Flexural stress analysis of uniform slender functionally graded material beams using non-linear finite element method

Functionally graded material (FGM) typically consists of two constituent materials combined together with a particular distribution. A non-linear flexural stress analysis of through-thickness functionally graded uniform slender beam, subjected to a uniformly distributed load, is studied using the versatile finite element method based on Euler-Bernoulli beam hypothesis. The von-Kármán strain-displacement relations are used to account for geometric non-linearity. Simply supported and clamped FGM beams with axially immovable ends are considered. Governing non-linear equations are obtained using the principle of virtual work. Numerical results are provided to show the effect of boundary conditions and volume fraction exponent on the non-linear structural behaviour, in terms of the strains and stresses, of the FGM beams, for the first time. A shift in the neutral axis, from the mid-thickness of the beam, is observed due to the large transverse deflections, for the homogenous as well as the FGM beams. The through thickness variation of the axial stress is observed to be non-linear for the FGM beams contrary to that of the homogenous beams, for which the axial stress variation is linear. The through thickness sudden change in the material properties, governed by higher values of volume fraction exponent, results in a steep gradient in the axial stress variation through the thickness of the FGM beam. © 2012 Copyright Taylor and Francis Group, LLC.