A simplified UI element using third-order Hermitian displacement field for static and free vibration analysis of FGM beam

Abstract A new two-node, 3 DOF per node beam element based on the unified and integrated (UI) approach of first-order shear deformation theory (FSDT) is developed for axial-bending-shear functionally graded material (FGM) beams. In this approach, to bridge the Timoshenko and Bernoulli beam theory smoothly, the total displacement v is split into bending displacement vb and shear displacement vs. A 3rd-degree polynomial C1 Hermitian function is used to approximate the bending displacement vb, and other derived variables are expressed in terms of bending displacement, leading to a shear-locking free state. Four types of beam support, i.e., hinged-roll, clamped-free, clamped-clamped, and clamped-hinged, are used to investigate how the displacement and natural frequency are affected by the variation of the power-law exponent and beam length-to-height ratio. Results of numerical analysis are compared with the published literature to evaluate the validity and robustness of the model theory for static and free vibration analysis. The numerical analysis confirms the presence of coupled axial-bending in static and vibration analysis of FGM beam. The comparison studies verify that the proposed element is: a) accurate and comparable with the literature; b) of fast convergence to the reference; c) valid for thin and thick beams.