由於奈米碳管為目前新興的補強材料，它具有優秀的機械性質，如高強度、高韌性、高硬度、高導電性和高導熱性之特性。從許多研究得知，添加了少量的奈米碳管就可以提升整體複合材料許多的機械性質，因此本文想了解在樹酯內單獨添加少量的奈米碳管或者碳纖維結合奈米碳管的機械性質並比較兩者之差異性。
本文是藉由等效均質法去估測，在各種形式下的奈米碳管複合材料的楊氏係數和剪力模數，並為了驗證本文所估測的力學性質之正確性，我們與Rule of Mixture、Eshelby’s Equivalent Inclusion Theory、Mori-Tanaka Method這三種理論解相互比較，其結果顯示本文藉由等效均質理論估測的力學性質具有一定的準確性。從數值模擬結果顯示添加1wt%短纖的奈米碳管，可使整體複合材料的軸向楊氏係數比基材楊氏係數成長了45%左右。此外添加少量的奈米碳管所形成之CF/CNT/polymer複合材料，可以大幅增加側向楊氏係數和剪力模數，並以奈米碳管隨機散佈於樹酯中所得到的力學性質效果最好。

The carbon nano-tube (CNT) is the emerging reinforcement materials which has excellent mechanical properties, like high strength, toughness, hardness, electric conductivity and heat conductivity. By reviewing many researches, we know that adding a few CNT in the polymer can enhance mechanical properties. Therefore, this paper will compare the mechanical properties of reinforcement polymer by adding carbon nano-tubes (CNT) individually or adding carbon fibers (CF) and carbon nano-tubes together.
In this paper, we estimate the Young’s modulus and shear modulus of carbon nano-tube composites by using equivalent homogeneous theory. To verify the simulated results, we compare our data with those estimated by the Rule of Mixture, the Eshelby’s Equivalent Inclusion Theory and the Mori-Tanaka Method. The results show the mechanical properties estimated by using equivalent homogeneous theory have certain level of accuracy. According to the numerical results, the addition of 1wt% (by weight) of short nano-tubes makes the Young's modulus of the composite material in longitudinal direction the growth of 45%. In addition, adding CNT to the material, composed of carbon fibers (CF) and polymer, enables the Young's modulus in transverse direction and shear modulus to increase greatly, and the strengthening effect are the best with a random and uniform distribution of nano-tubes in the matrix.

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