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In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading. [ABSTRACT FROM AUTHOR]

Purpose – A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues. Design/methodology/approach – Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions. Findings – In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems. Originality/value – To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions. [ABSTRACT FROM AUTHOR]

A new hyperbolic shear deformation theory applicable to bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates is presented. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The energy functional of the system is obtained using Hamilton’s principle. Analytical solutions of deflection and stresses are obtained using Navier-type procedure. Free vibration frequencies are then accurately calculated using a set of boundary characteristic orthogonal polynomials associated with Ritz method. Numerical comparisons are conducted to verify and to demonstrate the accuracy and efficiency of the present theory. Excellent agreement with the known results in the literature has been obtained. [ABSTRACT FROM AUTHOR]

This paper deals with the thermo-mechanical deformation behaviour of shear deformable functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation. 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 presented theory is variationally consistent, does not require shear correction factor and gives rise to transverse shear stress variation such that the transverse shear stresses vary in hyperbolic manner across the thickness satisfying shear stress-free surface conditions. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The sandwich plate faces are made of isotropic, two-constituent (ceramic–metal) material distribution through the thickness. The core layer is still homogeneous and made of an isotropic metal material. Several kinds of non-symmetric sandwich plates are presented. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical results of the present simple shear deformation theory are presented to show the effect of material distribution and foundation parameters on the deflections and stresses. A wide variety of results is presented for the static response of sandwich plates under thermo-mechanical loads. [ABSTRACT FROM AUTHOR]

Abstract: The bending response of functionally graded material (FGM) plate resting on elastic foundation and subjected to hygro-thermo-mechanical loading is studied. Using a four variable refined plate theory, both a quadratic variation of the transverse shear strains across the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are satisfied without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The elastic coefficients, thermal coefficient and moisture expansion coefficient of the plate are assumed to be graded in the thickness direction. The elastic foundation is modelled as two-parameter Pasternak foundation. Numerical results are presented to verify the accuracy of present theory and the influences played by many parameters are investigated. The study is relevant to the simulation of rocket launch pad structures subjected to intense thermal loading. [Copyright &y& Elsevier]

Abstract: An analytical model is developed for prediction of thermal residual stresses, arising from the fabrication of exponential functionally graded material (simply called E-FGM) systems. The thermomechanical properties of functionally graded layers are assumed to vary exponentially through the thickness. Residual stresses were found to increase when fully ceramic and/or fully metal regions are included in the structure, adjoining the graded zone. The effects of temperature dependent elastic and thermal expansion characteristics of constituents on residual stress were found to be small. [Copyright &y& Elsevier]