Mechanically based nonlocal Euler-Bernoulli beam model

This paper presents a nonlocal Euler-Bernoulli beam model. It is assumed that the equilibrium of a beam segment is attained because of the classical local stress resultants, along with long-range volume forces and moments exchanged by the beam segment with all the nonadjacent beam segments. Elastic long-range volume forces/moments are considered, built as linearly depending on the product of the volumes of the interacting beam segments and on generalized measures of their relative motion, based on the pure deformation modes of the beam. Attenuation functions governing the space decay of the nonlocal effects are introduced. The motion equations are derived in an integro-differential form by applying Hamilton’s principle. Numerical results are presented for a variety of nonlocal parameters. A comparison with experimental data is also provided.