A dual mesh finite domain method for the analysis of functionally graded beams

A method that employs a dual mesh, one for primary variables and another for dual variables, for the numerical analysis of functionally graded beams is presented. The formulation makes use of the traditional finite element interpolation of the primary variables (primal mesh) and the concept of the finite volume method to satisfy the integral form of the governing differential equations on a dual mesh. The method is used to analyze bending of straight, through-thickness functionally graded beams using the Euler-Bernoulli and the Timoshenko beam theories, in which the axial and bending deformations are coupled. Both the displacement and mixed models using the new method are developed accounting for the coupling. Numerical results are presented to illustrate the methodology and a comparison of the generalized displacements and forces/stresses computed with those of the corresponding finite element models. The influence of the coupling stiffness on the deflections is also brought out.