Mixed finite element analysis of nonlocal Euler–Bernoulli nanobeams

• The size-dependent behaviour of nanobeams is investigated by using nonlocal theory and Euler–Bernoulli beam theory.
• The mixed finite element method is proposed to overcome the confusing fact of nonlocal beam model subjected to concentrated load.
• The numerical results indicate that the proposed method is successful to describe static response of nanobeams subjected to concentrated load.

This paper aims to present the mixed finite element method for the static analysis of nanobeams. The size-dependent effect of nanostructures is taken into consideration by nonlocal continuum theory. The governing equation is derived for Euler–Bernoulli beam theory incorporated with nonlocal theory. The present mixed finite element method is first introduced to overcome the concentrated loading problem of nonlocal beam which is a major limitation of the regular finite element formulation. Numerical results are obtained and compared with previously published works to show the applicability and accuracy of the present model. By introducing two coefficients α1 and α2, the mixed finite element model could be useful to describe the static responses of nanobeams.