Analysis of large deflection of nanobeams based on the modified couple stress theory by using finite element method

A total Lagrangian finite element formulation was developed for investigating large deflection bending of nanobeams based on the modified couple stress theory. Timoshenko beam theory accompanied by the axial displacement with least kinematic assumptions has been used to model nanobeams. For the first time, the tangent stiffness matrix for nanobeams is extracted based on the modified couple stress theory. The present finite element formulation provides the possibility of solving the problems of nanobeams with arbitrary loading, boundary conditions and cross-sectional variation. The obtained results have been validated with the results reported in the other works. The influence of material length scale parameter on the maximum amount of displacement and rotation of nanobeams is discussed for different ratios of the nanobeam length to the thickness. Besides, for the illustration of abilities of the present formulation, large deflection of a tapered nanobeam under the sinusoidal distributed load for two types of boundary conditions (clamped and simply supported) has been presented.