**2.11 Torsional statics and dynamics of circular nanostructures**

Newer technologies for developing advanced materials [13] and structures are advancing towards a minute length scale (i.1., micro – or nano – scale). This is the root of nanotechnology. By reducing the size of the materials, the materials exhibit specific and interesting non classical mechanical, chemical and electrical properties. The classical continuum theories fail to replicate the minute length scale [13]. Hence explicitly new continuum mechanics /atomic dynamic simulation are required. Erignen developed Non local elasticity theory as one of the continuum models. In this research, the torsional static and dynamic nonlocal effects for circular nanostructures for concentrated and distributed torques were investigated based on nonlocal elasticity stress theory [13]. Variational energy principle is obtained to derive governing differential equation and strain energy and kinetic energy components are obtained. A new nonlocal finite element method (NL-FEM) had been developed to solve integral nonlocal equation. The statics and dynamics of nonlocal nanoshafts, nanorods, and nanotubes with various loads and boundary conditions revealed possible numerical solutions which were compared with analytical solutions.
