A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams

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Static and vibration analysis of functionally graded beams using refined shear deformation theory (2013, background): “Li [10] presented a new unified approach for analyzing the static and dynamic behaviours of FG beams with the rotary inertia and shear deformation included.”
Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams (2013, background): “Li [4] investigated static bending deformations and transverse vibrations of FGM Timoshenko beams (TBs) and introduced a function to uncouple governing equations for the deflection and the angle of rotation of a cross-section initially perpendicular to the neutral surface.”
Free vibration characteristics of a functionally graded beam by finite element method (2011, background): “Li [8] presented a new unified approach for analyzing the static and dynamic behaviors of functionally graded beams (FGB) with the rotary inertia and shear deformation.”
The modified couple stress functionally graded Timoshenko beam formulation (2011, background): “From the obtained expressions in the paper it can be deduced that when the thickness of the beam h increases, the response of the modified couple stress Timoshenko beam approaches to the classical one (with available formulation in the literature such as [31]).”