On the analysis of microbeams

The most widely used theory in the analysis of nanostructures is Eringen's nonlocal elasticity theory. But many researchers have mentioned that this theory has a paradox for the cantilever boundary condition. In order to overcome this paradox, different methods of mathematical complications have been applied. By adding additional parameters to Eringen's nonlocal elasticity theory, enhanced Eringen differential model was developed as an alternative solution method without the necessity of these complications. In this paper, bending of nano/micro beams under the concentrated and distributed loads has been investigated by using Euler Bernoulli beam theory via the enhanced Eringen differential model. Singularity function method is used to calculate the deflection of concentrated and distributed loaded beam. Various types of boundary conditions are considered for the beam such as cantilever, clamped, propped cantilever and simply supported. In each case of boundary conditions, closed form solutions for the bending of the beam are presented for various loading locations. Deflection, bending moment and shear force are presented comparatively for variable loadings in figures and tables.