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-Ka´rma´n 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.

Thermal Stress Compensation for an Aircraft Engine Duct System Based on a Structural Redesign of Tie Rods

“…Since the above-established model involves elastic-plastic deformation and contact problems, Static Structural and its built-in Newton-Raphson method [31][32][33][34][35][36][37] were used…”

“…Since the above-established model involves elastic-plastic deformation and contact problems, Static Structural and its built-in Newton-Raphson method [31][32][33][34][35][36][37] were used to calculate the von Mises stress of the duct system [38][39][40][41][42][43], and stress calculation results were obtained under the characteristic operating conditions of the duct system [44].…”

Non-Linear Structural Analysis of Shear Flexible FGM Beams

“…Two separate beam formulations, one neglecting shear flexibility effects (Euler-Bernoulli) and the other considering shear flexibility effects (Timoshenko) are developed. The details of Euler-Bernoulli beam theory are available from Anandrao [9]. The details of Timoshenko beam formulation are presented here.…”

“…They considered FGM beams with axially immovable ends with simply supported as well as clamped boundary conditions. A non-linear static analysis of uniform slender FGM beams was presented by Anandrao [9] using the finite element method. They established non-linear loaddeformation paths for various boundary conditions.…”

Post-Buckling Analysis of Axially Functionally Graded Three-Dimensional Beams

“…Askari et al [2012] studied nonlinear natural oscillations of FG beams with considering the Euler-Bernoulli beam theory and von Karman geometric nonlinearity. Anandrao et al [2012b] investigated nonlinear flexural stress analysis FG Euler-Bernoulli beams by using the versatile finite element method in the framework the von-Kármán strain-displacement relation. Ke et al [2012] investigated the nonlinear vibration of edge cracked FG Timoshenko beams by using differential quadrature method.…”