Functionally graded Timoshenko nanobeams: A novel nonlocal gradient formulation

A first gradient nonlocal model of bending for Timoshenko functionally graded nanobeams based on the Eringen model is proposed. The material properties vary in the thickness direction. A thermodynamic approach is used to provide the variational formulation of the nonlocal model. The governing equations for nanobeam bending with the relevant higher order boundary conditions are then consistently derived. Analytical solutions of the proposed nonlocal functionally graded nanobeam model are provided for a simply supported beam in terms of rotations and transverse displacements. Current results are then compared with existing ones to establish the validity of the present formulation.