Mechanical analysis of higher order gradient nanobeams

This paper figures out effective of a new proposed beam element to handle mechanical behaviors of size-dependent nanobeams on the basis of the higher order gradient model. A higher order strain gradient model is derived from the nonlocal Eringen differential equation. The kinematic assumption of nanobeam is proposed by Euler-Bernoulli theory. Galerkin finite element technique is employed for discretizing a beam domain and solves the equation of motion numerically. The output results are compared and verified with those previously published works. Static, buckling and dynamic behaviors of nonlocal and higher order gradient beams are investigated and discussed. Also, the effectiveness of a higher order gradient model to incorporate the size-dependent of nanobeams with different boundary conditions is presented. The applicability of proposed model to analyze a carbon nanotubes is illustrated.