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

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