臺灣博碩士論文加值系統

本文探討雙層圓柱正交性圓管受到扭力作用下端部效應的影響。依據彈性力學理論，探討一端固定另一端受到純扭矩的圓管，利用狀態空間法與特徵函數展開法求得解析解，再運用Mathematica去探討內層、外層與內外層受到均勻負載的情況，在不同異向性材料、功能性材料、複合材料對端部效應的影響，並與聖維南扭矩比較以得到聖維南定理的適用性，得到當材料異向性提高的時候，端部效應的影響會變大；改變材料非均質參數與連續性參數，使得材料的剛性產生變化，在內層受到負載的情況，剛性變小會使得端部效應增大；在外層受到負載的情況，剛性變小會使得端部效應減小，內外層受到負載的情況則必須考慮內、外層疊加的效應來決定。

The end effects of a two-layer circular tube subjected to end torsion are studied in this thesis. Both layers are made of functional graded materials and their properties are assumed to be cylindrically orthotropic. The twisting moment is simulated by applying uniform shear stress on the end surface. All the formulations are derived by employing the state space method and eigen-function expansion to obtain the closed form expressions of displacements and shear stresses. An anisotropic index ki(i=1,2) defined as the ratio of shear moduli are assigned to study the influence of the orthotropy on the end effects. The results of shear stresses obtained have been compared well with the solutions of so-called Saint-Venant’s torsion. Several factors, such as the anisotropic index, nonhomogeneous parameter, the types of applied surface tractions, and continuous parameter s, are then considered to discuss the decay of shear stresses starting from the end of the tube.

摘要 I
Abstract II
誌謝 III
目錄 IV
表目錄 VII
圖目錄 IX
符號說明 XVII
第一章　緒論 1
1.1　前言 1
1.2　文獻回顧 1
1.3　本文架構 2
第二章　基礎理論 4
2.1　聖維南定理與端部效應 4
2.2　彈性力學方程式 4
2.3　狀態空間方程式 6
2.4　Sturm-Liouville方程式 7
第三章　問題分析與推導 9
3.1　問題描述 9
3.2　邊界條件與連續條件 10
3.3　推導過程 11
3.4　退化案例 22
3.4.1　雙層圓柱正交性均質圓管 22
3.4.2　單層圓柱正交性均質圓管 24
第四章　數值驗證與討論 26
4.1　材料異向性對端部效應的影響 27
4.1.1　內圈受到均勻負載之材料異向性對端部效應的影響 27
4.1.2　外圈受到均勻負載之材料異向性對端部效應的影響 32
4.1.3　內外圈受到均勻負載之材料異向性對端部效應的影響 36
4.2　非均質參數對端部效應的影響 40
4.2.1　內圈受到均勻負載之非均質參數對端部效應的影響 41
4.2.2　外圈受到均勻負載之非均質參數對端部效應的影響 45
4.2.3　內外圈受到均勻負載之非均質參數對端部效應的影響 49
4.3　均質複合材料對端部效應的影響 53
4.3.1　內層受到均勻負載之均質材料連續性參數對端部效應的影響 54
4.3.2　外層受到均勻負載之均質材料連續性參數對端部效應的影響 59
4.3.3　內外層受到均勻負載之均質材料連續性參數對端部效應的影響 63
4.4　非均質複合材料對端部效應的影響 67
4.4.1　內層受到均勻負載之非均質材料連續性參數對端部效應的影響 68
4.4.2　外層受到均勻負載之非均質材料連續性參數對端部效應的影響 73
4.4.3　內外層受到均勻負載之非均質材料連續性參數對端部效應的影響 77
第五章　結論 82
附錄A 84
參考文獻 85

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