Reserch On Dynamic Modeling And Response Of Carbon Nanotube With The Multi-Scale Method Based On Intrinsic Formulation

With many outstanding mechanical properties that traditional materials is incomparable, Carbon nanotubes(CNTs) is a kinds of promising materials and is expected to be widely used in electronics, medicine, chemical, military, aerospace, and many other fields. The intent of this study is to develop a computationally efficient, dynamic, model of a carbon nanotube for later incorporation into a general framework of simulating the static and dynamic response of the carbon nanotubes.A recently-developed intrinsic beam formulation which is presented by Hodges is introduced in this paper. The formulation would suggest several computational advantages:, such as, a terse form, in first-order form, and easy to meet the boundary conditions, etc. A shooting mehod used for calculating the quasi-static response of CNTs is be presented. The method is capacity of computing three-dimen-sional equilibria of pre-curved non-linear beams. Then, we present a completed intrinsic continua meshfree development for dynamic response of non-linear beams. A point interpolation meshless method is used. In the light of Multi-scale modeling theory, we define a representative volume ele-ment and introduce the modified Morse potentials to fit with the intrisic formulatinon, with that an atomistic-based constitutive is obtained. The balance equations and meshless dynamic equations of the CNTs in intrinsic description are finally derived. With those equations, Equilibrium resonse and dynamical behaivor of CNTs are simulated. Bending, torsion stiffness and Young's modulus are invstigated, the fundamental bending frequency is predicted as well.