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.
Highlights
Due to a variety of organic and inorganic compounds, progress and growth has been made possible when it comes to present-day materials, advanced polymers, engineering alloys, structural ceramics, etc. [1]
The initial idea of developing Functionally graded materials (FGM) was aimed at obtaining a material with high resistance to temperature gradient on one side and good mechanical properties on the other side
It is important to note that the shape functions proposed by various p authors (Table 1) are not generally applicable to1 allztypes of problems
Summary
Due to a variety of organic and inorganic compounds, progress and growth has been made possible when it comes to present-day materials, advanced polymers, engineering alloys, structural ceramics, etc. [1]. Graded materials, beingmaterials modern inmaterials the group composite materials, consequence of discussed continuous change of properties at the interface, avoids delamination. The initial idea of developing FGM was aimed at obtaining a material with high resistance to temperature gradient on one side and good mechanical properties on the other side. For this reason, a number of authors have addressed the behavior problems of FG plates made of metal-ceramic constituents under mechanical and thermal, static, and dynamic loads, applying the theories mentioned above.
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