Bending Analysis of Functionally Graded Materials Beam Considering Different Shear Deformation Theory

Abstract

Static bending analysis of functionally graded materials(FGM) beam of rectangular cross section considering different shear deformation theory are presented. The FGM beams are assumed to be made of ceramics and metal, and the equivalent parameters of FGM are continuously variation across the beam thickness with a simple power law. Based on the principle of minimum potential energy, the differential equations for the FGM beam are obtained, in which the unknown functions are deflection, axial displacement and rotation angle. For simply supported FGM beam, considering 5 kinds of shear deformation theory, the curves of deflection, axial displacement and rotation angle of FGM beam are obtained respectively by the Fourier series method. The effect of length-to-height ratios and gradient index of the FGM beam on the bending deformation are discussed. The distribution characteristics of the shear stress and normal stress of FGM beams under different shear deformation theory are investigated. Then the static bending behaviors of beam with FGM and homogeneous material are compared. The curves between the neutral axis location and gradient index of FGM beam are given. The properties of the curves are analyzed.