Large deflection analysis of nanowires based on nonlocal theory using total Lagrangian finite element method

A model based on a nonlocal theory is developed for the large deflection analysis of nanowires for the first time. The nonlocal differential equation of Eringen is used as the nonlocal constitutive equation. Shear deformation is introduced by using the Timoshenko beam theory. The governing equations are derived by the variational formulation. The total Lagrangian finite element formulation is applied as a numerical method for the solution of the problem. In addition, a novel approach is used to overcome the difficulty in modeling concentrated loads on a nanowire with nonlocal theory. Several examples are presented for both of the small and large deflections. The numerical results for small deflections are verified with the results reported in the literature. The numerical results for large deflections can be used as benchmark.