ABSTRACT
In this chapter, the significance of the implementation of nanosize devices will be mentioned, and the essential role of such tiny elements in modern engineering designs will be emphasized. Then, it will be proven that the classical theories of solid mechanics (i.e., continuum mechanics theories) are not powerful enough to estimate the mechanical behaviors of a nanostructure. Next, the nonlocal theories of elasticity will be discussed to give knowledge about the physical facts which can be included in a nanomechanical analysis about nanostructures within the framework of each of these theories. Afterward, the mathematical differential equation of each of these hypotheses will be presented to clarify how the small-scale effects on the mechanical response of a tiny element can be covered using size-dependent theories for various simple and smart materials.
