Capturing the effect of thickness on size-dependent behavior of plates with nonlocal theory

The effective elastic properties of nano-structures are shown to be strongly size-dependent. In this paper, using a three dimensional strong nonlocal elasticity, we have presented a formulation to capture the size-dependent behavior of plate structures as a function of their thickness. This paper discusses some new aspects of employing a three dimensional nonlocal formulation for analysis of plates, namely, the confining of the nonlocal kernel in the near-boundary regions at the two surfaces of the plate. To address this aspect, we have studied two different types of nonlocal kernels, one bounded in a finite domain of the structure and the other, non-bounded. This study shows that the influence of the plate's thickness on its bending stiffness can be captured within the nonlocal elasticity framework, and this influence highly depends on the bounding of the nonlocal kernel. Particularly, for a uniformly deformed plate with a homogeneous isotropic material, using the nonlocal formulation with the bounded domain reflects the physics of the problem better.