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研究生： 雷詠妮
RAJESH, AJANI KAJAL
論文名稱： 以非線性有限元素法估測奈米錐之機械與熱性質
Estimation of Mechanical and Thermal Properties of Nanocone by using nonlinear Finite Element Method
指導教授： 胡潛濱
Hwu, Chyan-Bin
學位類別： 碩士
Master
系所名稱： 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年： 2018
畢業學年度： 106
語文別： 英文
論文頁數： 68
外文關鍵詞： Carbon Nanotubes, Carbon Nanocones, Molecular Mechanics, Finite Element Method, Mechanical Properties, Thermal Properties
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    • In this thesis, mechanical and thermal properties of carbon-based nanostructures such as carbon nanotubes and carbon nanocones are investigated by using a molecular mechanics based 3D finite element (FE) analysis. The proposed molecular mechanics based finite element approach links the molecular mechanics and structural mechanics, and is based on simulating the covalent bonds between carbon-carbon atoms with Timoshenko beam elements. The harmonic and modified Morse molecular mechanics potential functions are used for small and large deformation problems. Mechanical properties (Young’s modulus, shear modulus, Poisson’s ratio, and ultimate strength), and thermal properties (Coefficient of thermal expansion and specific heat) of carbon nanotubes, and carbon nanocones are investigated by using molecular mechanics based finite element approach. It is shown that the tube diameter, length, and chirality affects the mentioned properties and for nanocone, different apex angles, cone length and top radius affects the mentioned properties.

    ABSTRACT i TABLE OF CONTENTS iii LIST OF TABLES vi LIST OF FIGURES vii NOMENCLATURE x CHAPTER 1 INTRODUCTION 1 1.1 Problem statement 1 1.2 literature review 1 1.3 Structure of thesis 5 CHAPTER 2 ATOMIC STRUCTURES OF CARBON NANOTUBES AND CARBON NANOCONES 6 2.1 Carbon nanotube structures 6 2.2 Carbon nanocone structures 8 CHAPTER 3 FINITE ELEMENT MODELLING 12 3.1 Linear beam element with harmonic potential 12 3.2 Nonlinear beam element with modified Morse potential 14 CHAPTER 4 FORMULATION AND IMPLEMENTATION 17 4.1 Mechanical properties of CNCs 17 4.1.1 Expression of young’s modulus 17 4.1.2 Expression of shear modulus 19 4.1.3 Expression of Poisson’s ratio 20 4.1.4 Expression of Strength 21 4.2 Thermal properties of CNCs 21 4.2.1 Expression of coefficient of thermal expansion 22 4.2.2 Expression of specific heat 25 4.2.3 Application of FEM to get natural frequency 26 4.3 Implementation in ANSYS 28 4.3.1 Young’s modulus 28 4.3.2 Shear modulus 29 4.3.3 Poisson’s ratio 30 4.3.4 Strength 30 4.3.5 Simulation steps 30 CHAPTER 5 RESULTS & DISCUSSIONS 32 5.1 Mechanical properties of carbon nanotubes 32 5.1.1 Young’s Modulus 32 5.1.2 Shear Modulus 35 5.1.3 Poisson’s Ratio 36 5.1.4 Ultimate strength 37 5.2 Thermal properties of carbon nanotubes 38 5.2.1 Coefficient of thermal expansion 38 5.2.2 Specific heat 43 5.3 Mechanical properties of carbon nanocones 44 5.3.1 Young’s modulus and shear modulus 44 5.3.2 Poisson’s Ratio 50 5.3.3 Ultimate strength 50 5.4 Thermal properties of carbon nanocones 52 5.4.1 Coefficient of thermal expansion 52 5.4.2 Specific heat 59 CHAPTER 6 CONCLUSIONS 62 REFERENCES 65

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