Spatial bending and vibration analyses of functionally graded beam with varying thickness using a meshfree approach

The main purpose of this paper is to investigate the spatial bending and free vibration behaviors of functionally graded (FG) beams with varying thickness. For FG beams consisting of two material components, two types of material mixing rules are assumed: the material properties for the first type vary along the thickness direction and the material properties for the second type vary along the thickness direction and the axial direction. Hamilton's principle is adopted to derive the governing equations and boundary conditions of FG beams, whose displacement field is approximated by a meshfree moving least squares Legendre (MMLSL) shape function. Through some numerical examples, it is verified that the proposed method is effective to predict the spatial bending and vibration behaviors of FG beams with varying thickness. Finally, the effects of some parameters such as thickness gradient, power law index and boundary condition on the bending and vibration responses of FG beams are investigated.