Nonlocal integral elasticity for third-order small-scale beams

Small-scale beams are basic structural components of miniaturized electro-mechanical systems whose design requires accurate modeling of size effects. In this research, the size-dependent behavior of nonlocal elastic beams is investigated by adopting the stress-driven elasticity theory. Kinematics of beams is modeled by the Reddy variational third-order beam theory accounting for the effective distribution of shear stresses on cross sections without needing the evaluation of shear correction factors. Stress-driven integral elasticity is thus extended to third-order small-scale beams providing an equivalent constitutive formulation with boundary conditions. The relevant nonlocal elastic equilibrium problem is formulated and an analytical strategy is proposed to obtain closed-form solutions. The present approach is elucidated by solving some structural problems of current interest in Nanotechnology.