  Motivated by the existing complications of finding solutions of Eringen
nonlocal model, an alternative model is developed here. The new formulation of
the nonlocal elasticity is centered upon expressing the dynamic equilibrium
requirements based on a nonlocal residual stress field. This new nonlocal
elasticity is explained from the lattice mechanics and continuum mechanics
points of view. Boundary value problems obtained based on the new nonlocal
elasticity are solved following a proposed iterative procedure. This iterative
procedure is centered upon correcting the solution of the classical field
problem for the nonlocal residual field of the elastic domain. Convergence
analyses are presented to show the convergence of the iterative procedure to
the solution of the nonlocal field problem. The iterative procedure is an
integrated part of the proposed nonlocal elasticity. Therefore, the newly
developed nonlocal elasticity is give the name iterative nonlocal residual
elasticity.

Applied Physics