  Complications exist when solving the field equation in the nonlocal field.
This has been attributed to the complexity of deriving explicit forms of the
nonlocal boundary conditions. Thus, the paradoxes in the existing solutions of
the nonlocal field equation have been revealed in recent studies. In the
present study, a new methodology is proposed to easily determine the elastic
nonlocal fields from their local counterparts without solving the field
equation. This methodology depends on the iterative-nonlocal residual approach
in which the sum of the nonlocal fields is treaded as a residual field. Thus,
in this study the corrections of the local-linear elastic fields for the
nonlocal residuals in materials are presented. These corrections are formed
based on the general nonlocal theory. In the context of the general nonlocal
theory, two distinct nonlocal parameters are introduced to form the
constitutive equations of isotropic-linear elastic continua. In this study, it
is demonstrated that the general nonlocal theory outperforms Eringen-nonlocal
theory in accounting for the impacts of the material Poisson ratio on its
mechanics. To demonstrate the effectiveness of the proposed approach, the
corrections of the local static bending, vibration, and buckling
characteristics of Euler-Bernoulli beams are derived. Via these corrections,
bending, vibration, and buckling behaviors of simple-supported nonlocal
Euler-Bernoulli beams are determined without solving the beams equation of
motion.
