Nonlocal elasticity theory for static torsion of the bi-directional functionally graded microtube under magnetic field

The microtubes are important structures in nano electromechanical system .in this study a nonlocal model is presented to investigate the static torsion behavior of microtubes made of bi-directional factionally graded material (BDFGM) subjected to a longitudinal magnetic field. Mechanical properties of BDFGM microtube varies in the radial and longitudinal direction according to an arbitrary function. The governing equation is obtained using the principle of minimum potential energy. a sinusoidal distributed torque and uniform magnetic field with clamped boundary condition are considered to capture the effects of nonlocal parameter, FGM indexes and intensity of longitudinal magnetic field on the torsional angle of BDFGM microtube. The numerical solution of generalized differential quadrature (GDQ) is compared with Galerkin method which a reasonable agreement is observed. Result indicates that intensity of longitudinal magnetic has important role on the torsional angle of microtubes such that when intensity of longitudinal magnetic field increases the torsional angle of microtubes decreases