Analysis Model Of Equivalent Mechanical Properties Of Carbon Nanomaterials Based On Molecular Structural Mechanics

Since discovered in1980s, carbon nanomaterials attracted attention of a numberof researchers because of its excellent properties in mechanics, electricity and otherfields. Some researchers measured the mechanical properties of carbon nanotubes(CNTs) and graphene by experiment, while the others adopted theoretical andnumerical method to study. There are two types of models, discrete model andcontinuum model, widely used by researchers in simulations of CNTs and graphene.The discrete models are accurate but inefficient, while the continuum models, whichconclude beams, shells, et al., possess high efficiency but inaccuracy. This thesis aimsto evaluate the equivalent mechanical properties by discrete models which are basedon molecular mechanics to define the continuum model，then can achieve accurateand efficient analysis model of CNTs and graphene.The main subjects of the thesis are composed of the following parts:1. This thesis derives the relation between molecular mechanical constants andthe mechanical parameters of the two structural models by the use of energyequivalence in a basic cell.2. Based on molecular mechanics, this thesis evaluates the equivalent elasticmoduli and Poisson ratio of graphene, while derives the mechanicalproperties numerically adopting flexible connection model.3. The relationship of CNTs’ equivalent bending stiffness and their chiral,length, diameter and other factors are studied. The consequences derive anumerically inductive formula about CNTs’ equivalent bending stiffnesswhich matches well with the analytic results.4. Adopting the flexible connection model, this thesis analyzes the relationshipof CNTs’ natural mode and their chiral, length, diameter and other factors.The thesis derives the relationship of natural mode and equivalent bendingstiffness and compares with the numerical consequences, which predictsaccurate results of CNTs’ natural mode.Based on molecular structural mechanics model, this thesis analyzes the CNTs’equivalent bending stiffness and modes of vibration discretely adopting Shi’s flexibleconnection model. The thesis also derives a numerically inductive formula about the relationship between CNTs’ equivalent bending stiffness and tensile rigidity, whichyields the results matching well with the analytical solution. This formula providesaccurate parameters for the equivalent continuum model which combines the accuracyof discrete models with the efficiency of continuum model.