Non-linear Bending Of Ultra-Thin Plate-Type Nano-Materials

Based on a quasi-continuum model incorporating the effect of surface for ultra-thin plate-type cubic crystal nano-materials proposed by Nie, this thesis presents deformation energy of non-linear bending of such a plate-type structure and fundamental governing equations with the aid of the variational principle. The use of the asymptotic iteration leads to an asymptotic solution for the non-linear characteristic relation between the uniform pressure and the central displacement (deflection) of the clamped nano-plate for the case of cylindrical bending. In contrast, a closed-form analytical solution for the continuum structure is derived on the basis of classical large deflection theory of plate. In addition, a corresponding finite element model (lattice model) is constructed to simulate the behavior of the structure and acquire the numerical results using ANSYS code. Both the quasi-continuum and classical models are compared with the finite element model. The results show that the present model is valid for simulating the large deformation of such plate-type nano-structured materials, and the classical theory must be modified when used for the ultra-thin nano-plate structures.