Thermo-Mechanical Bending Response of Exponentially Graded Thick Plates Resting on Elastic Foundations

Abstract

The trigonometric shear and normal deformations plate theory is used to study the thermo-mechanical bending analysis of exponentially graded (EG) thick rectangular plates resting on Pasternak elastic foundations. Material properties of the plate are assumed to be graded in the thickness direction according to an exponential law distribution, meaning that Lamé coefficients vary exponentially in a given fixed z-direction. The governing equations are derived from the principle of virtual displacements. The analytical solutions are obtained by using Navier technique and the effects of stiffness of the foundations, thermal loading, and gradient index on thermo-mechanical responses of the plates are discussed. Numerical results for the bending response for EG rectangular plates are investigated and some of them are compared with those available in the literature.

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

“…In this theory, transverse shear strain distribution is assumed to be constant through the plate thickness and thus requires shear correction factor to appropriately represent the strain energy of deformation. To solve this problem, higher order plate theories are introduced such as third order shear deformable theory (TSDT) of Reddy [21][22][23][24], sinusoidal theory Zenkour [25][26][27][28][29], secant function based theory [30], hyperbolic theory [31][32][33], inverse trigonometric shear deformation theory [34][35][36][37][38].…”

Analytical study of the bending of isotropic plates, inhomogeneous in thickness

“…This is due to the fact that the difficulties faced during consideration of specific problems are relatively more complex than the similar problems of the classical theory of elasticity, since variable coefficients appear in its fundamental equations. These characteristic features offer explanation to the fact that analytical solutions to a limited number of tasks for the bodies of the simplest geometric shapes have been obtained until now: rectangular [1,5,6] and circular plate [2], structure [3] and dimensions [4,6] and elementary dependencies of the characteristics of materials elasticity on the coordinates of the points of the body [5].…”

“…As result of the research, it was found that the influence of elasticity module on the plate of (FG) and (EG) materials rested on the elastic foundation is produced according to the exponential law [5,6], and the influence of material properties and the strength of the elastic foundation on mechanical properties of the plate was studied.…”

Computational Development of a 4-Unknowns Trigonometric Quasi-3D Shear Deformation Theory to Study Advanced Sandwich Plates and Shells

“…The representative amount of research on the thermal behavior of FGMs is evidenced in these works. However, even the recent effort to study the bending and vibration analysis of FGMs, readers may consult the alphabetic list of reference from Bo et al [2000] to Zenkour et al [2015], these interesting research topics still deserves attention. In this sense, the present paper devotes attention to the static analysis of FGMs.…”