Size-dependent static characteristics of multicrystalline nanoplates by considering surface effects

Nanostructures have been receiving extensive attention during the last two decades, due to their peculiar mechanical and other physical properties as compared with other macrostructures and macrosystems. The mechanical properties of nanostructures are intensely size-dependent. Furthermore, in the absence of external forces, nanostructures have a great tendency to deform due to their surface effects. Moreover, since the atoms on the surface have different equilibrium configuration from that of in the bulk, the elastic stiffness of the surface can be different from that of the bulk. In this study an ultra-thin plate of nanoscale thickness with an arbitrary geometry and boundary conditions is analyzed. A rectangular plate with nanoscale thickness is presented. In order to generalize the study, a multicrystalline plate with varying crystal properties has been assumed. Furthermore, the mechanical properties of the plate are dependent on the orientation. In fact the multicrystalline nanoplate is an anisotropic plate. The shapes and orientations of each crystal have been chosen haphazardly. However, the entire shape of the plate is a rectangle of microdimension with nanothickness. Due to the fact that silicon is much more applicable than any other material in Nanoelectromechanical systems (NEMS), it is assumed that the plate is made of silicon. The plate is subjected to a static load and the deformation as well as the corresponding strain is demonstrated. Due to the fact that the governing equation of the plate and its solution is not too straightforward to be solved easily, the finite element method is implemented so as to obtain the corresponding results. The results which have been achieved by the method of finite element and by employing the ANSYS software are illustrated and compared. Accordance of the results is quite remarkable.