The Basic Research On Theatomic-scale Finite Method Applies In The Nanoscale Structure

Since the widely used in the nanomaterial and nanodevice, the numerical simulation for microscopic mechanics is a most important mission in nanotechnology. Based on the status, the thesis develops the modeling and numerical simulation in nanoscale of the nanotube. Detailed formulation and implementation are presented as the following:(1) First of all, the thesis introduces the popular numerical simulation methods in the learning field. Then proposing the atomic-scale finite method (AFEM) according to analyze the disadvantages aspects in the numerical simulation methods mentioned above.(2) The thesis develops the atomic-scale finite method. For the interatomic multi-body potential, a one-dimensional atomic chain is introduced to obtain the element stiffness matrix. Especially, the multiscale simulation is a critical problem in AFEM, which including the transitional element. Transitional element ensures the AFEM/FEM multiscale computation method accurately, which represents the material behavior at both atomic and continuum scales. The transitional element can smoothly link the AFEM and FEM elements.(3) The thesis discusses the multiscale method for the analysis of carbon nanotubes. In a two-scale system, the total displacement can be decomposed into two different components- coarse scale and fine scale, in which the coarse component represents by meshfree approximation, then the fine component to be resolved from the molecular dynamics. It is noted that the coarse scale component is present in the entire domain of the problem, and coexists with the fine scale representation in the enriched region. In this multiscale analysis, a virtual atom cluster (VAC) model is also proposed in the coarse scale treatment.(4) The bending mechanical behavior of carbon nanotubes are numerically investigated according to an advanced finite element analysis package, ABAQUS. ABAQUS is used to simulate the formation of the bending carbon nanotubes. Comparing the result from the finite element method and the molecular dynamics, which validates the validity of the finite element method. It investigates that the critical bending curvature is affected by the diameter and the length of the carbon nanotubes. Comparing the result with the molecular dynamics result, this can account for the dependability of the finite element method in simulation the nano-scale problem.