向量式有限元分析法於
鋼筋混凝土結構非線性行為之應用

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張鈴菀(Ling-Yuan Chang) 查詢紙本館藏

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土木工程學系

論文名稱

向量式有限元分析法於鋼筋混凝土結構非線性行為之應用
(Nonlinear Analysis of Reinforced Concrete Structures by the VFIFE Method )

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摘要(中)

本研究主要是採用向量式有限元素法來模擬鋼筋混凝土結構之非線性行為，因此利用向量式有限元素法之平面固體元來模擬混凝土受力之後的幾何非線性行為，以及利用向量式有限元素法之一維桁架桿件元來模擬鋼筋材受力之後的情形，將上述結合，構成鋼筋混凝土結構之數值模擬分析體系；在材料模型選擇中，混凝土採用非線性彈性模型，以Darwin和Pecknold之等效應變模型加以描述混凝土於加載過程中之非線性行為，鋼筋材料模型採用雙折線裡想彈塑性模型；鋼筋混凝土之間以完全握裹來模擬其效應；本文之數值算例針對三個部分來做驗證，首先針對Drawin 和Pecknold[21]提出之混凝土非線性彈性模型進行驗證，確認對其理論應用之正確性，接著針對混凝土材料模型進行驗證，因此針對混凝土單軸試驗進行驗證；最後針對鋼筋混凝土進行驗證，藉由無箍筋之鋼筋混凝土簡支梁以及含箍筋之鋼筋混凝土簡支梁數值算例，來驗證鋼筋混凝土結構之非線性行為。透過一系列數值算例和實驗結果比較進行驗證，發現所開發之數值模擬程序確實可以有效的模擬鋼筋混凝土結構之非線性行為。

摘要(英)

A novel motion analysis method so called Vector Form Intrinsic Finite Element (VFIFE) method was used to simulate the nonlinear behavior of reinforced concrete. Two-dimensional solid finite elements are used to model the concrete, and truss elements are used to model the steel reinforcements. An equivalent uniaxial strain model that can characterize the nonlinear monotonic loading behavior of concrete material by Darwin and Pecknold is applied. The elastic-plastic response of reinforcement is considered in the analysis. Concrete and reinforcing bars are represented by separate material model which are combine together with a model of the interaction between reinforcing bar and concrete through perfect bond to describe the behavior of the composite reinforced concrete material. In this study, there are three parts to verify the accuracy and effectiveness of this simulation code. The investigation first considers the development of a consistent material model that matches the analytical model made by Darwin and Pecknold. In the second part, VFIFE calculations are compared with experimental results for the behavior of concrete under monotonic, uniaxial and biaxial loadings. Finally, the composite material model is compared with experimental results for a simply supported unconfined reinforced concrete beam and a simply supported confined reinforced concrete beam. Numerical examples demonstrate that the nonlinear responses for RC structures can be effectively analyzed by the proposed equivalent uniaxial strain model of concrete.

關鍵字(中)

★ 向量式有限元素法
★ 鋼筋混凝土結構
★ 幾何非線性
★ Darwin和Pecknold模式

關鍵字(英)

★ vector form intrinsic finite element
★ reinforced concrete structure
★ equivalent uniaxial strain model

論文目次

目錄
摘要 I
ABSTRACT II
致謝 III
目錄 IV
圖表目錄 VI
第一章前言 1
1.1研究動機與目的 1
1.2文獻回顧 1
1.3研究方法與內容 3
第二章向量式有限元之基本理論 4
2.1平面固體元之向量式有限元基本理論 4
2.1.1基本假設 4
2.1.2運動解析的基本步驟 4
2.2一維桁架之向量式有限元基本理論 17
2.2.1 基本假設 17
2.2.2運動解析的基本步驟 19
第三章鋼筋與混凝土材料分析模型 25
3.1混凝土材料模型 25
3.1.1 正交異性之混凝土材料模型 25
3.1.2等效單軸應變分析模型之基本理念 28
3.1.3 單向加載之等效單軸應力-應變曲線 33
3.1.4混凝土材料模型計算程序 39
3.2鋼筋材料模型 47
3.2.1 單向加載下鋼筋應力-應變關係 47
3.2.2鋼筋材料模型計算程序 49
3.3鋼筋混凝土材料模型計算步驟 49
第四章數值算例驗證 52
4.1單向加載之混凝土材料模型數值模擬驗證 52
4.1.1單向加載雙軸壓力試驗曲線之比較 53
4.1.2單向加載拉-壓試驗曲線以及單軸壓力試驗之比較 59
4.1.3 單向加載之單軸壓力試驗驗證 62
4.1.4 單向加載之雙軸拉-壓力試驗驗證 66
4.2鋼筋混凝土材料模型簡支梁數值模擬驗證 67
4.2.1 無箍筋鋼筋混凝土材料模型簡支梁模擬 68
4.2.2含箍筋鋼筋混凝土材料模型簡支梁模擬 69
第五章結論與建議 72
5.1結論 72
5.2建議和展望 73
參考文獻 74
附錄A 應力-應變關係之轉換矩陣 81
附錄B 雙軸強度包絡線之公式推導 84

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指導教授

王仲宇(Chung-Yu Wang)

審核日期

2009-7-24

推文