INVESTIGATIONS ON THE MECHANICAL CHARACTERISTICS OF NANOBEAMS BASED ON THE NONLOCAL STRAIN GRADIENT THEORY¹⁾

A size-dependent mechanical model of nanobeam is built within the framework of the nonlocal strain gradient theory. The present model considers the nonlocal effects of the strain field and first gradient strain field, as well as the high-order shear deformation effect. Governing equations and boundary conditions are derived simultaneously by using Hamilton’s principle. The Navier-type solutions are developed for nanobeams with simply-supported boundary conditions. Parametric studies are performed to exhibit the static bending, free vibration and linear buckling behaviors of nanobeams with different groups of geometrical and material parameters. It is found that the non-local effect produces a softening effect on the stiffness of the beam while the strain gradient effect produces a hardening effect, the stiffness of nanobeams is significantly dependent on the ratio between the nonlocal parameter and strain gradient parameter. In addition, the stiffness-hardening or stiffness-softing effects become increasingly significant as the thickness is close to the material characteristic and can be negligible when the thickness is sufficient large.