Keywords: shear post-buckling, three dimensional elasticity, graded finite element method, functionally graded material, annular sector plate.

In this paper, shear post-buckling analysis of functionally graded material (FGM) annular sector plates is considered. In-plane shear loads have been applied to either radial, circumferential, or all edges of the annular sector plates. Material properties are graded asymmetrically in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents while the Poisson's ratio is assumed to be constant. The governing equations are based on the three dimensional theory of elasticity in conjunction with non-linear Green strain tensor instead of the approximate plate theories and Von Karman assumptions. The governing equations are developed based on the principle of virtual work and solved based on the graded finite element method. The effects of material gradient exponent, different sector angles and different boundary conditions on the post-buckling behavior of FGM annular sector plates have been investigated. Two different boundary conditions have been examined: (1) Movable simply supported edges. (2) Immovable simply supported radial edges and free circumferential edges. Results denote that due to weak coupling between applied shear loads and the resulting twisting moments, shear post-buckling behavior of simply supported FGM plates is of the bifurcation-type buckling following a stable post-buckling path.

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