Structural symmetry and boundary conditions for nonlocal symmetrical problems

The paper deals with the determination of the symmetric model and proper boundary conditions for solving nonlocal elastic symmetric structures. The above concepts, in the context of nonlocal integral elasticity, turnout to be different with respect to the standard ones, classically applied when dealing with local elastic symmetric structures. As in fact, when only a symmetric portion of the structure is analyzed, the nonlocal effects induced by the remaining (cut) portions are lost, this enforce to consider for the analysis an enlarged symmetric model on which appropriate nonlocal boundary conditions have to be imposed. It has to be point out how the wideness of such enlarged model depends on the nonlocal material parameters, while the correct unknown nonlocal boundary conditions are here obtained and enforced by an iterative procedure. The accuracy of the proposed approach in solving nonlocal structural symmetric problems is tested with the aid of two numerical examples.