Nonlocal integral static problems of nanobeams resting on an elastic foundation

Abstract

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.