Analysis of stationary and axially moving beams considering functionally graded material using micropolar theory and Carrera unified formulation. (1st September 2021) - Daraei, Behnam; Shojaee, Saeed; Hamzehei-Javaran, Saleh
Highlights: Finite element formulation based on Carrera unified formulation and micropolar theory. Taylor-like and Lagrange polynomials in terms of the cross-section coordinates. Material properties are assumed to be graded over the thickness of the beam. The proposed approach facilitates employing higher orders theories. Any order of expansions and also any order used to reach suitable results. Abstract: In this paper, finite element analysis of stationary and axially moving beams using micropolar theory is studied, and a higher order model based on Carrera unified formulation (CUF) approach is proposed and tested. Taylor-like and Lagrange polynomials in terms of the cross-section coordinates are employed to approximate the displacement and micro-rotation unknowns. Linear approximation along the beam axis is introduced to derive finite element matrices. Material properties are also assumed to be graded over the thickness of the beam. The stiffness, mass and gyroscopic matrices are derived in terms of fundamental nuclei, which are independent of type and order of the expansions used. Moreover, several numerical examples of both static and free vibration analysis, considering different boundary conditions, are presented. The effect of the travelling speed on the natural frequencies and beam stability is also important, which is demonstrated here. The equations can be used to analyze the beam structures in macro-, micro-, and nano-scale through taking the micropolar couple stress and micro-rotation effects into account.