1) To develop mechanistic models incorporating surface effects based on Gurtin-Murdoch continuum theory for analysis of nano-scale beams by means of the principle of equilibrium.
2) To verify the governing equation and identify admissible boundary conditions of nano-scale beams by means of the variational formulation. In addition, analytical solutions for nano-scale beams with different end boundary conditions are to be re-derived and examined.
3) To employ the nano-scale beam model and solutions obtained from 1) and 2) to investigate the influence of size effect and end boundary conditions on the response of nanobeams.
4) To develop mechanistic models incorporating surface effects based on Gurtin-Murdoch continuum theory for static and dynamic analysis of nano-scale rectangular plates.
5) To construct analytical and finite element (FE) solutions for static and dynamic analysis of nano-scale rectangular plates.
6) To employ the nano-scale rectangular plate model and solutions obtained from 4) and 5) to investigate the influence of size effects and boundary conditions on static and dynamic responses of rectangular nanoplates.
