Bending Analysis of Functionally Graded Axisymmetric Circular Plates using the Dual Mesh Finite Domain Method

Abstract

The dual mesh finite domain method (DMFDM) introduced by Reddy employs one mesh for the approximation of the primary variables (primal mesh) and another mesh for the satisfaction of the governing equations (dual mesh). The present study deals with the extension and application of the DMFDM to functionally graded circular plates under axisymmetric conditions. The formulation makes use of the traditional finite element interpolation of the primary variables with a primal mesh and a dual mesh to satisfy the integral form of the governing differential equations, the basic premise of the finite volume method. The method is used to analyze axisymmetric bending of through-thickness functionally graded circular plates using the classical plate theory (CPT) and first-order shear deformation plate theory (FST). The displacement model of the FST and the mixed model of the CPT using the DMFDM are developed along with the displacement and mixed finite element models. Numerical results are presented to illustrate the methodology and a comparison of the generalized displacements and bending moments computed with those of the corresponding finite element models. The influence of the extensional-bending coupling stiffness (due to the through-thickness grading of the material) on the deflections is also brought out.

Keywords:
Dual mesh finite domain method; axisymmetric bending of plates; mixed models; functionally graded materials; numerical results

Graphical Abstract