Nonlinear analysis of functionally graded beams using the dual mesh finite domain method and the finite element method

Abstract

In this paper, geometrically nonlinear analysis of functionally graded beams using the dual mesh finite domain method (DMFDM) and the finite element method is presented. The DMFDM makes use of a primal mesh of finite elements and associated approximation for the variables of the formulation and a dual mesh of control domains, which does not overlap the primal mesh, for the satisfaction of the governing equations. The dual variables can be postcomputed uniquely and accurately at the control domain interfaces. The method is used to obtain nonlinear (due to the von Kármán nonlinear strains) bending solutions of straight, through-thickness functionally graded beams using the Euler–Bernoulli and the Timoshenko beam theories. Mixed models, which contain displacements and the bending moment as degrees of freedom, and displacement models are developed. Numerical results of linear and nonlinear analyses are presented to illustrate the methodology and a comparison of the generalized displacements and bending moments obtained with the DMFDM and FEM models while bringing out certain interesting features of functionally graded beams.