A gradient model for torsion of nanobeams

A first-order gradient model based on the Eringen nonlocal theory is presented. The variational formulation, the governing differential equation and both classical and non-classical boundary conditions of nonlocal nanobeams subjected to torsional loading distributions are derived using a thermodynamic approach, thus providing closed-form solutions. Nanocantilevers and fully campled nanobeams are considered to investigate the size-dependent static behavior of the proposed model in terms of torsional rotations and moments. The results are thus compared to those of the Eringen model, gradient elasticity theory and classical (local) model.