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Showing papers on "Plate theory published in 2012"


Journal ArticleDOI
TL;DR: In this paper, the bending and free vibration analyses of thin-to-moderately thick composite plates reinforced by single-walled carbon nanotubes using the finite element method based on the first order shear deformation plate theory are presented.

585 citations


Journal ArticleDOI
TL;DR: In this paper, a trigonometric shear deformation theory for isotropic and composite laminated and sandwich plates is developed, which accounts for adequate distribution of the transverse shear strains through the plate thickness and tangential stress-free boundary conditions on the plate boundary surface, thus a shear correction factor is not required.

297 citations


Journal ArticleDOI
TL;DR: In this paper, a general nonlinear third-order plate theory that accounts for geometric nonlinearity, microstructure-dependent size effects, and two-constituent material variation through the plate thickness is presented using the principle of virtual displacements.

278 citations


Journal ArticleDOI
TL;DR: In this article, a new shear deformation theory for sandwich and composite plates is developed, which accounts for adequate distribution of the transverse shear strains through the plate thickness and tangential stress-free boundary conditions on the plate boundary surface, thus a shear correction factor is not required.
Abstract: A new shear deformation theory for sandwich and composite plates is developed. The proposed displacement field, which is “m” parameter dependent, is assessed by performing several computations of the plate governing equations. Therefore, the present theory, which gives accurate results, is relatively close to 3D elasticity bending solutions. The theory accounts for adequate distribution of the transverse shear strains through the plate thickness and tangential stress-free boundary conditions on the plate boundary surface, thus a shear correction factor is not required. Plate governing equations and boundary conditions are derived by employing the principle of virtual work. The Navier-type exact solutions for static bending analysis are presented for sinusoidally and uniformly distributed loads. The accuracy of the present theory is ascertained by comparing it with various available results in the literature.

270 citations


Journal ArticleDOI
TL;DR: In this paper, an isogeometric finite element method based on non-uniform rational B-splines (NURBS) basis functions is developed for natural frequencies and buckling analysis of thin symmetrically laminated composite plates based upon the classical plate theory.

194 citations


Journal ArticleDOI
TL;DR: In-plane–out-of-plane separated representation of the involved fields within the context of the Proper Generalized Decomposition allows solving the fully 3D model by keeping a 2D characteristic computational complexity, without affecting the solvability of the resulting multidimensional model.

175 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated and reviewed approaches to modeling laminated composite plates and assessed their suitability and functionality, and discussed the advantages and disadvantages of each model and how accurate and efficient the models can predict the transverse shear.
Abstract: This study investigates and reviews approaches to modelling laminated composite plates. It explores theories that have been proposed and developed and assesses their suitability and functionality. The particular focus in this study has been on normal stresses and the through-thickness distributions of transverse shear. These are important for composite plates as stress-induced failures can occur in three different ways. Therefore, it is essential to understand and calculate transverse shear and normal stress through the thickness of the plate accurately. In this study, previous laminated composite plate theories are categorised and reviewed in a general sense, i.e. not problem specific, and the advantages and disadvantages of each model are discussed. This research mainly focuses on how accurate and efficient the models can predict the transverse shear. It starts with displacement-based theories from very basic models such as Classical laminate plate theory to more complicated and higher-order shear deformation theory. Models are furthermore categorised by how the models consider the overall laminate. In this article, the theories are divided into two parts: Single layer theory, where the whole plate is considered as one layer; and Layerwise theory, where each layer is treated separately. The models based on zig-zag and Discrete Theories are then reviewed, and finally the mixed (hybrid) plate theories are studied.

161 citations


Journal ArticleDOI
TL;DR: In this article, the potential of single-layered graphene sheet (SLGS) as a nanomechanical sensor is explored based on the nonlocal Kirchhoff theory of plates which incorporates size effects into the classical theory.

160 citations


Journal ArticleDOI
TL;DR: In this article, the bending, buckling and free vibration of annular microplates made of functionally graded materials (FGMs) are investigated based on the modified couple stress theory and Mindlin plate theory.

156 citations


Journal ArticleDOI
TL;DR: In this article, the mechanical buckling of a functionally graded nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs) subjected to uniaxial and baoxial in-plane loadings is investigated.
Abstract: In this paper, the mechanical buckling of a functionally graded nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs) subjected to uniaxial and biaxial in-plane loadings is investigated. The material properties of the nanocomposite plate are assumed to be graded in the thickness direction and vary continuously and smoothly according to two types of the symmetric carbon nanotubes volume fraction profiles. The material properties of SWCNT are determined according to molecular dynamics (MDs), and then the effective material properties at a point are estimated by either the Eshelby–Mori–Tanaka approach or the extended rule of mixture. The equilibrium and stability equations are derived using the Mindlin plate theory considering the first-order shear deformation (FSDT) effect and variational approach. The results for nanocomposite plate with uniformly distributed CNTs, which is a special case in the present study, are compared with those of the symmetric profiles of the CNTs volume fraction. A numerical study is performed to investigate the influences of the different types of compressive in-plane loadings, CNTs volume fractions, various types of CNTs volume fraction profiles, geometrical parameters and different types of estimation of effective material properties on the critical mechanical buckling load of functionally graded nanocomposite plates.

154 citations


Journal ArticleDOI
TL;DR: In this article, a new four-variable refined plate theory for thermal buckling analysis of functionally graded material (FGM) sandwich plates is proposed, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors.
Abstract: The novelty of this paper is the use of a new four-variable refined plate theory for thermal buckling analysis of functionally graded material (FGM) sandwich plates. Unlike any other theory, the present new theory is variationally consistent and gives four governing equations. The number of unknown functions involved is only four, as against five in case of other shear deformation theories. In addition, the theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Material properties and thermal expansion coefficient of the sandwich plate faces 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. The core layer is still homogeneous and made of an isotropic material. ...

Journal ArticleDOI
TL;DR: In this paper, small and large-amplitude vibrations are presented for a functionally graded rectangular plate resting on a two-parameter (Pasternak-type) elastic foundation in thermal environments.

Journal ArticleDOI
TL;DR: In this paper, a finite element formulation for static, free vibration and buckling analyses of laminated composite plates is presented, which relies on a combination of node-based smoothing discrete shear gap method with the higher-order shear deformation plate theory to give a so-called NS-DSG3 element.

Book
04 Feb 2012
TL;DR: In this paper, the conservation laws of linear Elastostatics of Inhomogeneous Bernoulli-Euler Beams have been studied and compared to the classical theory of linear elasticity.
Abstract: 1 Mathematical Preliminaries.- 1.1 General Remarks.- 1.2 What is a Conservation Law?.- 1.3 Trivial Conservation Laws.- 1.4 System with a Lagrangian Noether's Method.- 1.5 System without a Lagrangian Neutral-Action Method.- 1.6 Discussion.- 2 Linear Theory of Elasticity.- 2.1 General Remarks.- 2.2 Elements of Linear Elasticity.- 2.3 Conservation Laws of Linear Elastostatics.- 2.4 Alternative Derivations of Conservation Laws.- 3 Properties of the Eshelby Tensor.- 3.1 General Remarks 81.- 3.2 Physical Interpretation of the Components of the Eshelby Tensor.- 3.3 Invariants, Principal Values, Principal Directions and Extremal Values of the Eshelby Tensor.- 4 Linear Elasticity with Defects.- 4.1 General Remarks.- 4.2 Path-Independent Integrals and Energy-Release Rates.- 4.3 Example: Hole-Dislocation Interaction.- 4.4 Path-Independent Integrals of Fracture Mechanics.- 5 Inhomogeneous Elastostatics.- 5.1 General Remarks.- 5.2 Symmetry Transformations.- 5.3 The Homogeneous Case.- 5.4 The Inhomogeneous Case.- 5.5 Relation to Stress-Intensity Factors.- 5.6 Examples.- 6 Elastodynamics.- 6.1 General Remarks.- 6.2 Time t as an Additional Independent Variable.- 6.3 Convolution in Time.- 6.4 Domain-Independent Integrals.- 6.5 Energy-Release Rates.- 6.6 Wave Motion.- 7 Dissipative Systems.- 7.1 General Remarks.- 7.2 Diffusion Equation.- 7.3 Non-Linear Wave Equation.- 7.4 Viscoelasticity.- 8 Coupled Fields.- 8.1 General Remarks.- 8.2 Piezoelectricity.- 8.3 Thermoelasticity.- 8.4 Mechanics of a Porous Medium.- 9 Bars, Shafts and Beams.- 9.1 General Remarks.- 9.2 Elements of Strength-of-Materials.- 9.3 Balance and Conservation Laws for Bars and Shafts.- 9.4 Balance and Conservation Laws for Beams.- 9.5 Energy-Release Rates and Stress-Intensity Factors.- 9.6 Examples.- 10 Plates and Shells.- 10.1 General Remarks.- 10.2 Plate Theories.- 10.3 Conservation Laws for Elastostatics of Mindlin Plates.- 10.4 Reduction to the Classical Theory.- 10.5 Conservation Laws for Shells.- Appendix A.- Conservation Laws for Inhomogeneous Bars under Arbitrary Axial Loading.- Appendix B.- B.1 Elastodynamics of Inhomogeneous Bernoulli-Euler Beams.- B.2 Reduction to Statics.- Appendix C.- C.1 Elastodynamics of Inhomogeneous Mindlin Plates.- C.2 Reduction to Statics.- References.- Symbol Index.- Author Index.

Journal ArticleDOI
TL;DR: In this article, the free vibration of single-layered graphene sheet (SLGS) resting on an elastic matrix as Pasternak foundation model is investigated by using the modified couple stress theory.

Journal ArticleDOI
TL;DR: In this article, an efficient and simple refined theory is presented for buckling analysis of functionally graded plates, which accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors.

Journal ArticleDOI
TL;DR: In this article, the surface effects on the vibration and buckling behavior of a simply supported piezoelectric nanoplate (PNP) were investigated using a modified Kirchhoff plate model.
Abstract: This work investigates the surface effects on the vibration and buckling behaviour of a simply supported piezoelectric nanoplate (PNP) by using a modified Kirchhoff plate model. Two kinds of in-plane constraints are defined for the PNP, and the surface effects are accounted in the modified plate theory through the surface piezoelectricity model and the generalized Young–Laplace equations. Simulation results show that the influence of surface effects on the plate resonant frequency depends on the in-plane constraints significantly. For the PNP with different in-plane constraints, the effects of the applied electric potential, the mode number, the plate aspect ratio and the plate thickness on the resonant frequency are examined with consideration of the surface effects. The possible mechanical buckling of the PNP is also studied, and it is found that the surface effects on the critical electric voltage for buckling are sensitive to the plate thickness and aspect ratio. Our results also reveal that there exists a critical transition point at which the combined surface effects on the critical electric voltage may vanish under certain conditions.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated compressive postbuckling under thermal environments and thermal post-buckling due to a uniform temperature rise of a sandwich plate with carbon nanotube-reinforced composite (CNTRC) face sheets resting on an elastic foundation.
Abstract: This paper investigates compressive postbuckling under thermal environments and thermal postbuckling due to a uniform temperature rise are presented of a sandwich plate with carbon nanotube-reinforced composite (CNTRC) face sheets resting on an elastic foundation. The material properties of CNTRC face sheets are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations of the plate are based on a higher-order shear deformation plate theory that includes plate-foundation interaction. The thermal effects are also included and the material properties of both CNTRC face sheets and homogeneous core layer are assumed to be temperature-dependent. 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 plates with functionally graded CNTRC face sheets resting on Pasternak elastic foundations under different thermal environmental conditions, from which results for the sandwich plate with uniformly distributed CNTRC face sheets are also obtained for comparison purposes. The results reveal that the foundation stiffness, the temperature changes, the nanotube volume fraction of face sheet, and the core-to-face sheet thickness ratio have significant effects on the compressive buckling load and postbuckling behavior of the sandwich plate, whereas this effect on the thermal postbuckling behavior is less pronounced for the same sandwich plate.

Journal ArticleDOI
TL;DR: Yang et al. as mentioned in this paper developed a model for composite laminated Reddy plate based on modified couple stress theory, and a new curvature tensor is defined for establishing the constitutive relations of laminated plate.

Journal ArticleDOI
TL;DR: In this article, a solution methodology based on the Differential Quadrature method (DQM) is developed for solving the partial differential equations of VAT plates with linear fiber angle orientations.

Journal ArticleDOI
TL;DR: In this paper, a unified technique for solving the plate bending problems by extending the scaled boundary finite element method is presented, which is based on the three-dimensional governing equation without enforcing the kinematics of plate theory.
Abstract: SUMMARY This paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method. The formulation is based on the three-dimensional governing equation without enforcing the kinematics of plate theory. Only the in-plane dimensions are discretised into finite elements. Any two-dimensional displacement-based elements can be employed. The solution along the thickness is expressed analytically by using a matrix function. The proposed technique is consistent with the three-dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon. Moreover, the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence. Numerical examples of various plate structures with different thickness-to-length ratios demonstrate the applicability and accuracy of the proposed technique. Copyright © 2012 John Wiley & Sons, Ltd.

Journal ArticleDOI
TL;DR: In this paper, the buckling analysis of orthotropic nanoplates such as graphene using the two-variable refined plate theory and nonlocal small-scale effects is presented, and the closed-form solution for buckling load of a simply supported rectangular orthotropic nanoplate subjected to inplane loading has been obtained by using the Navier's method.
Abstract: This article presents the buckling analysis of orthotropic nanoplates such as graphene using the two-variable refined plate theory and nonlocal small-scale effects. The two-variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the monolayer graphene are derived from the principle of virtual displacements. The closed-form solution for buckling load of a simply supported rectangular orthotropic nanoplate subjected to in-plane loading has been obtained by using the Navier’s method. Numerical results obtained by the present theory are compared with first-order shear deformation theory for various shear correction factors. It has been proven that the nondimensional buckling load of the orthotropic nanoplate is always smaller than that of the isotropic nanoplate. It is also shown that small-scale effects contribute significantly to the mechanical behavior of orthotropic graphene sheets and cannot be neglected. Further, buckling load decreases with the increase of the nonlocal scale parameter value. The effects of the mode number, compression ratio and aspect ratio on the buckling load of the orthotropic nanoplate are also captured and discussed in detail. The results presented in this work may provide useful guidance for design and development of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.

Journal ArticleDOI
TL;DR: In this paper, closed-form solutions for free vibration analysis of orthotropic plates are obtained based on two variable refined plate theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors.

Journal ArticleDOI
TL;DR: In this article, a new improved high-order theory is presented for biaxial buckling analysis of sandwich plates with soft orthotropic core, and equations of motion and boundary conditions are derived by principle of minimum potential energy.
Abstract: In the present paper, a new improved high-order theory is presented for biaxial buckling analysis of sandwich plates with soft orthotropic core. Third-order plate theory is used for face sheets and quadratic and cubic functions are assumed for transverse and in-plane displacements of the core, respectively. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of plate are satisfied. The nonlinear Von-Karman type relations are used to obtain strains. Also, transverse flexibility and transverse normal strain and stress of the orthotropic core are considered. The equations of motion and boundary conditions are derived by principle of minimum potential energy. Analytical solution for static analysis of simply supported sandwich plates under biaxial in-plane compressive loads is presented using Navier’s solution. Effect of geometrical parameters of face sheets and core and biaxial loads ratio are studied on the overall buckling of sandwich plates. Comparison of the present results with those of the three-dimensional theory of elasticity and some plate theories confirms the accuracy of the proposed theory.

Journal ArticleDOI
TL;DR: In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates, which accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors.
Abstract: In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The influences of many plate parameters on buckling temperature difference will be investigated. It is noticed that the present refined plate theory can predict accurately the critical temperatures o...

Journal ArticleDOI
TL;DR: In this paper, the sinusoidal shear deformation plate theory is used to study the response of multilayered angle-ply composite plates due to a variation in temperature and moisture concentrations.

Journal ArticleDOI
TL;DR: In this article, a two-variable refined plate theory was proposed to account for parabolic variation of transverse shear stress through the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factor.

Journal ArticleDOI
TL;DR: In this article, a theoretical and finite element (FE) investigation of the scattering characteristics of the fundamental anti-symmetric (A0) Lamb wave at delaminations in a quasi-isotropic composite laminate is presented.

Journal ArticleDOI
TL;DR: In this paper, a finite strip method is applied for analyzing the buckling behavior of rectangular functionally graded plates (FGPs) under thermal loadings, where the material properties of FGPs are assumed to vary continuously through the thickness of the plate, according to the simple power law distribution.

Journal ArticleDOI
TL;DR: In this article, the authors presented an analytical approach for buckling analysis and smart control of a single layer graphene sheet (SLGS) using a coupled polyvinylidene fluoride (PVDF) nanoplate.
Abstract: This study presents an analytical approach for buckling analysis and smart control of a single layer graphene sheet (SLGS) using a coupled polyvinylidene fluoride (PVDF) nanoplate. The SLGS and PVDF nanoplate are considered to be coupled by an enclosing elastic medium which is simulated by the Pasternak foundation. The PVDF nanoplate is subjected to an applied voltage in the thickness direction which operates in control of critical load of the SLGS. In order to satisfy the Maxwell equation, electric potential distribution is assumed as a combination of a half-cosine and linear variation. The exact analysis is performed for the case when all four ends are simply supported and free electrical boundary condition. Adopting the nonlocal Mindlin plate theory, the governing equations are derived based on the energy method and Hamilton's principle. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, stiffness of the internal elastic medium, graphene length, mode number and external electric voltage on the buckling smart control of the SLGS. The results depict that the imposed external voltage is an effective controlling parameter for buckling of the SLGS. This study might be useful for the design and smart control of nano-devices.