Nonlinear Bending of FCC Nanoplates Based on a Quasi-Continuum Model

A quasi-continuum model of plate-type nanomaterials with the face-centered cubic crystal structures is proposed in this paper. The fundamental governing equations for the nonlinear bending of the nanoplates are given by using the principle of minimum potential energy. Specifically, the analytical solution is derived for cylindrical bending deformation of the structure under uniform transverse loading fixed at two sides based on the modified iterative method. A lattice finite element model is established to verify the present quasi-continuum model. Meanwhile, the corresponding solution by adopting the classical continuous plate theory is presented, in which two cases are considered for use of bulk values (limit values) and nanovalues of both elastic modulus and Poisson's ratio. The difference among the quasi-continuum and continuous models are discussed by computation.