Extended Kantorovich method for static analysis of moderately thick functionally graded sector plates
In this paper, an iterative procedure based on the extended Kantorovich method (EKM) is presented to gain highly accurate solution for bending of moderately thick functionally graded (FG) fully clamped sector plates. Effective mechanical properties of the sector plates assumed to be defined by a power law distribution. The governing equations, using First Order Shear Deformation Theory (FSDT), include five second order partial differential equations in terms of displacements and rotations. Successive application of the EKM converts the governing partial differential equations (PDEs) to two sets of five ordinary differential equations (ODEs) in terms of r and theta. These ODE systems are then solved iteratively which shows very fast convergence. It is shown that how the same method and formulation can be used for solid sector and rectangular plates. It is also demonstrated that the method is very fast convergent as three to four iterations are enough to obtain final results with desired accuracy. Predictions for fully clamped FG sector plates are compared with finite element code ANSYS, which show close agreement. Comparison of the results for rectangular plates shows good agreement with existing literature. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
extended kantorovich method fully clamped sector plates bending analysis functionally graded material