Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

Abstract

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

Analysis of the Vibration Behaviors of Rotating Composite Nano-Annular Plates Based on Nonlocal Theory and Different Plate Theories

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“…FGMs have wide applicability in aircraft, spacecraft, and space structures, which space exploration depends on, as well as in car parts, electronic and medical equipment, thermal coatings for ceramic engines, the marine industry, gas turbines, and biomedicine, among other applications [4][5][6][7][8]. Although functionally graded materials still have high production costs, this type of material is a topic that has been significantly discussed by numerous authors in recent years, with many publications on the subject being published, making it a very current and important topic that should be explored further [1,9,10].…”

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