Analysis of axially functionally graded nano-tapered Timoshenko beams by element-based Bernstein pseudospectral collocation (EBBPC)

In this paper, static bending, buckling and free vibration of axially functionally graded (AFG) nano-tapered Timoshenko (NTTB) or Bernoulli Euler (NTEB) beams are examined based on the nonlocal Timoshenko beam theory (NTBT). This theory incorporates the length scale parameter (nonlocal parameter) to capture the small-scale effect. The material properties and geometry properties of the nanobeam are assumed to vary along the length direction. The governing equations and the associated boundary conditions are derived using Hamilton’s principle. The model is then applied on the studies of static, buckling and free vibration analysis of NTTB or NTEB using element-based Bernstein pseudo-spectral collocation approach (EBBPC). After the Bernstein pseudo-spectral collocation method is validated, detailed numerical analyses about the effect of boundary conditions, load types are carried out. Non-local parameter and axial load effects on the static and dynamic response of AFG-NTTB and AFG-NTEB are discussed. The approach is tested on benchmark problems of static, buckling and free vibration analyses, showing high accuracy.