臺灣博碩士論文加值系統

本研究主旨在探討利用顯性有限元素法數值分析鋼筋混凝土之受力行為，以作為日後鋼筋混凝土構件修補數值分析之基礎。鋼筋混凝土樑受力行為之數值模擬，其主要的問題在混凝土本身材料複雜的性質、混凝土開裂對整體構件性質的改變及鋼筋和混凝土之間的黏結與滑移。在混凝土開裂方面，採用結點開裂的方式，於計算過程中，判斷混凝土結點是否到達開裂條件，開裂則將結點於開裂方向一分為二，而重新編排元素及計算應力分佈。另外在鋼筋與混凝土黏結方面，在鋼筋結點與混凝土結點之間添加一聯結彈簧元素，使鋼筋與混凝土之間的黏結力，能由聯結彈簧元素去模擬，並使鋼筋結點與混凝土結點之間能夠相對滑移。由上述鋼筋混凝土樑之性質，然後使用顯性有限元素法數值分析其受力行為，其間由於鋼筋混凝土樑實驗時，其控制方式並不是直接控制外加荷載，而是控制加載點之位移，因此在數值模擬分析時，也是以相同的方式控制加載點的位移，然後反算加載點的施力。
在此一架構之下，本論文探討了四個例子，包括純混凝土樑試驗、鋼筋拉拔試驗、鋼筋拉伸試驗及鋼筋混凝土樑試驗；藉以瞭解聯結彈簧模式對整體數值分析的影響，還有試體受力後，開裂狀況的影響。由於顯性有限元素法是有條件收斂的狀況，因此在數值分析時，同時必須考慮到時間步程間格、元素幾何大小及材料性質對收斂狀況的影響；由於加載是由位移控制，因此也必須考慮到加載位移增量是否會造成數值的發散。最後由此一鋼筋混凝土樑模擬與實際實驗之位移-加載圖作一比較，以瞭解此一方法的適用性。

In this thesis, a computer code is developed for 2D numerical simulations of reinforced concrete beams by the explicit finite element method (FEM). The material non-linearity of the concrete and the reinforcement are considered into the analysis. Besides, the bonding and sliding behaviors between the reinforcement and the concrete are modeled by using the so called "linkage element". Releasing the connecting nodes between neighboring elements is used to simulate the cracking behavior of concrete, once a failure criterion was satisfied. The main benefit of applying the explicit finite element method to conduct the analysis is the avoidance of solving large simultaneous equation. Then, it can save much storage space and some complex process, which is required by the implicit FEM.
In order to simulate the process of the real test of RC beams, a displacement control algorithm is written into the explicit finite element code. Four examples were studied to evaluate the performance of this newly developed RC structural analysis program. Through the study, it is found that the time step size of the explicit FEM is coupled with the element size and the material stiffness. For the displacement control algorithm, the size of displacement increment is also a critical factor for the convergence of the simulation.

目錄……………………………...………………………………………..Ⅰ
圖目錄…………………………………………………………………….Ⅳ
摘要…………………………………………………………………….....Ⅶ
英文摘要………………………………………………………………….Ⅷ
第一章 緒論
1-1研究背景……………...……………………………………..……1
1-2研究動機………………...…………………………………..……2
1-3研究方法………………...…………………………………..……3
1-4論文內容……………………….…………………………....……4
第二章 文獻回顧
2-1顯性有限元素法簡介…………………………………..…...……5
2-1.1 相互旋轉法………………………….………………....……5
2-1.2 轉換座標旋轉角度之計算…………….……………………5
2-1.3 平面元素之形狀函數…………………….…………………6
2-1.4 應力﹑應變與位移之關係………………………………..…7
2-1.5 虛功原理…………………………………………….....……8
2-1.6 動力方程式…………………………………………...……10
2-1.7 質量矩陣之建立……………………………………...……12
2-1.8 顯性時間積分……….………………………………..……12
2-2混凝土裂縫模式…………………………………………...……13
2-2.1分佈裂縫模型………………………………………....……15
2-2.2離散裂縫模型………………………………………....……16
2-2.3斷裂力學的應用……………………………………....……18
2-3鋼筋與混凝土之黏結與滑移……………………….……..……19
2-3.1黏結滑移的試驗………………………………..…………..20
2-3.2黏結與滑移之理論分析……………………..……………..21
第三章 鋼筋混凝土樑之模擬方法
3-1鋼筋混凝土之材料性質………………………….……………..23
3-1.1混凝土材料之性質……………………………..…………..23
3-1.2混凝土材料之有限元素模型……………………………....24
3-1.3 鋼筋材料之性質…………………………………....……...26
3-1.4 鋼筋之有限元素模型………………………………….…..27
3-2聯結介質之數學模型……………………………….…………..29
3-2.1雙彈簧聯結元素………………………..…………………..29
3-2.2虛擬彈簧剛度之試驗值…………………………..…….….31
3-3開裂模式…………………………..………………...…………..32
第四章 鋼筋混凝土樑之數值模擬
4-1位移控制法…………………………..…………………...……..34
4-2鋼筋混凝土樑特殊之固結方式…………………...…………....35
4-3程式流程圖…………………………..…………………...……..38
4-4純混凝土樑之模擬……………………..…………...…………..39
4-5鋼筋拉拔模擬…………………………..………...……………..40
4-6鋼筋拉伸模擬…………………………..……...………………..41
4-7鋼筋混凝土樑之模擬…………………..………...……………..43
第五章 結果與討論
5-1純混凝土樑數值分析之結果…………………….……………..45
5-2鋼筋拉拔試驗數值分析之結果…………………….…………..47
5-3鋼筋拉伸試驗數值分析之結果……………………….………..50
5-4鋼筋混凝土樑數值分析之結果………………………………...52
第六章 結論與建議
6-1結論…..……………………………………………...…………..54
6-2建議…..………………………………………………...………..55
參考文獻…..……………………………………………………...……....56

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