators voltage, results in both external and parametric excitation. The governing equations of the piezoelectric CNTRC plates are derived based on first order shear deformation plate theory (FSDT) and von Karman geometric non-linearity. The material properties of FG-CNTRC plate are assumed to be graded in the thickness direction. The single-walled carbon nanotubes (SWCNTs) are assumed aligned, straight and a uniform layout. The linear buckling and vibration behavior of perfect and imperfect plates are obtained in the first step. Then, Galerkin's method is employed to derive the non-linear governing equations of the problem with quadratic and cubic non-linearities associated with mid-plane stretching. Periodic solutions and their stability are determined by using the harmonic balance method with simply supported boundary conditions. The effect of the applied voltage, temperature change, plate geometry, imperfection, the volume fraction and distribution pattern of the SWCNTs on the parametric resonance, in particular the positions and sizes of the instability regions of the smart CNTRC plates as well as amplitude of steady state vibration are investigated through a detailed parametric study.

Spatial resolution of wrinkle patterns in thin elastic sheets at finite strain

Abstract: Koiter's nonlinear plate theory is used to simulate the wrinkling patterns observed in stretched thin elastic sheets. The phenomenon considered is associated with wrinkle patterns distributed over the interior of the sheet, in regions where the stretching and bending energies are of the same order of magnitude. Numerical solutions to several equilibrium boundary-value problems are obtained by the method of dynamic relaxation based on a dissipative dynamical system and compared with existing experimental, numerical, and analytical results.

A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates

Abstract: In the present paper, a new sinusoidal higher-order plate theory is developed for bending of exponential graded plates. The effects due to transverse shear and normal deformations are both included. The number of unknown functions involved in the present theory is only five as against six or more in case of other shear and normal deformation theories. The theory accounts for sinusoidal distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Based on the sinusoidal shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and efficient in predicting the bending response of exponential graded plates.

Flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nanoplate

Abstract: Flexoelectricity, referring to the coupling between electric polarization and strain gradients, is a universal effect in all dielectrics and may become manifest at the nano-scale. The current work aims to investigate the flexoelectric effect on the electroelastic responses and the free vibrational behaviors of a piezoelectric nanoplate (PNP). Based on the conventional Kirchhoff plate theory and the extended linear piezoelectricity theory, the governing equation and the boundary conditions of a clamped PNP with the consideration of the static bulk flexoelectricity are derived. Ritz approximate solutions of the electroelastic fields and the resonant frequencies demonstrate the size-dependency of the flexoelectric effect, which is more prominent for thinner plates with smaller thickness as expected. Simulation results also indicate that the influence of the flexoelectricity upon the electroelastic fields of a bending PNP and the transverse vibration of the PNP is sensitive to the plate in-plane dimensions as well as the applied electric voltage. Moreover, it is suggested that the possible frequency tuning of a PNP resonator by adjusting applied electrical load warrants the consideration of the flexoelectricity. This study is claimed to provide a theoretical predicition on the trend of the flexoelectric effect upon the static and dynamic behaviors of a bending PNP, thus sheding light on understanding the underlying physics of electromechanical coupling at the nano-scale to some extent.

Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium

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.

A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass

Abstract: The novelty of this paper is the use of trigonometric four variable plate theory for free vibration analysis of laminated rectangular plate supporting a localized patch mass. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The Hamilton's Principle, using trigonometric shear deformation theory, is applied to simply support rectangular plates. Numerical examples are presented to show the effects of geometrical parameters such as aspect ratio of the plate, size and location of the patch mass on natural frequencies of laminated composite plates. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of laminated rectangular plate supporting a localized patch mass.

MODELING AND STRESS ANALYSIS OF SMART CNTs/FIBER/POLYMER MULTISCALE COMPOSITE PLATES

Abstract: Modeling and nonlinear stress analysis of piezolaminated CNTs/fiber/polymer composite (CNTFPC) plates under a combined mechanical and electrical loading are investigated in this study. The governing equations of the piezoelectric CNTFPC plates are derived based on first-order shear deformation plate theory (FSDT) and von Karman geometric nonlinearity. Halpin–Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The CNTs are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. An analytical solution is employed to determine the large deflection response and stress analysis of the nanocomposite plates. Finally, by solving some numerical examples for simply supported plates, the effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of SWCNTs and MWCNTs on the deflection and stress analyses of the piezoelectric CNTs/fiber/polymer multiscale composite plate are studied. It is shown that the deflections significantly decrease with a small percentage of CNTs. Also, it is found that the SWCNTs reinforcement produces more pronounced effect on the bending and stress of the nanocomposite plates in comparison with MWCNTs.

Analytical modeling and experimental validation of a structurally integrated piezoelectric energy harvester on a thin plate

Abstract: Vibration-based energy harvesting using piezoelectric cantilevers has been extensively studied over the past decade. As an alternative to cantilevered harvesters, piezoelectric patch harvesters integrated to thin plates can be more convenient for use in marine, aerospace and automotive applications since these systems are often composed of thin plate-like structures with various boundary conditions. In this paper, we present analytical electroelastic modeling of a piezoelectric energy harvester structurally integrated to a thin plate along with experimental validations. The distributed-parameter electroelastic model of the thin plate with the piezoceramic patch harvester is developed based on Kirchhoff’s plate theory for all-four-edges clamped (CCCC) boundary conditions. Closed-form steady-state response expressions for coupled electrical output and structural vibration are obtained under transverse point force excitation. Analytical electroelastic frequency response functions (FRFs) relating the voltage output and vibration response to force input are derived and generalized for different boundary conditions. Experimental validation and extensive theoretical analysis efforts are then presented with a case study employing a thin PZT-5A piezoceramic patch attached on the surface of a rectangular aluminum CCCC plate. The importance of positioning of the piezoceramic patch harvester is discussed through an analysis of dynamic strain distribution on the overall plate surface. The electroelastic model is validated by a comparison of analytical and experimental FRFs for a wide range of resistive electrical boundary conditions. Finally, power generation performance of the structurally integrated piezoceramic patch harvester from multiple vibration modes is investigated analytically and experimentally.

Physically and geometrically non-linear vibrations of thin rectangular plates

Abstract: Static deflection as well as free and forced large-amplitude vibrations of thin rectangular rubber plates under uniformly distributed pressure are investigated. Both physical, through a neo-Hookean constitutive law to describe the non-linear elastic deformation of the material, and geometrical non-linearities are accounted for. The deflections of a thin initially flat plate are described by the von Karman non-linear plate theory. A method for building a local model, which approximates the plate behavior around a deformed configuration, is proposed. This local model takes the form of a system of ordinary differential equations with quadratic and cubic non-linearities. The corresponding results are compared to the exact solution and are found to be accurate. Two models reflecting both physical and geometrical non-linearities and geometrical non-linearities only are compared. It is found that the sensitivity of the deflection to the physically induced non-linearities at moderate strains is significant.

A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation

Abstract: A refined and simple shear deformation theory for thermal buckling of solar functionally graded plate (SFGP) resting on two-parameter Pasternak's foundations is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. It is assumed that the material properties of the plate vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the present plate theory based on exact neutral surface position is employed to derive the governing stability equations. The nonlinear strain-displacement relations are also taken into consideration. The boundary conditions for the plate are assumed to be simply supported in all edges. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. The effects of the foundation parameters, plate dimensions, and power law index are presented comprehensively for the thermal buckling of solar functionally graded plates.