Showing papers on "Plate theory published in 2007"

Non-local elastic plate theories

Abstract: A non-local plate model is proposed based on Eringen's theory of non-local continuum mechanics. The basic equations for the non-local Kirchhoff and the Mindlin plate theories are derived. These non-local plate theories allow for the small-scale effect which becomes significant when dealing with micro-/nanoscale plate-like structures. As illustrative examples, the bending and free vibration problems of a rectangular plate with simply supported edges are solved and the exact non-local solutions are discussed in relation to their corresponding local solutions.

Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory

Abstract: Axisymmetric bending of micro/nanoscale circular plates is studied using a nonlocal plate theory. The nonlocal theory allows for small scale effects. The governing equations and boundary conditions are derived for the aforementioned problem. By using a variable transformation technique, exact nonlocal solutions for axisymmetric bending of circular plates under general loading are obtained. A detailed examination of the effects of small scale on nonlocal solutions is carried out using uniformly loaded circular plates with either clamped or simply-supported edges. When compared with local plate theory, the nonlocal solutions show larger deflections, moments and shear force and lower bending stiffness.

Lamb waves in binary locally resonant phononic plates with two-dimensional lattices

Abstract: The authors study the propagation of Lamb waves in two-dimensional locally resonant phononic-crystal plates, composed of periodic soft rubber fillers in epoxy host with a finite thickness. Our calculations are based on the efficient plane wave expansion formulation which utilized Mindlin’s plate theory. Calculated results show that the low-frequency gaps of Lamb waves are opened up by the localized resonance mechanism. The resonant frequencies of flexure-dominated plate modes are significantly dependent not only on the radius of circular rubber fillers but also on the plate thickness. The properties of localized resonance are qualitatively analogous to the vibration of a circular thin plate.

Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layerwise theory

Abstract: Thermal buckling analysis of rectangular composite multilayered plates under uniform temperature rise is investigated using a layerwise plate theory. von Karman strain–displacement equations are employed to account for large deflections occurrence. It is already proven that the layerwise theory results are compatible with the three-dimensional theory of elasticity results. The accuracy of the present results is increased by substituting each layer by many virtual sub-layers. The final governing equations are not simplified or linearized. Material properties are assumed to vary with temperature. Hermitian finite element formulation is used to ensure a C1 continuity for the lateral deflections. No semi-analytic solution is employed to reduce the problem to an eigenvalue one. Layerwise formulations are usually displacement-based. Therefore, force or moment boundary conditions (e.g. simply supported boundary condition), are approximately satisfied. A FEM algorithm is presented to exactly incorporate the boundary conditions. A proposed numerical scheme and a modified Budiansky instability criterion presented by the author are used to determine the buckling temperature in a computerized solution. Finally, results of the present techniques are compared with the results of the high-order theories presented by some well-known researchers and the influences of various geometric and mechanical properties parameters of the composite plate on the buckling temperature are studied.

Classical and mixed finite elements for static and dynamic analysis of piezoelectric plates

Abstract: This paper addresses the problem of multilayered plates with embedded piezoelectric layers by finite element method (FEM). Original ideas in previous papers (Int. J. Numer. Methods Eng. 2002; 195: 191–231, 253–291) have been extended to the static and dynamic analysis of coupled electro-mechanical problems. Two variational statements, the Principle of Virtual Displacements (PVD) and the Reissner Mixed Variational Theorem (RMVT) are employed to derive classical and mixed finite element matrices, respectively. Transverse stress assumptions are made in the framework of RMVT and the resulting finite elements describe a priori interlaminar continuous transverse shear and normal stresses. The unified formulation (UF) has been referred to in order to derive hierarchical finite elements (FEs) in term of a few fundamental nuclei for a large variety of piezoelectric plate theories. Both modellings that preserve the number of variables independent from the number of layers (equivalent single layer models, ESLM) and layer-wise models (LWM) in which the same variables are independent in each layer have been treated. The expansion order N assumed for displacement, transverse stress and electrical potential fields in the plate thickness direction z as well as the number of the element nodes Nn have been taken as free parameters of the considered formulations. By varying N, Nn, variable treatment (LW or ESL) as well as variational statements (PVD and RMVT), a large number of FEs have been presented. Compliances and/or stiffness are accumulated from layer to multilayered level according to the corresponding variable treatment. The numerical evaluations and assessment for the presented plate elements have been provided. The superiority of RMVT applications with respect to classical ones based on PVD has been confirmed for piezolectric plates. The proposed RMVT elements, in fact, are able to give a quasi-three-dimensional description of stress/strain mechanical and electrical fields in multilayered thick and thin piezolectric plates. Copyright © 2006 John Wiley & Sons, Ltd.

Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection

Abstract: Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates 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. Based on von Karman's plate theory, equilibrium equations governing a large axi-symmetric deformation of the FGM circular plate under thermomechanical loads are derived. In the analysis, the geometric imperfections of the plate are taken into account. By using a shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved numerically. Responses for the nonlinear thermomechanical post-buckling responses of the FGM plate are obtained. Numerical examples are presented that relate to the performances of perfect and imperfect, homogenous and graded plates. Characteristic curves of the post-buckling deformation of the imperfect FGM circular plate varying with thermal loads, imperfection parameters and volume fraction index are plotted. And then effects of the load parameters, materials constitution, and the geometric imperfection of the plate on the deformation are discussed in detail.

Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support

Abstract: In this paper, a study on the vibration of thin cylindrical shells with ring supports made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The cylindrical shells have ring supports which are arbitrarily placed along the shell and which impose a zero lateral deflection. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to the volume fraction power-law distribution. The analysis is carried out with strains-displacement relations from Love's shell theory. The governing equations are obtained using an energy functional with the Rayleigh-Ritz method. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

Nonlinear thermal bending response of FGM plates due to heat conduction

Abstract: Nonlinear thermal bending analysis is presented for a simply supported, shear deformable functionally graded plate without or with piezoelectric actuators subjected to the combined action of thermal and electrical loads Heat conduction and temperature-dependent material properties are both taken into account The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction and the electric field considered only has non-zero-valued component E Z The material properties of functionally graded materials (FGMs) 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 and piezoelectric layers are assumed to be temperature-dependent The governing equations of an FGM plate are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects A two step perturbation technique is employed to determine the thermal load–deflection and thermal load–bending moment curves The numerical illustrations concern nonlinear bending response of FGM plates without or with surface bonded piezoelectric actuators due to heat conduction and under different sets of electric loading conditions The results reveal that for the case of heat conduction the nonlinear thermal bending responses are quite different to those of FGM plates subjected to transverse mechanical loads, and the temperature-dependency of FGMs could not be neglected in the thermal bending analysis

Micromechanical Analysis of Composite Corrugated-Core Sandwich Panels for Integral Thermal Protection Systems

Abstract: termsA44 andA55 werecalculatedusinganenergyapproach.Usingtheshear-deformableplatetheory,aclosed-form solution of the plate response was derived. The variation of plate stiffness and maximum plate deflection due to changing the web angle are discussed. The calculated results, which require significantly less computational effort and time, agree well with the three-dimensional finite element analysis. This study indicates that panels with rectangular webs resulted in a weak extensional, bending, and A55 stiffness and that the center plate deflection was minimum for a triangular corrugated core. The micromechanical analysis procedures developed in this study were used to determine the stresses in each component of the sandwich panel (face and web) due to a uniform pressure load.

New First-Order Shear Deformation Plate Theories

Abstract: First-order shear deformation theories, one proposed by Reissner and another one by Mindlin, are widely in use, even today, because of their simplicity. In this paper, two new displacement based first-order shear deformation theories involving only two unknown functions, as against three functions in case of Reissner’s and Mindlin’s theories, are introduced. For static problems, governing equations of one of the proposed theories are uncoupled. And for dynamic problems, governing equations of one of the theories are only inertially coupled, whereas those of the other theory are only elastically coupled. Both the theories are variationally consistent. The effectiveness of the theories is brought out through illustrative examples. One of the theories has striking similarity with classical plate theory.

A posteriori error estimates for the Morley plate bending element

Abstract: A local a posteriori error indicator for the well known Morley element for the Kirchhoff plate bending problem is presented. The error indicator is proven to be both reliable and efficient. The technique applied is general and it is shown to have also other applications.

Temperature gradient mechanism in laser forming of thin plates

Abstract: To obtain further insight into the deformation of a plate in the laser forming process, the temperature gradient mechanism (TGM) is studied. Through the investigation, it can be found that, under the processing conditions of TGM, the plate not only bends about the x -axis but also about the y -axis. An analytical model estimate of the bending angle about the y -axis is constructed based on the theories of heat transfer and the mechanics of elastoplasticity. Numerical simulations are carried out to investigate the deformation of the plate about the y -axis by choosing the different process parameters. The analytically based estimate is used to suggest suitable starting values for the simulation process of calculated results. The study of the bending about the y-axis may describe more fully the deformation of a plate, which is helpful in high-precision forming.

A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates

Abstract: Using a differential quadrature (DQ) method, large amplitude free vibration analysis of laminated composite skew thin plates is presented The governing equations are based on the thin plate theory (TPT) and the geometrical nonlinearity is modeled using Green's strain in conjunction with von Karman assumptions To cause the impact due to nonlinear terms more significant, in-plane immovable simply supported, clamped and different combinations of them are considered The effects of different parameters on the convergence and accuracy of the method are studied The resulted solutions are compared to those from other numerical methods to show the accuracy of the method Some new results for laminated composite skew plates with different mixed boundary conditions are presented and are compared with those obtained using the first order shear deformation theory based DQ (FSDT-DQ) method Excellent agreements exist between the solutions of the two approaches but with much lower computational efforts of the present DQ methodology with respect to FSDT-DQ method

Thermal Buckling and Nonlinear Flutter Behavior of Functionally Graded Material Panels

Abstract: The nonlinear flutter and thermal buckling of an functionally gradient material panel under the combined effect of elevated temperature conditions and aerodynamic loading is studied. A nonlinear finite element model based on the first-order shear deformable plate theory and von Karman strain-displacement relations is adopted. The governing nonlinear equations are obtained using the principal of virtual work, adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature-dependent material properties. The aerodynamic pressure is modeled using the quasi-steady first-order piston theory. This system of nonlinear equations is solved by the Newton-Raphson numerical technique. It is found that the temperature increase has an adverse effect on the functionally gradient material panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics, but this is limited by structural integrity aspect. The presence of aerodynamic flow results in postponing the buckling temperature and in suppressing the postbuckling deflection, and the temperature increase gives way for higher limit-cycle amplitude.