A new simple "four-variable shear deformation" plate model is proposed in this work to demonstrate the hygro-thermal environment effects on dynamic and buckling of functionally graded material "sandwich plates" supported by "Winkler-Pasternak" elastic foundations. Equations of motion are obtained from Hamilton's principle

The paper examines a static bending of porous functional plates (FGP) and rectangular plate solutions, based on an underlying high-order shear deformation theory. The proposed high-order shear deformation theory, as opposed to other theories, includes four unknowns. For this reason, a new shear strain function is considered. The technique of Navier is used in closed-form FGP solutions. Results of deflections and stresses are presented for simply supported border conditions. Current figures are contrasted with the non-poreous plate deflecting solutions and the literature's stresses. Effects of different parameters, including thickness, gradient index and porosity of FGM plates, are discussed.

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This study presents the analytical solutions of free vibration analysis of simply supported nanoplate FG porous using nonlocal high order shear deformation plate theory. This theory contains four unknowns without the use of shear correction factors unlike the others. The objective of this article is to develop a model to use the function f (z) on vibration and the natural frequencies of functionally graded nanoplates nonlocal to study the effect of the various parameters. The validity of the theory is shown by comparing the present results with obtained with those reported in the literature. The effects of various parameters are all discussed.

This work deals with the analysis of the mechanical bending behavior of a rectangular plate simply supported on four sides (FGM), subjected to transverse static loading. The high order theory is used in this work, The developed models are variably consistent, have a strong similarity with the classical plate theory in many aspects, do not require correction to the shear factor, and give rise to variations transverse shear stresses such as transverse shear parabolically varies across the shear thickness and satisfies surface conditions without stresses. Equilibrium equations are obtained by applying the principle of virtual works. The mathematical expressions of the arrow, the stresses are obtained using Navies approach to solve the system of equilibrium equations. The influence of mechanical loading and the change of the parameter of the material on mechanical behavior of the plate P-FGM are represented by a numerical example.