有限元素法計算奈米碳管力學性質

Mechanical Properties of the Carbon Nano-Tube with Finite Element Method

劉羽軒(Yu-Hsuan Liu)

指導教授 ： 林輝政

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.02848

摘要

本文以碳-碳鍵的能量曲線為出發點，配合結構力學對奈米碳管的基本力學性質，包括楊氏係數、剪力模數及自然振頻等做探討。本文簡述奈米碳管結構外觀，包函了扶手倚奈米碳管、鋸齒奈米碳管和對掌奈米碳管，並以石墨平面晶格向量捲曲成奈米碳管，計算晶格向量與奈米碳管半徑之相對關係，進一步利用碳-碳鑑結向量關係，計算不同半徑奈米碳管鍵角與鍵長，經計算發現半徑越大，鍵角與鍵長會趨近於石墨平面。而搭配Tersoff能量公式，以計算不同半徑奈米碳管之鍵結參數，再以能量函數相等關係，可把分子力學與結構力學連接起來，本文利用套裝軟體ANSYS進行有限元素法數值模擬計算奈米碳管之楊氏係數與剪力模數，本文發現奈米碳管半徑越大，楊氏係數與剪力模數則趨近於一定值。本文同時也計算奈米碳管前八個模態自然振頻，並發現奈米碳管在微小的變形量下，奈米碳管自然振頻有明顯的改變。

關鍵字

楊氏係數 ； 剪力模數 ； 分子力學 ； 有限元素 ； 奈米碳管

並列摘要

In the study, the energy curve of carbon-carbon bonding is expressed. Then, the mechanical properties such as Young’s modulus, shear modulus and nature frequencies of nano-tubes are investigated by structural mechanics. Further, the nano-tubes including armchair, zigzag and chiral are described in the study. The nano-tube is shaped from rolling graphite lattice. The relation between lattice vectors and radius of nano-tube had been calculated. Thus, the bonding angles and length of nano-tube with various radiuses could be estimated by the relation. In the results, if the radius of nano-tube is large, the bonding angles and length of nano-tube is very close to those of graphite sheet. Moreover, the bonding parameters of nano-tube with various radiuses are also evaluated by Tersoff’s potential energy Equations. Therefore, the molecule mechanics and structural mechanics can be cooperated from the energy function. Furthermore, the FEM software, ANSYS, is used in simulation. In the numerical results, if the radius of a nano-tube is large, the Young’s modulus and shear modulus will tend to constants. Further, the nature frequencies of nano-tube, from the first mode to the eighth, had been also calculated in the study. In the results, the nature frequencies of nano-tube could vary with the change of the radius of nano-tube.

並列關鍵字

shear modulus ； molecule mechanics ； structural mechanics ； carbon nanotube

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