Static analysis of nanobeams using nonlocal FEM

A very efficiently finite element model is developed for static analysis of nanobeams. Nonlocal differential equation of Eringen is exploited to reveal a scale effect of nanobeams through nonlocal Euler-Bernoulli beam theory. The equilibrium equation of nonlocal beam is derived based on the variational statement. The element stiffness matrix and force vector are presented. The novelty and accuracy of this model is presented and verified. It is found that, this model is more accurate than others and can consider as a benchmark. The effects of nonlocality, boundary conditions, and slenderness ratio are figured out. The deflection of multi-span nanobeam is also illustrated. The present model can be used for static analysis of single-walled carbon nanotubes. Complex geometry and nonlinear boundary conditions can also be included.