臺灣博碩士論文加值系統

本篇論文分為兩部分，第一部份探討RZT (Refined zigzag theory)應用於脫層之三明治樑(cracked sandwich beam, CSB)，第二部分為RZT理論應用於功能梯度複合樑，皆以RZT理論為基礎。在論文第一部分中，除了描述RZT之理論架構外，也給出裂縫尖端之連續條件以及CSB的邊界條件，可解出脫層三明治樑之位移、應力、柔度以及能量釋放率。在RZT理論中，考慮因層間剪力模數差異所造成的軸向位移之轉折現象，而FSDT (First-order shear deformation theory)假設各層具有相同之剪應變，此簡化造成FSDT所計算之柔度小於實際值。藉由比對有限元素分析結果，也證實本論文利用RZT所得到的理論解析解比FSDT更正確。在第一部分的最後，本研究針對楊氏係數、剪力模數、各層厚度等各種參數對脫層三明治樑力學參數的影響，並就力學角度提出解釋。一般三明治樑因表層與中間層剛性差異容易在接合面上產生脫層現象，解決方式之一是引入功能梯度材料，消除介面之材料性質差異以降低應力。因此本篇論文在第二部分將功能梯度材料應用於上下對稱之三明治樑，並將RZT理論擴展至適用於功能梯度複合樑，探討各種受力及邊界條件以及材料性質變化，並與有限元素分析比較，結果顯示本論文提出以RZT為基礎之理論解之準確度相當高。由本論文提出之方法，可在少量的計算資源下，獲得準確的位移及應力。

In this thesis, the refined zigzag theory is used to solve the deflections and stresses of composite sandwich beam. According to the configurations of the sandwich beam, two parts are included in this study. In the first part, the cracked sandwich beam (CSB) is investigated by using the Refined Zigzag Theory (RZT). To solve the displacements, stresses, compliance and energy release reates, the continuity conditions at the crack tip and the boundary conditions are derived. By comparing the results between the theroretical predictions and finite element computations, the solutions by RZT are more accurate than those by FSDT (First-order Shear Deformation Theory). In the present study, parameters such as elastic modulus, shear modulus, layer thickness are considered to investigate their effects on the energy release rates of the CSB.
In the second part, the RZT is extended to investigated the sandwich beam with functionally graded material. Various boundary conditions, loading conditions and spacial distribution models are considered to investigated their effects on the FGM sandwich beam. It reveals that the solutions by RZT agree very much with those by FEM and has low computational resources. Material properties equation in thickness direction and the effect of isotropic or orthotropic materials. In general, FGM is an isotropic material. Although FGM with orthotropic material has not developed on the market, it is expected that the numerical simulation results for FGM with orthotropic material presented of this paper will be applied to this new material in the future.

摘要 I
Abstract II
致謝 IX
目錄 X
表目錄 XII
圖目錄 XIII
第 1 章 緒論 1
1.1 前言 1
1.2 文獻回顧 1
1.2.1 樑理論 1
1.2.2 脫層三明治樑(CSB) 3
1.2.3 功能梯度複合樑 3
1.3 研究動機與本文架構 4
第 2 章 RZT相關理論介紹 6
2.1 FSDT (First-order Shear Deformation Theory)理論 6
2.2 基於FSDT之脫層樑公式及其通解 9
2.3 RZT (Refined Zigzag Theory)理論 11
2.4 基於RZT之脫層樑公式及其通解 15
2.5 剪力修正因子(Shear Correction Factor) 18
2.6 能量釋放率(Energy Released Rate) 20
2.7 邊界條件與參數設定 22
第 3 章 脫層三明治樑理論分析與FEM結果比較 25
3.1 有限元素模型與參數設定 25
3.2 基本參數下之結果比較 26
3.2.1 位移、應力、柔度與能量釋放率結果比較 26
3.2.2 有限元素模型之網格數量 37
3.2.3 不同剪力修正因子之影響 39
3.3 rE變化下之結果比較 41
3.4 rμ變化下之結果比較 51
3.5 rh變化下之結果比較 60
第 4 章 RZT相關理論擴展至功能梯度複合樑 69
4.1 RZT理論擴展至功能梯度複合樑 69
4.2 FSDT理論擴展至功能梯度複合樑 72
4.3 功能梯度複合樑之模型與參數設定 73
第 5 章 功能梯度複合樑之分析結果與討論 80
5.1 等向性材料之靜態分析結果 80
5.2 正交性材料受集中力之靜態分析結果 88
5.2.1 冪次變化之材料性質 88
5.2.2 雙曲線變化之材料性質 108
5.3 受等分布力之靜態分析結果 122
5.3.1 冪次變化之材料性質 122
5.3.2 雙曲線變化之材料性質 136
第 6 章 結論與未來展望 139
6.1 結論 139
6.2 未來展望與研究方向 140
第 7 章 參考文獻 141
附錄 145

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