Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multi-term extended Kantorovich method

Abstract

Multi-term extended Kantorovich method (MTEKM) is used to solve the bending problem of thin skew (parallelogram) functionally graded plate resting on the Winkler elastic foundation under uniformly distributed transverse load. Formulations are based on the classical plate theory (CPT) with the physical neutral surface is considered as the reference plane. Various configurations of clamped, simply supported and free edges are considered. By implementing the concept of Galerkin’s weighted residual method, the fourth-order partial differential governing equation and boundary conditions are converted into two sets of ordinary differential equations (ODE), which are then solved numerically using “Chebfun” numerical computation package. Convergence and accuracy of MTEKM are investigated. Results obtained with MTEKM are compared to finite element method (FEM) solutions. FEM has been implemented using ANSYS software, in which the plate is modeled with shell elements, while the elastic foundation is modeled as a pair of contact/target elements. In addition, the effects of both the Winkler foundation stiffness and material power index have been investigated. Applying MTEKM in bending analysis of thin skew plates offered more accurate results than the single-term EKM but with the cost of more computation time but still provides simplicity and rapid convergence. It is found that MTEKM well suits the bending problem of skew FGM plates resting on elastic foundation.