In this paper the Finite Element Method (FEM) for the mechanically-based non-local elastic continuum model is proposed. In such a model non-adjacent elements are considered mutually interacting by means of central body forces that are monotonically decreasing with their interdistance and proportional to the product of the interacting volume elements. The resulting governing equation is an integro-differential one and for such a model both kinematical and mechanical boundary conditions are exactly coincident with the classical boundary conditions of the continuum mechanics. The solution of the integro-differential problem is framed in the paper by the finite element method. Finally, the solution obtained in the context of FEM is compared with finite difference method (FDM)
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