Showing papers on "Plate theory published in 2008"
TL;DR: In this paper, a theoretical analysis to the FGM (functionally graded materials) thin plates based on the physical neutral surface is presented, which has more merits in the engineering application, because it is easier and simpler than classical laminated plate theory based on geometric middle surface.
272 citations
TL;DR: In this article, the free vibration of functionally graded material sandwich rectangular plates with simply supported and clamped edges is studied based on the three-dimensional linear theory of elasticity, and the natural frequencies of simply supported power-law FGM sandwich plates are compared with results from different two-dimensional plate theories.
259 citations
TL;DR: In this paper, a unified formulation and principle of virtual displacements are employed to obtain both closed-form and finite element solutions for the static analysis of functionally graded material plates subjected to transverse mechanical loadings.
Abstract: This work addresses the static analysis of functionally graded material plates subjected to transverse mechanical loadings. The unified formulation and principle of virtual displacements are employed to obtain both closed-form and finite element solutions. The use of the unified formulation permits a large variety of plate models with variable kinematic assumptions to be compared in the same framework. These differ according to the order of the expansion in the thickness direction and the variable description: the order of the expansion ranges from 1 to 4, thus covering first-order as well as higher-order theories; the description of the unknowns can be equivalent single layer or layerwise. The dependence of the material data on the thickness direction was introduced by employing thickness functions that are derived from the Legendre polynomials that are used in the layerwise case. The proposed approach is independent of the used transition function, and as a result, any continuous variations of the material properties in the thickness direction may be easily implemented. The obtained solutions (closed form and finite element) are validated through comparison with three-dimensional exact solutions and other available solutions. These show the limitations of classical plate theories as well as the convenience of the use of the proposed variable kinematic models for the analysis of functionally graded material plates.
231 citations
TL;DR: In this article, the authors discuss the thickness locking mechanism, also known as Poisson locking, which is caused by the use of simplified kinematic assumptions in the plate analysis, and introduce penalty numbers to force ϵ zz ǫ = 0 condition in the 3D solution and refined plate theories.
226 citations
TL;DR: In this paper, it was shown that a proper choice of the reference surface can eliminate the coupling between the inplane and bending deformations, so that the bending of the plate is governed by the same equation of motion as that of homogeneous plates.
Abstract: In recent years many articles concerned with the mechanics of functionally graded plates have been published. Usually new analysis methods are developed to handle the continuous variation in material properties through the thickness of the plate and extensive results are presented. This article shows that no special tools are required because functionally graded plates behave like homogeneous plates. This simple result is developed using the classical plate theory and is shown to hold true when higher order plate theories or the three dimensional elasticity theory is used. The variation in material properties through the thickness of the plate introduces a coupling between the inplane and bending deformations which complicates the analysis. Here we show that by a proper choice of the reference surface, this coupling can be eliminated so that the bending of the plate is governed by the same equation of motion as that of homogeneous plates.
222 citations
TL;DR: In this paper, first-order shear deformation plate models for modeling structures made of functionally graded materials are proposed and the identification of transverse shear factors is investigated through these models by energy equivalence.
203 citations
TL;DR: In this article, the free vibration behavior of thin circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material based on the classical plate theory was investigated.
Abstract: Analytical investigation of the free vibration behavior of thin circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material based on the classical plate theory (CPT) is presented in this paper. The material properties of the FG substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from three-dimensional finite element analyses.
170 citations
TL;DR: In this article, the nonlinear dynamics of a simply supported functionally graded materials (FGMs) rectangular plate subjected to the transversal and in-plane excitations is presented in a thermal environment for the first time.
166 citations
TL;DR: In this article, the displacement component is expanded along the thickness of the plate by using a powerful compact formulation, and infinite different types of expansions can be independently used for the displacements ux, uy and uz.
155 citations
TL;DR: In this article, the analysis of thickness locking mechanism, which is a plate/shell-theory mechanism, caused by the use of simplified kinematic assumptions, is extended to shell geometries.
143 citations
TL;DR: In this article, the authors proposed a solution of the problem of buckling and deflection of a circular porous plate with simply supported edge under radial uniform compression and uniformly distributed load (pressure).
Abstract: The main goal of this paper is a solution of the problem of buckling and deflection. A circular porous plate with simply supported edge under radial uniform compression and uniformly distributed load (pressure) is considered. Mechanical properties of the isotropic porous material vary across the thickness of the plate. Middle plane of the plate is its symmetry plane. A field of displacements (geometric model of nonlinear hypothesis) is described. The principle of stationarity of the total potential energy allowed to get a system of differential equations that govern the plate stability. A critical load and a deflection are determined. The results obtained for porous plates are compared to homogeneous circular plates.
TL;DR: In this paper, a modified continuum model of elastic films with nano-scale thickness is proposed by incorporating surface elasticity into the conventional nonlinear Von Karman plate theory, and the governing equations and boundary conditions of the ultra-thin film including surface effects are derived within the Kirchhoff's assumption, where the effects of nonzero normal stress and large deflection are taken into account simultaneously.
TL;DR: In this paper, an improved higher order zigzag theory is proposed for the static analysis of laminated sandwich plate with soft compressible core, where the variation of in-plane displacements is cubic for both the face sheets and the core and transverse displacement is assumed to vary quadratically within the core while it remains constant through the faces.
TL;DR: In this article, a mesh-free formulation for the static and free vibration analyses of composite plates is presented via a linearly conforming radial point interpolation method, where the radial and polynomial basis functions are employed to construct the shape functions bearing Delta function property.
TL;DR: In this paper, a simply supported, sandwich plate with FGM face sheets and a simple power law distribution in terms of the volume fractions of the constituents is presented for compressive postbuckling under thermal environments.
Abstract: Compressive postbuckling under thermal environments and thermal postbuckling due to heat conduction are presented for a simply supported, sandwich plate with FGM face sheets. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM face sheets and homogeneous substrate are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation plate theory that includes thermal effects. The initial geometric imperfection of the plate is taken into account. A two-step perturbation technique is employed to determine buckling loads (temperature) and postbuckling equilibrium paths. The numerical illustrations concern the compressive and thermal postbuckling behavior of perfect and imperfect, sandwich plate with FGM face sheets under different thermal environmental conditions. The results reveal that the temperature changes, the volume fraction distribution of FGM face sheets, and the substrate-to-face sheet thickness ratio have a significant effect on the buckling load and postbuckling behavior of sandwich plates. The results also confirm that for the case of heat conduction, the postbuckling path is no longer of the bifurcation type.
TL;DR: In this article, the authors used the Mindlin plate theory to study buckling of in-plane loaded isotropic rectangular plates with different boundary conditions, and developed an analytical closed-form solution without any use of approximation for a combination of six different boundary condition; specifically, two opposite edges are simply supported and any of the other two edges can be simply supported, clamped or free.
TL;DR: In this article, the natural neighbour radial point interpolation method (NNRPIM) is extended for the analysis of thick plates and laminates, where the displacement field and the strain field are defined by the Reissner-Mindlin plate theory.
Abstract: In this work the natural neighbour radial point interpolation method (NNRPIM) is extended for the analysis of thick plates and laminates. In order to define the displacement field and the strain field the Reissner–Mindlin plate theory is considered. The nodal connectivity and the node dependent integration background mesh are constructed resorting to the Voronoi tessellation and to the Delaunay triangulation. Within NNRPIM the obtained shape functions pass through all nodes inside the influence-cell providing shape functions with the delta Kronecker property. Optimization tests and examples of well-known benchmark examples are solved in order to prove the high accuracy and convergence rate of the proposed method.
TL;DR: In this paper, an extension of Zhilin's direct approach to plates made of functionally graded materials is presented, where a conceptional different direction is connected with the direct approach in the plate theory.
Abstract: The classical plate theory can be applied to thin plates made of classical materials like steel. The first theory allowing the analysis of such plates was elaborated by Kirchhoff. But this approach was connected with various limitations (e.g., constant material properties in the thickness direction). In addition, some mathematical inconsistencies like the order of the governing equation and the number of boundary conditions exist. During the last century many suggestions for improvements of the classical plate theory were made. The engineering direction of improvements was ruled by applications (e.g., the use of laminates or sandwiches as the plate material), and so new hypotheses for the derivation of the governing equations were introduced. In addition, some mathematical approaches like power series expansions or asymptotic integration techniques were applied. A conceptional different direction is connected with the direct approach in the plate theory. This paper presents the extension of Zhilin’s direct approach to plates made of functionally graded materials.
TL;DR: A nonlinear free vibration analysis of a thin annular functionally graded (FG) plate integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material on the top and bottom surfaces of the annular FG plate is presented in this paper.
Abstract: In this paper, a nonlinear free vibration analysis of a thin annular functionally graded (FG) plate integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material on the top and bottom surfaces of the annular FG plate is presented based on Kirchhoff plate theory. The material properties of the functionally graded core plate are assumed to be graded in the thickness direction according to the power law distribution in terms of the volume fractions of the constituents and the distribution of the electric potential field along the thickness direction of piezoelectric layers is simulated by a sinusoidal function such that the Maxwell static electricity equation is satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. The analytical solutions are derived and validated by comparing the obtained resonant frequencies of the piezoelectric coupled FG annular plate with those of an isotropic core plate. In a numerical study the emphasis is placed on investigating the effect of varying the gradient index of the FG plate on the free vibration characteristics of the structure. Also the good agreement between the results of this paper and those of the finite element (FE) analyses validated the presented approach.
TL;DR: In this article, the meshless local Petrov-Galerkin (MLPG) method with radial basis functions (RBFs), and the higher order shear and normal deformable plate theory (HOSNDPT) are used to analyze static infinitesimal deformations of thick laminated composite elastic plates under different boundary conditions.
Abstract: The meshless local Petrov–Galerkin (MLPG) method with radial basis functions (RBFs), and the higher order shear and normal deformable plate theory (HOSNDPT) are used to analyze static infinitesimal deformations of thick laminated composite elastic plates under different boundary conditions. Two types of RBFs, namely, multiquadrics (MQ) and thin plate splines (TPS), are employed for constructing trial functions while a fourth order spline function is used as the test function. Computed results for different lamination schemes are found to match well with those obtained by other researchers. A benefit of using RBFs over those generated by the moving least squares approximation is that no special treatment is needed to impose essential boundary conditions, which substantially reduces the computational cost. Furthermore, the MLPG method does not require nodal connectivity which reduces the time required to prepare the input data.
TL;DR: In this paper, the authors investigated fiber-reinforced composite plates subjected to low velocity impact by the use of finite element analysis (FE) and found that matrix cracking appeared in the upper 90° plies with the dominance of transverse shear stress.
TL;DR: In this paper, a detailed procedure for the implementation of a discrete singular convolution (DSC) approach to the free vibration analysis of composite plates based on classical laminated plate theory (CLPT) is presented.
TL;DR: In this article, the authors derived equilibrium and stability equations of a FGM circular plate under uniform radial compression, based on the higher order shear deformation plate theory (HSDT), assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method.
TL;DR: In this paper, an improved higher order zigzag theory is presented and applied to study the buckling of laminated sandwich plates, which satisfies the conditions of transverse shear stress continuity at all the layer interfaces.
Abstract: An improved higher order zigzag theory is presented and it is applied to study the buckling of laminated sandwich plates The present theory satisfies the conditions of transverse shear stress continuity at all the layer interfaces including transverse shear stress free conditions at the top and bottom surfaces of the plate The variation of in-plane displacements through thickness direction is assumed to be cubic for both the face sheets and the core, while transverse displacement is assumed to vary quadratically within the core but it remains constant over the face sheets The core is modeled as a three-dimensional elastic continuum An efficient C 0 finite element is proposed for the implementation of the improved plate theory The accuracy and range of applicability of the present formulation are established by comparing the present results with 3D elasticity solutions and other results available in literature
TL;DR: In this article, the small and large-amplitude vibrations of compressively and thermally post-buckled sandwich plates with functionally graded material (FGM) face sheets in thermal environments are taken into account.
TL;DR: In this article, a mathematical formulation for determining the dynamic instability due to transverse doublet modes in the self-excited vibration of a thin annular plate is presented, and an analytical approach to obtain the stability results from the eigenvalue problem of a stationary disc with a finite contact area.
TL;DR: Considering the viscoelastic behavior of polymer foams, a new plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM) as mentioned in this paper.
Abstract: Considering the viscoelastic behavior of polymer foams, a new plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface and the stiffness parameters are identified for the linear viscoelastic isotropic material behavior. It is assumed that the material properties are changing in thickness direction. Solving the plate bending problem of the global mechanical analysis, it will be demonstrated that in some cases, the results significantly differ from the results based on the classical Kirchhoff-type theory.
TL;DR: In this article, the optimal spatial distribution of single-channel actuation voltage in static structural shape control problem is investigated, where a least-square function measuring the structural shape error is minimized under a constraint on the control effort.
TL;DR: In this paper, two triangular plate elements based on the absolute nodal coordinate formulation (ANCF) are introduced, which can exactly describe arbitrary rigid body motion when their mass matrices are constant.
Abstract: In this paper, two triangular plate elements based on the absolute nodal coordinate formulation (ANCF) are introduced. Triangular elements employ the Kirchhoff plate theory and can, accordingly, be used in thin plate problems. As usual in ANCF, the introduced elements can exactly describe arbitrary rigid body motion when their mass matrices are constant. Previous plate developments in the absolute nodal coordinate formulation have focused on rectangular elements that are difficult to use when arbitrary meshes need to be described. The elements introduced in this study have overcome this problem and represent an important addition to the absolute nodal coordinate formulation. The two elements introduced are based on Specht's and Morley's shape functions, previously used in conventional finite element formulations. The numerical solutions of these elements are compared with previously proposed rectangular finite element and analytical results.