Investigating Deflection of Nano-Cantilevers with Casimir Effect Using Monotone Solution

In this paper a monotone iterative solution is studied for a nano cantilever beam subject to distributed electrical and intermolecular forces. The intermolecular force including the Casimir force is taken into account. An iterative monotone solution base on Green’s function in the form of a nonlinear integral is introduced, to obtain a solution for deflection of a nano cantilever beam. The corresponding nonlinear integral, solved numerically for two typical cases of nano cantilevers. The results compared with numerical results which obtained by boundary value method. The monotone iterative solution can be start from different initial states. By using one of the initial states (u0(x) =0) the monotone solution converged to boundary value solution with less iteration than other initial state.

Keywords:

Nano , Cantilever , Monotone Solution , Numerical