Numerical modelling of a Timoshenko FGM beam using the finite element method. (2016) - Ziou, Hassina; Guenfoud, Hamza; Guenfoud, Mohamed
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.