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.

中文翻译：

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适当核归一化程序在纳米梁非局部积分连续体建模中的重要性

使用非局部积分 (NI) 模型提高纳米梁的弯曲分析精度是本文的主题。本研究表明，如果 NI 模型的内核没有正确归一化，自然边界条件将被违反，挠度将被明显高估。严格检查了从其他学科借用的两个核归一化程序，并详细研究了它们对纳米束偏转的影响。结果表明，最近已用于分析纳米梁的这些程序之一导致 NI 模型显示软化和硬化行为，并意外收敛到非常大的非局部参数的经典连续模型。这种令人惊讶的行为，使 NI 模型在某些情况下无法校准，并可能导致两个不同的校准非局部参数令人困惑。这是通过与原子模型的比较在这里得到证实的。另一个归一化方案显示出一致的软化行为，没有这些缺点，因此这里建议用于纳米梁的弯曲分析。还彻底研究了核函数分布（代表原子间内聚力）和边缘支撑条件对归一化非局部纳米束模型的最大偏转的影响。此外，还通过组合模型研究了表面能的影响。另一个归一化方案显示出一致的软化行为，没有这些缺点，因此这里建议用于纳米梁的弯曲分析。还彻底研究了核函数分布（代表原子间内聚力）和边缘支撑条件对归一化非局部纳米束模型的最大偏转的影响。此外，还通过组合模型研究了表面能的影响。另一个归一化方案显示出一致的软化行为，没有这些缺点，因此这里建议用于纳米梁的弯曲分析。还彻底研究了核函数分布（代表原子间内聚力）和边缘支撑条件对归一化非局部纳米束模型的最大偏转的影响。此外，还通过组合模型研究了表面能的影响。