Bending Analysis of a Thin Annular Sector Plate Resting on a Nonlinear Winkler Foundation under Uniform and Nonuniform Loadings using Extended Kantorovich Method

In this paper, the bending analysis of a thin circular sector plate (with inner and outer radius) made of homogeneous material with various boundary conditions including simply support and clamped edges under the act of uniformly and non-uniformly loadings resting on a nonlinear Winkler foundations (elastic) is studied. To do this, for bending analysis of sector thin plate subjected to uniform and nonuniform loading a combination of the Extended Kantorovich Method (EKM) along with weighted residual method was employed to solve the fourth-order governinig bending partial differential equation (PDE) of the plate in the polar coordinates of r and θ. The obtained results for bending deflection of the plate are compared with those from finite element method (FEM) and also with the literature in special cases. Also, the effect of changes in different parameters including geometry of the plate, linear and nonlinear stiffnesses of Winkler foundation, types of various boundary conditions and uniform and nonuniform loading in the bending response of the plate is investigated.