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

Abstract

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-Karman 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 throu...