Three-dimensional transient analysis of functionally graded material annular sector plate under various boundary conditions

In this study, an analytical solution for the buckling of a functionally graded annular sector plate resting on an elastic foundation is presented. The buckling analysis of the functionally graded annular sector plate is investigated for two typical, Winkler and Pasternak, elastic foundations. The equilibrium and stability equations are derived according to the Kirchhoff's plate theory using the energy method. In order to decouple the highly coupled stability equations, two new functions are introduced. The decoupled equations are solved analytically for a plate having simply supported boundary conditions on two radial edges. Satisfying the boundary conditions on the circular edges of the plate yields an eigenvalue problem for finding the critical buckling load. Extensive results pertaining to critical buckling load are presented and the effects of boundary conditions, volume fraction, annularity, plate thickness, and elastic foundation are studied.

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NONLINEAR MECHANICAL BENDING OF FUNCTIONALLY GRADED MATERIAL PLATES UNDER TRANSVERSE LOADS WITH VARIOUS BOUNDARY CONDITIONS

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962311000451 ◽

2011 ◽

Vol 02 (02) ◽

pp. 237-258 ◽

Cited By ~ 11

Author(s):

MOHAMMAD TALHA ◽

B. N. SINGH

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Functionally Graded Material ◽

Functionally Graded ◽

Nonlinear Strain ◽

Various Boundary Conditions ◽

Transverse Loads ◽

Nonlinear Mechanical ◽

Graded Material ◽

Mechanical Bending

Nonlinear mechanical bending of functionally graded material (FGM) plates under transverse loads with various boundary conditions are presented. The material properties of the FGM plates are graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The theoretical nonlinear finite element formulations are based on the higher-order shear deformation theory, with a special modification in the transverse displacement in order to estimate the parabolic distribution of transverse shear strains through the plate thickness. The Green–Lagrange nonlinear strain–displacement relation with all higher-order nonlinear strain terms is included to account for the large deflection response of the plate. The fundamental equations for FGM plates with traction-free boundary conditions on the top and bottom faces of the plate are accomplished using variational approach. Results have been achieved using a C0 continuous isoparametric Lagrangian finite element with 13 degrees of freedom per node. Convergence and comparison studies have been performed to ascertain the effectiveness of the present model. Numerical results are highlighted for different thickness ratios, aspect ratios, and role played by the constituent volume fraction index with different boundary conditions.

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