An analytical solution for buckling of moderately thick functionally graded sector and annular sector plates

Abstract

In this article, an analytical solution for buckling of moderately thick functionally graded (FG) sectorial plates is presented. It is assumed that the material properties of the FG plate vary through the thickness of the plate as a power function. The stability equations are derived according to the Mindlin plate theory. By introducing four new functions, the stability equations are decoupled. The decoupled stability equations are solved analytically for both sector and annular sector plates with two simply supported radial edges. Satisfying the edges conditions along the circular edges of the plate, an eigenvalue problem for finding the critical buckling load is obtained. Solving the eigenvalue problem, the numerical results for the critical buckling load and mode shapes are obtained for both sector and annular sector plates. Finally, the effects of boundary conditions, volume fraction, inner to outer radius ratio (annularity) and plate thickness are studied. The results for critical buckling load of functionally graded sectorial plates are reported for the first time and can be used as benchmark.

A review of theories for the modeling and analysis of functionally graded plates and shells

“…Bending analysis of a FG rotating disk was investigated by Bayat et al [103] using the FSDT and a semi-analytical method. Based on the FSDT, Naderi and Saidi [104] derived analytical solutions for the buckling load of FG sector and annular sector plates by decoupling governing equations. A similar approach was adopted by Saidi et al [105] to derive analytical solutions for the natural frequency of FG annular sector plates on the basis of the FSDT.…”

Thermally induced buckling of thin annular FGM plates

“…(2), while Poisson's ratio, ν, is considered to be constant across the thickness [20][21][22]. This assumption has been established in a large number of studies, since Poisson's ratio generally varies in a small range.…”

“…To compare the influences of three available homogenization schemes on critical buckling temperature and heat flux and also post-buckling equilibrium path of FGM solid circular plates, a Ritz-based formulation with polynomial shape functions is used by Kiani and Eslami [19]. Mechanical buckling, thermal buckling, and elastic foundation effect of mechanical buckling of sectorial plates are reported by Saidi and co-authors [20][21][22]. All of these works are formulated based on the firstorder plate theory and five partially differential equations are established as stability equations.…”

Post-buckling analysis of FGM annular sector plates based on three dimensional elasticity graded finite elements

“…Hence it is important to investigate the post-buckling behavior of FGM annular sector plates subjected to in-plane mechanical loads to determine an accurate design of these structural elements. A survey in the literature reveals the existence of limited works on buckling of the FGM annular sector plates [58][59][60][61][62]. For example, Hosseini-Hashemi et al [58] investigated buckling and free vibration behaviors of radially graded circular and annular sector thin plates subjected to uniform in-plane compressive loads and resting on the Pasternak elastic foundation.…”

“…They obtained critical buckling loads of the FGM circular/annular sector plates under simply supported and clamped boundary conditions based on the classical plate theory by using differential quadrature method. Naderi and Saidi [59,60] presented an exact analytical solution for buckling analysis of moderately thick FG sector and annular plates having simply supported boundary condition on the straight edges resting on Winkler elastic foundation by using the first order shear deformation plate theory. Based on three dimensional elasticity graded finite elements, Asemi et al [62] investigated biaxial buckling analysis of FGM annular sector plates fully or partially supported on Winkler elastic foundation.…”