Shear post buckling analysis of FGM annular sector plates based on three dimensional elasticity for different boundary conditions

Abstract

In this paper, shear post-buckling analysis of functionally graded annular sector plates is considered. In-plane shear loads have been applied to either radial, circumferential, or all edges of annular sector plates. Moreover, post-buckling of annular sector plates subjected to in-plane shear load at upper/lower surfaces is investigated for the first time. 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 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 graded finite element method. Non-linear equilibrium equations are solved based on iterative Newton–Raphson method. The effects of material gradient exponent, different sector angles, thickness ratio and four different boundary conditions on the post-buckling behavior of FGM annular sector plates have been investigated. 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.