Title: Numerical modelling of a Timoshenko FGM beam using the finite element method

Authors: Hassina Ziou; Hamza Guenfoud; Mohamed Guenfoud

Addresses: Department of Civil Engineering, University of Biskra, B.P. 145, R.P. 07000, Biskra, Algeria ' LGCH Laboratory, University of 08 May 1945, Guelma, Algeria ' LGCH Laboratory, University of 08 May 1945, Guelma, Algeria

Abstract: Functionally graded material (FGM) beams possess a smooth variation of material properties due to continuous change in micro structural details. The variation of material properties is along the beam thickness and assumed to follow the power-law. An exact element based on the first order shear deformation theory was developed. The finite element method is used here to study extensively the static analysis. A cantilever beam subjected to a concentrated force P at the free end for different length-to-thickness ratio has been chosen here for the analysis. For each example, Poisson's ratio of the P-FGM beam is assumed to be varied continuously throughout the thickness direction according to the power law, and other time it is held constant. Timoshenko beam theory is used to capture the shear deformation. The governing equations and boundary conditions are derived from virtual work principle. In this study, the influences of the volume fraction index, length-to-thickness ratio and the Poisson's ratio on the mid plane deflections, stresses distribution and strain energy along the thickness of FGM beam are examined.

Keywords: functionally graded materials; FGM; power law; finite element method; FEM; Timoshenko beam theory; numerical modelling; shear deformation; cantilever beams; volume fraction index; length-to-thickness ratio; Poisson ratio; mid plane deflections; stress distribution; strain energy.

DOI: 10.1504/IJSTRUCTE.2016.077719

International Journal of Structural Engineering, 2016 Vol.7 No.3, pp.239 - 261

Received: 20 Jul 2015
Accepted: 27 Oct 2015

Published online: 13 Jul 2016 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article