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研究生:張志明
研究生(外文):Chih-Ming Chang
論文名稱:力法式有限纖維元素模式之二維纖維初步研究
論文名稱(外文):Study on 2-D Fibers for Force-based Finite Fiber Element Model
指導教授:鄭全桓
指導教授(外文):Chyuan-Hwan Jeng
學位類別:碩士
校院名稱:國立暨南國際大學
系所名稱:地震與防災工程研究所
學門:環境保護學門
學類:環境防災學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:179
中文關鍵詞:力法式有限纖維元素剪力效應鋼筋混凝土彈塑性
外文關鍵詞:Force-basedFinite Fiber ElementOpenSeesShear EffectReinforce ConcreteElasto-Plastic
相關次數:
  • 被引用被引用:5
  • 點閱點閱:333
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  • 下載下載:38
  • 收藏至我的研究室書目清單書目收藏:0
在鋼筋混凝土梁柱構件及構架的非線性有限元素分析上,應用力法式有限纖維元素模式配合一組迭代演算流程,僅需要較少的元素自由度,就可以將鋼筋混凝土梁柱構件以及構架的撓曲行為,以很穩定的演算流程模擬出來,並得到高準確度與穩定性的分析結果。由美國加州大學柏克萊分校的太平洋地震工程研究中心所開發的物件導向式有限元素分析軟體OpenSees,即內建有力法式有限纖維元素類別。對於鋼筋混凝土梁柱構件及構架在靜力、動力分析上,使用OpenSees中單軸材料模組與力法式梁柱元素模組,能有效的反映出材料的正向應力應變行為。然而,由於剪力效應的複雜性,此分析方法目前並未考慮剪力效應,因此仍無法反映如pinching effect等剪力行為。當分析需包含剪力效應時,至少需考慮雙軸之應力應變行為。
本論文依據力法式有限纖維元素模式建立一可包含剪力效應之二維纖維元素數學組成模式,並將此模式配合美國休士頓大學所提出的軟化薄膜模式與反覆軟化薄膜模式,推導鋼筋混凝土二維纖維材料組成模式與纖維剖面勁度矩陣;除此之外,另將二維纖維元素數學組成模式配合古典塑性力學理論中的von Mises降伏準則與Prandtl-Reuss塑性流法則,推導彈塑性二維纖維材料組成模式與纖維剖面勁度矩陣,並將其實作為OpenSees軟體架構下的PlasticPlaneStree類別,以探討此分析方法應用於靜力與動力分析時所能反映的剪力效應。
The force-based finite fiber element model with an iterative element state determination procedure has been regarded as one of the most promising simulation methods for reinforced concrete (RC) frames subjected to cyclic-static or dynamic excitations. Compared to the conventional displacement-based approach, the force-based method can accurately simulate the flexural behavior of RC frames with robust computational stability. The OpenSees software framework developed at UC Berkeley has built-in the force-based finite fiber element model.
This force-based method, however, does not incorporate the trickier shear effect due to the use of uniaxial fibers and thus is unable to reflect the shear behavior of RC frames. To reflect the shear effect, the fibers sub-dividing the cross sections need to take into account at least the bi-axial or 2-D stress state. Hence, the objective of this thesis is developing a 2-D fiber suitable for the force-based finite fiber element model.
In this thesis, the general formulation of 2-D fibers for both RC sections and elasto-plastic sections is presented. The sectional tangent stiffnesses of these two types of sections are derived. The elasto-plastic fiber using the von Mises yielding criteria and the Prandtl-Reuss flow rule is implemented in OpenSees and analyses using the 2-D elasto-plastic fibers are conducted to verify the newly proposed formulation. The analytical results of the static-monotonic, static-cyclic, and dynamic analyses of a cantilever beam basically verify the feasibility of the formulation of 2-D elasto-plastic fibers proposed in this thesis.
誌謝.........................................................................................................................................I
中文摘要...............................................................................................................................II
英文摘要..............................................................................................................................III
目錄.......................................................................................................................................V
表目錄................................................................................................................................. IX
圖目錄...................................................................................................................................X
符號說明...........................................................................................................................XIII

第一章 緒論..........................................................................................................................1
1-1前言..........................................................................................................................1
1-2研究動機與目的......................................................................................................2
1-3研究內容..................................................................................................................2
1-4文獻回顧..................................................................................................................3
1-4-1有限纖維元素模式文獻回顧.......................................................................3
1-4-2鋼筋混凝土剪力牆元素文獻回顧...............................................................5

第二章 二維纖維元素數學組成模式..................................................................................8
2-1 前言.........................................................................................................................8
2-2 位移法與力法.........................................................................................................8
2-3 剖面力-變形關係...............................................................................................11
2-4 力法式元素組成模式...........................................................................................15
2-5 元素狀態決定.......................................................................................................18
2-6 分析流程...............................................................................................................23
2-6-1 靜力分析之位移控制法...........................................................................24
2-6-2 動力分析之積分法...................................................................................26

第三章 鋼筋混凝土二維纖維............................................................................................28
3-1 前言.......................................................................................................................28
3-2 鋼筋混凝土二維纖維組成模式...........................................................................28
3-2-1 應力平衡方程式.......................................................................................28
3-2-2 應變諧合方程式.......................................................................................31
3-2-3 材料組成律...............................................................................................31
3-2-4 混凝土反覆應力應變曲線.......................................................................32
3-2-5 鋼筋反覆應力應變曲線...........................................................................35
3-3 鋼筋混凝土纖維剖面切線勁度矩陣推導...........................................................38
3-3-1推導 ....................................................................................................38
3-3-2推導 ....................................................................................................49
3-3-3推導 ....................................................................................................50
3-3-4推導 ....................................................................................................51

第四章 彈塑性二維纖維....................................................................................................53
4-1 前言.......................................................................................................................53
4-2 單軸非彈性彎矩理論...........................................................................................53
4-3 古典塑性力學理論...............................................................................................56
4-3-1 塑性流理論...............................................................................................57
4-3-2 變形理論...................................................................................................58
4-3-3 降伏準則...................................................................................................59
4-3-4 塑性流法則...............................................................................................61
4-3-5 應變硬化法則...........................................................................................62
4-3-6 荷載準則...................................................................................................64
4-4彈塑性二維纖維數學組成模式...........................................................................66
4-4-1彈塑性二維纖維理論模式.........................................................................66
4-4-2彈塑性二維纖維加載卸載流程.................................................................69
4-4-3彈塑性二維纖維剖面切線勁度矩陣推導.................................................70

第五章 模式之建置............................................................................................................72
5-1 前言......................................................................................................................72
5-2 物件導向式有限元素分析軟體..........................................................................72
5-2-1 物件導向方法論.......................................................................................72
5-2-2 OpenSees簡介..........................................................................................73
5-2-3 OpenSees之開發.......................................................................................73
5-3 二維纖維元素模式實作.......................................................................................75
5-3-1 雙軸纖維元素開發..................................................................................75
5-3-2 鋼筋混凝土二維纖維之建置..................................................................83
5-3-3 彈塑性二維纖維之建置..........................................................................85
5-4 分析結果.............................................................................................................97
5-4-1程式測試.................................................................................................97
5-4-2 參數測試...............................................................................................107
5-4-3 靜力單向側推分析...............................................................................108
5-4-4 靜力反覆荷載分析................................................................................109
5-4-5 動力歷時分析........................................................................................111

第六章 結論與建議.........................................................................................................117
6-1 結論....................................................................................................................117
6-2 建議....................................................................................................................118

參考文獻...........................................................................................................................119

附錄....................................................................................................................................127
附錄A ........................................................................................................................128
A-1 Section Force-Deformation Relation..........................................................128
A-2 Derivation of Section Tangent Stiffness Matrix..........................................132
附錄B… ........................................................................................................................162
B-1 TclModelBuilder.cpp..................................................................................162
附錄C.........................................................................................................................166
C-1懸臂梁分析模式指令流.............................................................................166
C-2彈塑性二維纖維model.tcl檔.....................................................................167
C-3靜力單向側推pushover.tcl檔.....................................................................169
C-4靜力反覆側推cyclic.tcl檔..........................................................................175
C-5動力歷時分析dynamic.tcl檔......................................................................177


表目錄
表2.1 位移法有限元素分析過程........................................................................................9
表2.2 力法式的分析流程..................................................................................................23
表3.1 加載與卸載路徑折點之決定與計算......................................................................35
表3.2 反覆荷載路徑之偏微分計算值..............................................................................46
表5.1 封裝方式與說明......................................................................................................77
表5.2 Modelbuilder指令與說明.......................................................................................100
表5.3 Analysis指令與說明...............................................................................................101
表5.4 OpenSees輸入檔plastic.tcl.....................................................................................101
表5.5 懸臂梁自由端加載節點質量.................................................................................111


圖目錄
圖1.1 Illustration of numerical problems at member level....................................................4
圖2.1 Newton-Raphson迭代計算過程圖示.........................................................................8
圖2.2 元素局部座標圖......................................................................................................10
圖2.3 纖維剖面示意圖......................................................................................................11
圖2.4 元素結點力向量與變形向量示意圖......................................................................16
圖2.5 自由體圖..................................................................................................................16
圖2.6 元素狀態決定過程..................................................................................................19
圖2.7 剖面力與剖面變形向量之迭代過程......................................................................20
圖3.1 RC纖維座標系統轉換關係圖..................................................................................28
圖3.2 混凝土二維纖維應力狀態圖..................................................................................29
圖3.3 受拉鋼筋二維纖維應力狀態圖..............................................................................30
圖3.4 受壓鋼筋二維纖維應力狀態圖..............................................................................30
圖3.5 Cyclic smeared stress-strain curve of concrete..........................................................32
圖3.6 混凝土纖維反覆應力-應變曲線..........................................................................34
圖3.7 鋼筋反覆平均應力應變曲線圖..............................................................................37
圖3.8 鋼筋反覆平均應力應變曲線簡化模式..................................................................37
圖4.1 彈塑性材料之應力-應變曲線..............................................................................53
圖4.2 矩形剖面彈塑性梁之變位......................................................................................54
圖4.3 (a)懸臂梁之力對轉角曲線圖;(b)懸臂梁之力對位移曲線圖................................56
圖4.4 (a)非線彈性與塑性行為;(b)理想彈塑性;(c)應變硬化塑性..............................57
圖4.5 完全彈塑性材料之降伏平面..................................................................................59
圖4.6 (a) Tresca降伏準則;(b) von Mises降伏準則.......................................................61
圖4.7 在π平面上之Tresca與von Mises降伏準則.......................................................61
圖4.8 塑性流法則示意圖..................................................................................................62
圖4.9 (a)等向硬化模式;(b)運動硬化模式......................................................................63
圖4.10 Qu與Yin荷載準則................................................................................................64
圖4.11彈塑性二維纖維之加載卸載路徑示意圖..............................................................69
圖5.1 OpenSees主要物件...................................................................................................73
圖5.2 Material之衍生類別圖.............................................................................................76
圖5.3 BiaxialBeamFiberMaterial2D類別圖.......................................................................76
圖5.4 Fiber之衍生類別圖..................................................................................................79
圖5.5 BiaxialFiber2d類別圖.............................................................................................80
圖5.6 BiaxialFiberSection2d類別圖...................................................................................81
圖5.7 Material之衍生類別圖.............................................................................................83
圖5.8 SMMUniaxialConcrete01之反覆應力-應變曲線圖.............................................83
圖5.9 SMMUniaxialSteel01之反覆應力-應變曲線圖....................................................84
圖5.10 Material之衍生類別圖...........................................................................................85
圖5.11 PlasticPlaneStress類別圖........................................................................................86
圖5.12 函式setTrialStrain()流程圖....................................................................................87
圖5.13 應力狀態變化路徑示意圖....................................................................................88
圖5.14 函式elastic()流程圖...............................................................................................88
圖5.15 計算交會點............................................................................................................89
圖5.16 函式interSecPoint()流程圖....................................................................................90
圖5.17 修正應力向量........................................................................................................91
圖5.18 函式forwardEuler()流程圖....................................................................................91
圖5.19 校正應力向量........................................................................................................92
圖5.20 函式correctStress()流程圖....................................................................................92
圖5.21 函式determineState ()流程圖................................................................................93
圖5.22 應力修正示意圖....................................................................................................93
圖5.23 函式plasticLoading()流程圖..................................................................................94
圖5.24 函式unloading()流程圖.........................................................................................95
圖5.25 矩形剖面懸臂梁....................................................................................................97
圖5.26 Beam23元素幾何圖................................................................................................99
圖5.27 BISO應力-應變曲線圖........................................................................................99
圖5.28 OpenSees執行介面...............................................................................................105
圖5.29 TclEditor使用介面................................................................................................105
圖5.30 不同梁長之側向力-側向位移曲線圖..............................................................106
圖5.31 不同斷面數量分析結果......................................................................................107
圖5.32 不同纖維數量分析結果......................................................................................108
圖5.33 不同梁長之單向側向力-側向位移曲線圖......................................................109
圖5.34 不同梁長之反覆側向力-側向位移曲線圖.......................................................110
圖5.35 地震加速度歷時紀錄(1940 El Centro) ..............................................................112
圖5.36(a) 位移歷時圖(梁長為18英呎) .........................................................................113
圖5.36(b) 位移歷時圖(梁長為30英呎) .........................................................................113
圖5.36(c) 位移歷時圖(梁長為42英呎) .........................................................................114
圖5.36(d) 位移歷時圖(梁長為54英呎) .........................................................................114
圖5.37(a) 剪力-側向位移曲線圖(梁長為18英呎) .....................................................115
圖5.37(b) 剪力-側向位移曲線圖(梁長為30英呎) .....................................................115
圖5.37(c) 剪力-側向位移曲線圖(梁長為42英呎) .....................................................116
圖5.37(d) 剪力-側向位移曲線圖(梁長為54英呎) .....................................................116
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