Finite Element Analysis of Non-Uniform Beam Made of Axially FGM Subjected to Multiple Loads

Abstract

The dynamic response of non-uniform Timoshenko beams made of axially functionally graded materials subjected to multiple moving point loads is studied by using the finite element method. The material properties are assumed to vary continuously in the axial direction according to a power law. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials obtained from the governing differential equations of a homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving loads. The effects of the distance between the moving loads, material non-homogeneity, section profile as well as aspect ratio on the dynamic response of the beams are investigated in detail and highlighted.