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Journal of Applied Mechanics and Technical Physics

2016 year, number 4

Three-Dimensional Stress and Free Vibration Analyzes of Functionally Graded Plates with a Circular Hole by the Use of the Graded Finite Element Method

K. Asemi1, H. Ashrafi2, M. Shariyat3
1Amirkabir University of Technology, Tehran, Iran
2University of Kashan, Kashan, Iran
3Toosi University of Technology, Tehran, Iran
Keywords: трехмерная теория упругости, метод градиентных конечных элементов, пластина с круговым отверстием, функционально-градиентный материал, энергетический метод Рэлея -- Ритца, свободные колебания, three-dimensional elasticity theory, graded finite element method, functionally graded material, Rayleigh-Ritz energy formulation, free vibrations


Static and free vibration analyses of plates with circular holes are performed based on the three-dimensional theory of elasticity. The plates are made of a functionally graded material (FGM), and the volume fraction of the material varies continuously over the plate thickness. The effective properties of the FGM plate are estimated by using the Mori-Tanaka homogenization method. A graded finite element method based on the Rayleigh-Ritz energy formulation is used to solve the problem. The effects of different volume fractions of the material and hole sizes on the behavior of FGM plates under uniaxial tension are investigated. Natural frequencies of a fully clamped FGM plate with a circular cutout are derived. The results obtained are compared with available experimental data.