comparison of different local unrefined beam theories for bending and nano beams buckling analysis

In this study, non unified local shear deformation theory is proposed to consider the bending and buckling of nano beams. This theory is based on the assumption that the cross-sectional and planar displacements consist of bending and shear components, shear components do not contribute to the bending moments. Motion equations are derived using the Hamilton’s principle. Analytical solutions for deformation, buckling load, and the natural frequency are presented to a nano simply supported beam, and the results obtained are compared to those proposed by the nonlocal Timoshenko beam theory and Reddy beam theories