A Local/Nonlocal elasticity model for the euler-bernoulli beam

In this paper a local/nonlocal elasticity model is presented for the statics of the Euler-Bernoulli beam. An integral form of the local/nonlocal elastic constitutive equations for axial deformation and bending are considered with a particular choice of the attenuation function. Equivalent differential forms are proposed, if suitable non standard boundary conditions are considered. New differential equations for axial and transversal displacements for the local/nonlocal elastic Euler-Bernoulli beam are determined, whose order is greater than that of the local case. By imposing the standard and the non standard boundary conditions in terms of new mechanical quantities, it is possible to obtain closed form solutions. Variational formulations enable numerical solutions using the finite element method.