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.

A microstructure-dependent nonlinear third-order beam theory which accounts for through-thickness power-law variation of a two-constituent material is developed using Hamilton's principle. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Kármán nonlinear strains. The modified couple stress theory contains a material length scale parameter that can capture the size effect in a functionally graded material beam. The influence of the material length scale parameter on linear bending is investigated. The finite element models are also developed to determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on linear and nonlinear response.