Eringen’s nonlocal theory has been widely used for the study of micro- and nano-structures exhibiting size effect phenomena. Eringen’s nonlocal differential constitutive equation has been employed to structural engineering applications, and a number of inconsistencies and paradoxes has been raised. This work centers on exploring static engineering benchmark problems of a nanobeam resting on a Pasternak-type elastic foundation by means of the nonlocal integral elasticity for the first time. The modified kernel’s model and the two phase stress model leading to well-posed problems are used. The static responses of the integral models show to have a flexible behavior in comparison with those of the classic and the nonlocal differential models for all the investigated problems. Neither paradoxes nor inconsistencies are raised for the integral models. The modified kernel highlights the model’s robustness from a physical point of view. The conclusions are promising to spur the applications of nanomaterials, nanocomposites and biomaterials.

Eringen的非局部理论已被广泛用于研究表现出尺寸效应现象的微观和纳米结构。Eringen的非局部微分本构方程已被应用到结构工程应用中，并且引发了许多不一致和悖论。这项工作的重点是首次通过非局部积分弹性来探索基于Pasternak型弹性基础的纳米束的静态工程基准问题。使用了改进的核模型和两相应力模型，这些模型会导致出现适度的问题。对于所有已研究的问题，与经典模型和非局部差分模型相比，积分模型的静态响应都显示出灵活的行为。积分模型既没有提出矛盾也没有矛盾。修改后的内核从物理角度突出了模型的鲁棒性。这些结论有望刺激纳米材料，纳米复合材料和生物材料的应用。