本文推衍三維(three-dimensional, 3D)漸近非局部彈性力學理論，對嵌入在彈性介質中之簡支承單層奈米碳管(single-walled carbon nanotube, SWCNT)於內外表面受橫向法向荷載作用，進行其靜力分析。文中利用Eringen的非局部彈性力學組成關係，將微小尺度效應納入考慮，用以檢驗SWCNT靜力行為。文中SWCNT及其周圍基礎之間的相互作用分別以Winkler型或Pasternak型之模型來模擬。理論推衍結果顯示二維（two-dimensional, 2D）非局部古典殼理論（classical shell theory, CST）是3D非局部彈性力學理論的一階近似，其結果可以逐階修正，以階級式且一致的方式漸近地逼近精確的3D非局部彈性力學解。文中也對與嵌入式SWCNT靜力行為有關之參數進行研究，其中包括縱橫比、SWCNT周圍介質的勁度與剪力模數以及非局部參數。

A three-dimensional (3D) asymptotic local elasticity theory is reformulated for the static analysis of a simply-supported, single-walled carbon nanotube (SWCNT) embedded in an elastic medium under a transverse normal load at its inner and outer surfaces. Eringen’s nonlocal constitutive relations are used to account for the small length scale effects in the formulation examining the static behavior of the SWCNT. The interaction between the SWCNT and its surrounding foundation is modelled as either a Winkler-type or a Pasternak-type model. The two-dimensional (2D) nonlocal classical shell theory (CST) is derived as a first-order approximation of the 3D nonlocal elasticity theory. The 2D nonlocal CST solutions can be modified order-by-order to asymptotically approach the exact 3D nonlocal elasticity solutions in a hierarchic and consistent manner. A parametric study related to some effects on the static behavior of the embedded SWCNT is undertaken, including the aspect ratio, the stiffness and shear modulus of the surrounding medium of the SWCNT, and the nonlocal parameter.

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