Eringen's nonlocal theory for nonlinear bending analysis of
bi-directional functionally graded Timoshenko nanobeams
Abstract
In this paper, the nonlinear static analysis of Timoshenko nanobeams
consisting of bi-directional functionally graded material (BFGM) with
immovable ends is investigated. The scratching in the FG nanobeam
mid-plane, is the source of nonlinearity of the bending problems . The
non-local theory is used to investigate the nonlinear static deflection
of nanobeam. In order to simplify the formulation, the problem formulas
is derived according to the physical middle surface. The Hamilton
principle is employed to determine governing partial differential
equations as well as boundary conditions. Moreover, the differential
quadrature method (DQM) and direct iterative method are applied to solve
governing equations. Present results for nonlinear static deflection
were compared with previously published results in order to validate the
present formulation. The impacts of the nonlocal factors, beam length
and material property gradient on the nonlinear static deflection of BFG
nanobeams are investigated. It is observed that these parameters are
vital in the value of the nonlinear static deflection of the BFG
nanobeam.