Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures

Scale effect on static deformation of micro- and nano-rods or tubes is revealed through nonlocal Euler–Bernoulli beam theory and Timoshenko beam theory. Explicit solutions for static deformation of such structures with standard boundary conditions are derived. Results show that the scale effect would not manifest itself for micro-structures with length of the order of micro-meters, however, will be noticeable for nano-structures in their static responses. In addition, the shear effect is evident for nano-structures, especially for carbon nanotubes in most of current references, indicating the importance of applying higher-order beam theory in static analysis of nano-structures.