Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 45 2 2013 12 22 Static Analysis of Bending, Stability, and Dynamic Analysis of Functionally Graded Plates by a Four-Variable Theory Static Analysis of Bending, Stability, and Dynamic Analysis of Functionally Graded Plates by a Four-Variable Theory 11 25 317 10.22060/mej.2013.317 FA Farid Kaviani H. R. Mirdamadi Journal Article 2014 06 19 In this article, static analysis of bending, elastic stability, and free vibration analysis of functionally graded plates (FGP) are investigated using a four-variable theory. In this four-variable theory, hyperbolic sine distribution is used for satisfying boundary conditions of out-of-plane shear stresses of zero value, in the neighborhood of upper and lower surfaces of plate. One of the mechanical characteristics of FGM material is continuous variations of properties along the thickness, with a power law distribution, which is a function of volume ratio of different constituent parts of FGM plate. The purpose of this article is acquiring more exact analytical results than those of simple form of four-variable plate theory, i.e., refined plate theory (RPT). Furthermore, for parametric study, influential parameters on the analysis of FGM plate are investigated. The plate equations of motion are derived by extended Hamilton’s variational principle. Analytical results are developed based on classical method of Navier and simply-supported conditions on all four edges. Numerical results are analyzed for different power distributions of mechanical properties along the thickness and different plate length to thickness ratios. The results, obtained from this theory, are compared with those of different variants of RPT theories. In this article, static analysis of bending, elastic stability, and free vibration analysis of functionally graded plates (FGP) are investigated using a four-variable theory. In this four-variable theory, hyperbolic sine distribution is used for satisfying boundary conditions of out-of-plane shear stresses of zero value, in the neighborhood of upper and lower surfaces of plate. One of the mechanical characteristics of FGM material is continuous variations of properties along the thickness, with a power law distribution, which is a function of volume ratio of different constituent parts of FGM plate. The purpose of this article is acquiring more exact analytical results than those of simple form of four-variable plate theory, i.e., refined plate theory (RPT). Furthermore, for parametric study, influential parameters on the analysis of FGM plate are investigated. The plate equations of motion are derived by extended Hamilton’s variational principle. Analytical results are developed based on classical method of Navier and simply-supported conditions on all four edges. Numerical results are analyzed for different power distributions of mechanical properties along the thickness and different plate length to thickness ratios. The results, obtained from this theory, are compared with those of different variants of RPT theories. https://mej.aut.ac.ir/article_317_ba734e14301bdc50cedcbbb8e0a5cda6.pdf