本文利用多壁奈米碳管之有限元素模型來估測其各種力學性質，諸如楊氏係數、剪力模數、自然頻率、臨界挫屈力等力學性質。其研究方法為將奈米碳管模擬成空間構架，將其連結兩相鄰原子之共價鍵結等效為樑元素，而本文由能量等效原理連結分子力學和結構力學來計算此樑元素的材料性質。而在多壁碳管中的層間凡得瓦爾力則以彈簧元素模擬，其中勁度值以Lennard-Jones勢能函數為基礎所推導出之碳管層間壓力-距離的關係式來進行推算，本文在微小變形的前提下取層間壓力-距離關係式的線性部份，將層間壓力等效成彈簧力，進而計算取得彈簧之勁度值。在定義了元素的力學性質之後，接著再建立起各種不同尺寸的雙壁奈米碳管有限元素模型(依此原理，可建立起三層壁或更多層壁以上之碳管有限元素模型)，再經由有限元素分析後，則碳管的軸向楊氏係數、徑向楊氏係數、剪力模數以及自然頻率和臨界挫屈力可經由分析後的結果去推算出來。為了驗證有限元素分析所估測的碳管力學性質的正確性，我們也以已知的單壁碳管楊氏係數配合力學理論去推算其餘不同的碳管力學性質，例如自然頻率、臨界挫屈力等，並和相關文獻上的結果相互比較，其結果顯示本文使用有限元素法所估測出的碳管力學性質具有相當的吻合度，同時也驗證了本研究方法的有效性與準確性。

Finite element models of multi-walled carbon nanotubes (MWCNTs) are established and the mechanical properties, such as Young’s moduli, shear moduli, natural frequencies and buckling loads etc., of MWCNTs are computed by these models. Individual carbon nanotube is simulated as a frame-like structure and the primary bonds between two nearest-neighboring atoms are treated as beam members. The beam properties for input into the finite element model are calculated via the concept of energy equivalence between molecular dynamics and structural mechanics. The effect of the interlayer van der Waals forces represented in terms of the interlayer pressure based on Lennard-Jones potential are simulated by spring elements. The stiffness of the spring elements is derived from the equivalent force concept between the interlayer pressure and the spring forces under the assumption of small deformation such that the variation of the van der Waals force confined to a linear region. Then, finite element models of doubled-walled carbon nanotubes with different sizes are established (the procedure can be extended to the modeling work of triple or above-walled carbon nanotubes), and the axial Young’s moduli, shear moduli, radial Young’s moduli etc., as well as the natural frequencies and buckling loads of the different tubes are computed from the numerical results. Possible verifications of some of the above results by analytical solutions are also performed. The comparison of the estimated mechanical properties to the analytical solutions or the results found in the existing literatures shows good agreement, which can be used to illustrate the effectiveness and accuracy of this approach.

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