Iterative Nonlocal Residual Elasticity

Abstract

Motivated by the existing complications of finding solutions of Eringen’s 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 given the name “iterative nonlocal residual elasticity”.