A Simplified Stress Analysis of Functionally Graded Beams and Influence of Material Function on Deflection

This paper aims at providing a simplified analytical solution for functionally graded beam stress analysis and optimized material gradation on the beam deflection. The power-law (P-FGM) and exponential (E-FGM) material functions were considered for an exact solution of the normal and shear stress distributions across the beam thickness. Optimization of material function on the FGM beam deflection, which is new of its kind, was also investigated considering both simply supported and cantilever beams. It was observed that the non-dimensional normal stress and shear stress are independent of the elastic moduli values of the constituent materials but rather depends on both the ratio of the elastic moduli and the location across the beam thickness in the E-FGM material function model. This observation was first validated from available kinds of literature and through numerical simulation using ABAQUS and extended to the P-FGM stress analysis. The maximum deflection on the FGM beam occurred for a homogenous steel beam while the minimum deflection was observed on the beam with a P-FGM material function. The results of this work demonstrate that if properly designed and optimized, FGMs can provide an alternative material solution in structural applications.

Vibration characteristics and stable region of a parabolic FGM thin-walled beam with axial and spinning motion

This paper focuses on the vibration characteristics of the parabolic functionally graded material (FGM) beam considering the axially moving and spinning motion. Based on the Hamilton’s principle, the governing equation of the beam is derived. Then, the Galerkin’s method is employed to solve the equation. The combined influence of axial speed, spinning speed, and geometric parameters on natural frequencies of the beam are investigated. What’s more, the axially moving and spinning motion can lead to a critical axial speed and critical spinning angular speed, respectively. These two critical speeds and stable region affected by different parameters are also discussed.

Dynamics of a rotating hollow FGM beam in the temperature field

Dynamic responses and vibration characteristics of a rotating functionally graded material (FGM) beam with a hollow circular cross-section in the temperature field are investigated in this paper. The material properties of the FGM beam are assumed to be temperature-dependent and vary along the thickness direction of the beam. By considering the rigid-flexible coupling effect, the geometrically nonlinear dynamic equations of a hub–FGM beam system are derived by employing the assumed modes method and Lagrange’s equations. With the high-order coupling dynamic model, the effect of temperature variations under two different laws of motion is discussed, and the free vibration of the system is studied based on the first-order approximate coupling model. This research can provide ideas for the design of space thermal protection mechanisms.