Increasing the bending analysis accuracy of nanobeams employing the nonlocal integral (NI) models is the subject of this paper. It is shown in this study that if the kernel of the NI model is not properly normalized, the natural boundary conditions will be violated and the deflections will be noticeably overestimated. Two kernel normalization procedures, borrowed from other disciplines, are rigorously examined and their influence on the nanobeam deflections is studied in detail. It is shown that one of these procedures, which has recently been used for the analysis of nanobeams, causes the NI model to show both softening and hardening behaviors with unexpected convergence to the classical continuum model for very large nonlocal parameters. This surprising behavior, makes the NI model incapable of being calibrated in some cases and may lead to two distinct calibrated nonlocal parameters which is confusing. This is confirmed here via a comparison with atomistic models. The other normalization scheme shows a consistent softening behavior without such shortcomings and therefore is proposed here for bending analysis of nanobeams. Effect of kernel function distribution, as a representative of interatomic cohesive forces, and edge support condition on the maximum deflection of normalized nonlocal nanobeam model is also thoroughly investigated. Moreover, the effect of surface energy is also investigated via a combined model.

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