Large deflection analysis of planar curved beams made of Functionally Graded Materials using Variational Iterational Method

Abstract

In this paper, arbitrarily large in-plane deflections of planar curved beams made of Functionally Graded Materials (FGM) are examined. Geometrically exact beam theory is revisited, but the material properties are considered as an arbitrary function of the position on the cross-section of the beam, to derive the governing differential equation system. Axial, and shear deformations are taken into account. Equations are solved by the method called Variational Iterational Method (VIM). Solution steps are given explicitly. Presented formulation is validated by solving some examples existing in the literature. It is seen that the solution method is easy, and efficient. Deflection values, and deflected shapes of half, and quarter circular cantilever beams made of FGM are given for different variations of the material. Snap-through, and bifurcation buckling of pinned–pinned circular arches made of FGM are examined. Effects of material variation on the deflections, and bifurcation buckling load are examined. New results are also given for arbitrarily large in-plane deflections of planar curved beams made of FGM.