臺灣博碩士論文加值系統

本文基於Reissner’s混合變分理論(RMVT)，推衍非局部Timoshenko梁理論(TBT)，並應用於具組合邊界單壁奈米碳管(SWCNT)嵌入彈性介質，且受軸向載荷作用下的結構穩定性分析。文中以Eringen非局部彈性理論解釋微小尺度效應，呈現基於RMVT非局部TBT的強形公式及其相關可能的邊界條件。SWCNT及其周圍彈性介質之間的相互作用則以Pasternak基礎模型模擬。應用微分擬合法求得，在不同邊界條件之嵌入式SWCNT的臨界載重參數，其中np佈點數選擇使用np階Chebyshev多項式的根作為佈點位置。文中亦進行RMVT非局部TBT的結果與虛位移(PVD)原理非局部TBT之結果相互比較，討論一些重要的效應對嵌入式SWCNT臨界載重參數的影響，例如不同的邊界條件、Winkler勁度和剪切模數的基礎、外樣比及非局部參數。

On the basis of Reissner’s mixed variational theory (RMVT), a nonlocal Timoshenko beam theory (TBT) is developed for the stability analysis of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, with various boundary conditions and under axial loads. Eringen’s nonlocal elasticity theory is used to account for the small length scale effect. The strong formulations of the RMVT- based nonlocal TBT and its associated possible boundary conditions are presented. The interaction between the SWCNT and its surrounding elastic medium is simulated using the Pasternak foundation models. The critical load parameters of the embedded SWCNT with different boundary conditions are obtained using the differential quadrature (DQ) method, in which the locations of np sampling nodes are selected as the roots of np-order Chebyshev polynomials.

目錄

摘要 I
Abstract II
誌謝 VII
表目錄 IX
圖目錄 X
第1章 緒論 1
第2章 RMVT局部Timoshenko梁理論 5
2.1 場量主變數假設 5
2.2 Euler-Lagrange方程式 6
第3章 RMVT非局部Timoshenko梁理論 9
3.1 非局部之基本組成關係 9
3.2 Euler-Lagrange方程式 9
第4章 PVD非局部Timoshenko梁理論 11
第5章 微分擬合法 13
第6章 應用 15
6.1 分析基於RMVT之非局部TBT 15
6.2 分析基於PVD之非局部TBT 19
6.3 分析非局部TBT解析解 21
第7章 範例說明 24
7.1 受軸向載重且無彈性支承之非局部梁 24
7.2 受軸向載重且具或不具彈性支承之SWCNT 25
7.3模擬與討論 27
第8章 結論 28
參考文獻 29

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