近年來，在科技進步之帶領下已有許多奈米等級結構被製造出來。但礙於現今奈米等級量測技術仍無法有突破性之發展，以致於至今尚且無法完整地描述奈米尺度下材料的特性。因此諸多學者為瞭解奈米結構材料特性，進而提出各式模擬分析法及勢能函數，以供描述材料處於奈米尺度下之機械性質。
本研究採有限元素法及原子等效理論，探討奈米尺度下材料的楊氏係數及尺寸效應，並比較奈米材料與塊材材料的差異處。此法可簡化晶體結構模型，亦能兼顧計算精確度及效率。本文採用摩斯勢能函數描述原子間吸斥力情形，並以彈簧元素取代原子間作用力的關係，再將各原子等效為節點。進而利用此法來比較，探討同樣材料於單一晶格結構與不同尺寸結構機械性質的差異。分析結果發現，尺寸的改變將影響整體結構的鍵結數目，而使得材料性質亦隨之改變。
本研究建立銅金屬晶體結構(100)、(110)、(111)各晶格面模型後，分別分析比較各晶格面的楊氏係數，再對於銅金屬於塊材結構與與奈米尺度下材料性質的差異進行探討分析。研究結果發現，所獲得之數值解與目前文獻上之楊氏係數已相當接近，亦由此結果得以驗證此方法的可行性。
此次分析方式係採有限單元數值解。計算結構在承受拉伸下所得之反力，並以虎克定律推算材料的楊氏係數；另一方面則利用晶體結構之模態分析，推算其楊氏係數。並比較上述兩種方法計算所得之楊氏係數再行互相佐證。
本研究探討隨著點缺陷分佈的不同對於模態的影響程度。而其分析結果顯示，當空缺缺陷發生於自由端時，隨著結構的差異，使得由自由共振頻率所獲得的材料楊氏係數將會較承受拉力下所獲得之楊氏係數高。另外，在處理含點缺陷狀況下之結構體，因該結構體承受拉伸負載下，此結構體因點缺陷分佈的差異，使得結構位移分佈狀況與晶格滑移面有相似之位移行為發生，而本研究亦藉此結果延伸探討其可能發生此行為之原因。

In recent years, there has been much advancement in the field of science and technology. As a result, many nanostructures have been manufactured. However, current measurement systems are still not accurate enough to describe the physical behavior of these nanostructures. Scholars thus developed a renewed interest in the field of potential function in describing the diatom interaction.
In light of this, the current study uses finite element methods (FEM) and the atomistic-continuum mechanics method (ACM) to explore Young’s modulus, and the size effect of nanostructures. This method could examine the nanostructures’ mechanical properties with high efficiency and accuracy. The diatom binding energy is described by the Morse potential function. Meanwhile, the interatomic force and the position of atoms are replaced by an equivalent spring element and nodes, respectively. The size effect of the nanostructure will affect the atoms’ mechanical properties.
The copper element is used as the test vehicle in this research. A comparison of different crystallography planes of (100), (110), and (111) on Young’s modulus is presented. The results show that different crystallography planes have different material properties which agree with the results of other studies.
Both analytical and numerical solutions are adopted in this research. The numerical model conducted by ANSYS software analysis obtained the reaction forces and natural frequency of the nanostructures in order to examine their mechanical properties. The results of both
tensile and modal analysis are found to be reliable and acceptable.
On the other hand, this research also investigates the point defect’s distribution under tensile testing and modal analysis. The results reveal that the point defect distribution will affect the structure’s mechanical properties especially when the vacancy defect distribution concentrates at the free side of the specimen. The slip planes in the greatest planar density are also observed when the specimen with defects undergoes tensile testing.

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