1、 邁達邁達斯程序的非斯程序的非線線形形動動力力分析分析 Jong-Min KIM Analysis Tech., MIDASITModeling, Integrated Design & Analysis SoftwareMIDAS Information Technology Co., Ltd.MIDAS PROGRAMSHANGHAI 2008.04.252MidasIT China (Shanghai) Technical Seminar 介紹介紹邊界非線性分析邊界非線性分析隔震結構分析隔震結構分析243彈塑性動力分析彈塑性動力分析5內容內容11基礎隔振控制基礎隔振控制3Mida

2、sIT China (Shanghai) Technical Seminar Northridge Earthquake(1994, USA) 1994年年1月月17日日 04時時30分分- Magnitude : ML=6.7- 死亡人死亡人數數: 57人人- 受災人受災人數數: 約約20,000人人 - 財產損財產損失失: 400億億美元美元1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic D

3、ynamic Analysis4MidasIT China (Shanghai) Technical Seminar Kobe Earthquake(1995, JAPAN) 阪神高速公路阪神高速公路橋橋墩墩采用采用1980之前老之前老規規范范采用新采用新規規范范(1980年年)的的橋橋墩墩1993竣工竣工RC建筑物（建筑物（5層層） 1995年年1月月17日日 05時時46分分- Magnitude : ML=7.2- 死亡人死亡人數數 : 5,373人人- 受災人受災人數數: 約約32,000人人- 財產損財產損失失: 9兆兆 9,630億億日元日元1. Introduction2. Ba

4、se Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis5MidasIT China (Shanghai) Technical Seminar 非彈性行為非彈性行為較易更換或不用更換較易更換或不用更換彈性行為彈性行為低維修成本或不需要維修低維修成本或不需要維修能力保護措施能力保護措施強度基基礎礎的隔離的隔離與與震震動動控制控制新抗震新抗震設計設計地震新地震新概概念念設計設計延性 + 對舊抗震規范提出安全性疑問

5、開發新抗震設計方法論 預測結構物確實效應 + 確保抗震性能 評測已有結構的抗震性能抗震性能抗震性能設計設計 為了能夠精確計算出結構的實際地震效應，采用非線性地震分析 結構自身能力與抗震需求的比較結構物隔離裝置 / 抑制裝置1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis6MidasIT China (Shanghai) Technical Seminar 地震地震

6、響應響應分析分析等效等效靜靜力分析力分析地震地震響應響應分析分析設計設計反反應譜應譜Pushover分析分析靜靜力分析力分析 動動力分析力分析時時程分析程分析模模態態分析分析線形分析線形分析非線形分析非線形分析非非線線性性動動力分析力分析基基礎礎的隔離的隔離與與振振動動控制分析控制分析1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis7MidasIT China (

7、Shanghai) Technical Seminar MIDAS的非的非線線性性動動力分析力分析1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis 邊界非線形分析非線性振型疊加法內內力作用力作用類類型的一般型的一般連連接接 黏黏彈彈性消能器性消能器 滯滯回系回系統統 鉛鉛芯橡芯橡膠膠支座支座 摩擦摩擦擺擺隔振系隔振系統統 油阻尼油阻尼(2007)非線性直接積分法

8、非非線線性性時時程分析程分析非線形直接積分法彈塑性梁-柱 集中鉸類型 分布鉸類型 纖維模型單元類型的一般連接非非彈彈性性墻墻: CRB, General Wall非彈性桁架8MidasIT China (Shanghai) Technical Seminar MIDAS下的非下的非線線性性動動力分析力分析1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis9Midas

9、IT China (Shanghai) Technical Seminar 基礎隔震控制基礎隔震控制2110MidasIT China (Shanghai) Technical Seminar 常常規規抗震抗震設計設計抗震建筑抗震建筑結構結構的常的常規設計規設計常常規規抗震抗震設計設計結構結構:塑性損壞塑性損壞高維修成本高維修成本損害滿足要求損害滿足要求地震能量地震能量1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5.

10、 Inelastic Dynamic Analysis11MidasIT China (Shanghai) Technical Seminar 基基礎礎的隔離的隔離與與振振動動控制控制地震的隔離地震的隔離能量能量損損耗裝置耗裝置1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis12MidasIT China (Shanghai) Technical Seminar

11、地震能量地震能量基基礎礎隔離隔離與與振振動動控制控制隔離隔離 / 阻尼阻尼非彈性行為非彈性行為易更換或不需要更換易更換或不需要更換結構結構:近似彈性行為近似彈性行為低維修成本或不需要維修低維修成本或不需要維修能力保護措施能力保護措施基基礎礎隔離隔離被被動動振振動動控制控制1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis13MidasIT China (Shangh

12、ai) Technical Seminar 基基礎礎隔離隔離概概念念固定支座: 加速度響應響應基礎礎隔離后: 加速度響應響應1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis14MidasIT China (Shanghai) Technical Seminar 基基礎礎隔離基本原理隔離基本原理改變周期隔離器屈服后柔度 力減小: 建筑損失降低 隔離器位移增加阻尼增加

13、 隔離器塑性形變下的能量損耗 隔離器位移降低 建筑損失降低周期周期位移位移響應譜響應譜周期周期擬擬加速度反加速度反應譜應譜改改變變周期周期阻尼阻尼改改變變周期周期阻尼阻尼1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis15MidasIT China (Shanghai) Technical Seminar 鉛芯橡膠支座鉛芯橡膠支座(LRB)(LRB)鉛芯 : 能量

14、損耗 抗風 變形恢復橡橡膠膠 : 橫橫向柔度向柔度鋼鋼板板: 豎豎向承向承載載力力1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4 Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis16MidasIT China (Shanghai) Technical Seminar 鉛芯橡膠支座應用鉛芯橡膠支座應用Yamaguchi Dome, 日本日本1. Introduction2. Base Isolation &

15、 Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis17MidasIT China (Shanghai) Technical Seminar 摩擦擺隔振摩擦擺隔振 (FPS) (FPS)摩擦摩擦擺動擺動系系統區統區凹球面(曲率半徑= R)摩擦材料(摩擦系數 = )WMRM擺動擺動滑滑動擺動動擺動Period:2/Stiffness:/TR gkW R1. Introduction2. Base Isolation & Vib. Con

16、trol3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis18MidasIT China (Shanghai) Technical Seminar FPS應應用用Ishikawa Science Park, Ishikawa Japan1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. In

17、elastic Dynamic Analysis19MidasIT China (Shanghai) Technical Seminar 阻尼的基本原理阻尼的基本原理1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis位移力Area = A1 : dissipated energyArea = A0 : dissipated energy位移力 = FD + FS10

18、4dAA阻尼F=sin(t)M粘彈性阻尼滯滯回阻尼回阻尼 等效阻尼A0A1A0A120MidasIT China (Shanghai) Technical Seminar 阻尼基本原理阻尼基本原理周期周期位移位移響應譜響應譜改改變變周期周期阻尼阻尼阻尼增加 能量損耗 由黏性阻尼 或 塑性變形產生的阻尼 建筑損失降低1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis2

19、1MidasIT China (Shanghai) Technical Seminar 黏彈性阻尼黏彈性阻尼(Kelvin Model)(Kelvin Model)變形過程變形過程Maxwell Maxwell 模型模型液壓黏彈性裝置液壓黏彈性裝置1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis22MidasIT China (Shanghai) Technica

20、l Seminar 黏彈性阻尼黏彈性阻尼(Kelvin Model)(Kelvin Model)固體類型的黏彈性裝置固體類型的黏彈性裝置Kelvin(Voigt) Kelvin(Voigt) 模型模型1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis23MidasIT China (Shanghai) Technical Seminar 金屬屈服阻尼金屬屈服阻尼分離

21、支撐系統分離支撐系統1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis24MidasIT China (Shanghai) Technical Seminar 邊界非線性分析邊界非線性分析1325MidasIT China (Shanghai) Technical Seminar 【邊界非線形分析簡述邊界非線形分析簡述fN , fN :非非線線性性彈彈簧簧，非，非線

22、線性力性力 , fL :等效等效剛剛度度，等效力，等效力pfLfNfL應用振型疊加應用振型疊加p 適用于結構的一部分有非線性特性的情況 將非線性單元轉換成線性彈性 非線性效果將非線性構件內力轉換為外力來考慮1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis26MidasIT China (Shanghai) Technical Seminar 有效剛度有效剛度: :

23、 非線性彈簧替代非線性彈簧替代=+-()=非非線線形形彈彈簧簧彈彈性性彈彈簧簧彈彈性性彈彈簧簧非非線線形形彈彈簧簧非非線線形形時時程分程分析析線線形形靜靜力分析力分析特征特征值值分析分析1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis27MidasIT China (Shanghai) Technical Seminar 等效等效動動力荷力荷載載 , fN :No

24、nlinearspring& force , fL :Effectivestiffness& forcefNfLfLppppfLfNfLfNfLfNpfNfLfLfL應應用振型用振型疊疊加法加法1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis28MidasIT China (Shanghai) Technical Seminar 振型疊加法分析簡述

25、振型疊加法分析簡述隔離器隔離器 / 阻尼器阻尼器: 非彈性行為非彈性行為結構結構: 近似近似 彈性行為彈性行為SMuCuFRLSLK uMuCuRFK u2( )( )2)( )TTTiPiNiNiiiiiTTTiiiiiiLNB p tBBq tq tq tMMtffMt + 杜哈梅積分1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis29MidasIT Chin

26、a (Shanghai) Technical Seminar 直接直接積積分法分法簡簡述述隔離隔離 器器/ 阻尼器阻尼器: 非彈性行為非彈性行為結構結構: 近似近似 彈性行為彈性行為. 有效剛度有效剛度 : 常量常量. 非線形恢復力非線形恢復力SMuCuFRLSLK uMuCuRFK u( )2(1)( )( )( )1)()11iiitittiitttttttttttttLS, LKM+CKuFuuRMuCuNewmark-Beta 1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysi

27、s4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis30MidasIT China (Shanghai) Technical Seminar 一般一般連連接接: 多多樣彈樣彈簧簧連連接接1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis31MidasIT China (Shanghai) Tech

28、nical Seminar General Link without Shear Spring Location. Shear & Moment Decouple. Moment of Spring does not depend on Spring Location 1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis32MidasIT China (Sha

29、nghai) Technical Seminar General Link with Shear Spring Location. Moment of Spring depends on Spring Location. Shear & Moment Couple. Similar to Beam Element1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analys

30、is33MidasIT China (Shanghai) Technical Seminar 一般一般連連接接 : 多多樣彈樣彈簧簧連連接接1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis應用類型單元類型基本連接Forty Type General Link性能類型彈簧線形阻尼器彈簧和線形阻尼器線性特征剛度阻尼剛度阻尼剛度阻尼有效剛度有效阻尼靜力分析彈性-彈性-彈

31、性-反應譜彈性-彈性-彈性-線形時程分析模態分析彈性-線性彈性線性1)彈性線性1)直接積分彈性-線性彈性線性2)彈性線性2)非線形時程分析模態分析彈性-線性彈性線性1)彈性(假想)線性1)直接積分彈彈性性-線性彈性線性2)彈性(假想)線性2)1) 應變能比2) 質量& 剛度比& 單元質量& 剛度比: 阻尼矩陣 應變能比 : 模態阻尼比34MidasIT China (Shanghai) Technical Seminar 一般一般連連接的接的節節點力點力1. Introduction2. Base Isolation & Vib. Control3. Bound

32、ary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis不不帶線帶線性有效阻尼性有效阻尼帶線性有效阻尼35MidasIT China (Shanghai) Technical Seminar 力力類類型一般型一般連連接的有效接的有效剛剛度度不不穩穩定定結構結構有效有效剛剛度度下的下的穩穩定定帶帶隔離隔離類類型的非型的非線線性性連連接接結構結構有效有效剛剛度的度的測測定定 非零非零值值 有效有效剛剛度支撐下的度支撐下的樣樣式式1. Introduction2. Base Isolation

33、 & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis36MidasIT China (Shanghai) Technical Seminar kbkdcdffdddbN1N2MIDAS Civil中的被中的被動動振振動動控制控制黏黏彈彈性阻尼性阻尼 dddddbbdbfk dc sign ddk ddddS輸輸入入變變量量 cd : VED Damping Constant kd : VED 剛剛度度 S : 阻尼系阻尼系數數 k

34、b : 支撐支撐剛剛度度1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis37MidasIT China (Shanghai) Technical Seminar MIDAS Civil下的被下的被動動振振動動控制控制黏黏彈彈性阻尼性阻尼 阻尼系數(S)線線形形 (s=1.0)非非線線形形 (0.0s 邊邊界界條條件件 一般一般連連接特性接特性值值Applicati

35、on Type : 非非線線性性連連接接單單元的作用元的作用類類型型 Element Type:直接更新直接更新單單元元剛剛度矩度矩陣來陣來反映非反映非線線性。性。 Force Type:根據非根據非線線性的特性性的特性計計算出算出來來的的內內力力置置換換成外部荷成外部荷載載，間間接的考接的考慮慮非非線線性。性。Property Type Element Type : 彈彈簧簧 線線性阻尼器性阻尼器 彈彈簧簧與線與線形阻尼器形阻尼器 Force Type : 黏黏彈彈性消能器性消能器 滯滯后系后系統統 鉛鉛芯橡芯橡膠膠支座隔震裝置支座隔震裝置 摩擦摩擦擺擺隔震裝置隔震裝置 間間隙隙 鉤鉤一般一

36、般連連接特性接特性1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis54MidasIT China (Shanghai) Technical Seminar 1. Main 對話對話框框模型模型 邊邊界界條條件件 一般一般連連接特性接特性值值Linear Properties : 輸輸入入線線性性彈彈簧的簧的剛剛度以及阻度以及阻尼尼 Effective Stiffn

37、ess : 有效有效剛剛度度Effective Damping : 有效阻尼有效阻尼Nonlinear Properties : 定定義義非非線線性特性性特性LRB Isolator Modeling: Linear Properties1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis55MidasIT China (Shanghai) Technical Sem

38、inar LRB 隔離器建模隔離器建模: 線線形特性形特性- 有效有效剛剛度度1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis56MidasIT China (Shanghai) Technical Seminar 2. 非非線線性特性性特性對話對話框框Stiffness (k) 彈彈簧屈服之前的初始簧屈服之前的初始剛剛度度Yield Strength (Fy)

39、彈彈簧的屈服強度簧的屈服強度Post Yield Stiffness Ratio (r) 屈服后的切屈服后的切線剛線剛度除屈服前初始度除屈服前初始剛剛度的比度的比值值Hysteretic Loop Parameter () 決決定恢定恢復復力曲力曲線線形形狀狀的的參數參數Hysteretic Loop Parameter () 決決定恢定恢復復力曲力曲線線形形狀狀的的參數參數| + | = 1.0LRB Isolator Modeling: 非非線線性特性性特性1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonl

40、inear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis57MidasIT China (Shanghai) Technical Seminar , : 屈服后的屈服后的滯滯回曲回曲線參數線參數 + 0: 軟軟化體系化體系 + 結構類結構類型型 . 模型模型質質量量節節點點質質量量. 模型模型質質量量將將荷荷載轉換載轉換成成質質量量質質量量輸輸入入1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analys

41、is4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis60MidasIT China (Shanghai) Technical Seminar 時程函數時程函數: : 荷載荷載 時程分析數據時程分析數據 時程荷載函數時程荷載函數定義時程函數定義時程函數 1) 1) 用戶定義用戶定義 2) 2) 地震波數據庫地震波數據庫 : 32 : 32種地震荷載種地震荷載 3) 3) 導入導入 外部數據導入示例fn.thd.* UNIT,M,KN*TYPE,ACCEL*DATA0.0000, -0.00470.0200, -0.00570

42、.0400, -0.00700.0600, -0.00840.0800, -0.00610.1000, -0.00630.1200, -0.0090時程函數時程函數#1#11. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis61MidasIT China (Shanghai) Technical Seminar 時時程函程函數數#21. Introduction2.

43、Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis重力荷載重力荷載62MidasIT China (Shanghai) Technical Seminar 1) Analysis Method Modal Analysis(振型振型疊疊加法加法) Direct Integration（直接（直接積積分法）分法）2) Time History Type Transient : （瞬（瞬態態）單單次加次加

44、載載，地震荷，地震荷載載 Periodic :（周期）（周期） 按周期重按周期重復復加加載載，機械振，機械振動動3) End Time : 分析分析時間時間4) Time Increment : 分析分析時間時間步步長長5) Step Number Increment for Output : 輸輸出出結結果的子步果的子步數數增量增量6) Order in Sequential Loading : 連續連續施加的施加的動動力荷力荷載載加加載順載順序序7) Damping Method （阻尼（阻尼計計算方法）算方法）時時程荷程荷載載工工況況#11. Introduction2. Base Is

45、olation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis63MidasIT China (Shanghai) Technical Seminar 時時程荷程荷載載工工況況#2迭代控制迭代控制1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. In

46、elastic Dynamic Analysis64MidasIT China (Shanghai) Technical Seminar 非非線線性分析控制性分析控制參數參數1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis( )(1)( )(1)22( )(0)( )(0)22TiiiittttttttTiitttttttterrororor upupupup C

47、onvergence Check Full Newton Raphson Method65MidasIT China (Shanghai) Technical Seminar 基基礎礎隔離隔離結構結結構結果果#1屋屋頂絕對頂絕對加速度加速度固定支座結構結構屋屋頂頂位移位移屋屋頂絕對頂絕對加速度加速度屋屋頂頂位移位移基礎礎隔離后結構結構1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic

48、 Analysis66MidasIT China (Shanghai) Technical Seminar 基基礎礎隔離隔離結構結結構結果果#2固定支座結構結構屋屋頂頂位移位移: 頻頻率率響應響應基礎礎隔離后結結果F=0.562Hz T=1.78secF=0.940Hz T=1.06sec屋屋頂頂位移位移: 頻頻率率響應響應特征特征值值分析分析結結果果特征特征值值分析分析結結果果1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Stru

49、c. 5. Inelastic Dynamic Analysis67MidasIT China (Shanghai) Technical Seminar 基基礎礎隔離隔離結構結結構結果果#3Story Drift固定支座固定支座結構結構隔離隔離結構結構1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis68MidasIT China (Shanghai) Techni

50、cal Seminar 基基礎礎隔離隔離結構結結構結果果#4固定支座結構結構1st 柱剪力柱剪力基礎礎隔離后結結果1st 柱剪力柱剪力1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis69MidasIT China (Shanghai) Technical Seminar 基基礎礎隔離隔離結構結結構結果果#5滯滯回曲線線: 鉛鉛芯橡膠膠支座1st Column Sh

51、ear Force1st Column Shear Force滯滯回曲線線: 摩擦擺擺隔震1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis70MidasIT China (Shanghai) Technical Seminar 1. Introduction2. Boundary Nonlinear Analysis3. Inelastic Dynamic Ana

52、lysis4. Hysteresis Model5. Fiber Model Runge-Kutta Method: Stepsize Sub-Division ControlMIDAS程序程序邊邊界非界非線線形分析指形分析指導導方方針針執執行迭代行迭代非線性振型疊加法非線形直接積分時間時間步步長長: t 0.005sec一般一般連連接有效接有效剛剛度度特征值分析阻尼模型動力方程有效剛度1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated

53、Struc. 5. Inelastic Dynamic Analysis71MidasIT China (Shanghai) Technical Seminar 51非彈性動力分析非彈性動力分析72MidasIT China (Shanghai) Technical Seminar ,EfftttD ttS, FP=RMu +GMIDAS程序的直接程序的直接積積分法分法時時程分析程分析ttttttttD, S, MuGFREffttKuEffP21effttttKMKC 有效荷有效荷載載: : 有效有效剛剛度度: : ,tttttD ttttS ttttotal damping forceto

54、tal restoring forceMuC uGK uFRStatic Solver(Sky-line / Multi-frontal)tttttuuu1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis73MidasIT China (Shanghai) Technical Seminar 非非線線性性動動力平衡方程力平衡方程線線性振性振動動非非線線性振性振動動非

55、非彈彈性振性振動動線線性性 :非非線線性性 :ttttElttttMuCuK uR,ttD ttS tttttotaltotaldamping forcerestoring forceMuGFR1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis74MidasIT China (Shanghai) Technical Seminar 鋼筋混凝土結構非線性響應分析鋼筋混

56、凝土結構非線性響應分析. 自由集中度自由集中度整體模型整體模型離散有限元模型離散有限元模型. 集中鉸模型集中鉸模型. 分布鉸模型分布鉸模型 . 纖維模型纖維模型非非彈彈性性鉸鉸纖維區纖維區細細部分析的有限元模型部分析的有限元模型Smeared Crack Model有限元有限元網網格格MIDAS1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis75MidasIT C

57、hina (Shanghai) Technical Seminar flexibility 1EIFlexibility DistributionmBending MomentCurvatureEI1Tri-linear Skeleton Curve: Inelastic Hinge (Gauss Integration Point) 帶帶分布分布鉸鉸的非的非彈彈性梁性梁- 高斯積分點(1-20)- 精確的力分布函數- 沒用到形函數（近視值）0( ) ( ) ( )FbfbLTxxx dx: 精確的截面力差精確的截面力差值值函函數數( )b x: x 處處的截面柔度矩的截面柔度矩陣陣 ( )f

58、 x: 單單元柔度矩元柔度矩陣陣Fdx1( )dxdx( )M xx. 柔度矩陣柔度矩陣1K = F. 剛度矩陣剛度矩陣1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis76MidasIT China (Shanghai) Technical Seminar 1FFFK = FBSI帶帶集中集中鉸鉸的非的非彈彈性梁性梁EIfAfBL21126tttmelastich

59、ingeABLEffIFFFAAtmBBddMddMFwhere. 柔度矩陣柔度矩陣. 剛度矩陣剛度矩陣ABBMAM1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis77MidasIT China (Shanghai) Technical Seminar 屈服強度的自屈服強度的自動計動計算算P (+)yzMy(+)Mz(+)1st Yielding2nd Yield

60、ing- -+ +CompressionTensionStressFscFstN.A.- -+ +CompressionTensionStressFscFyFstFyN.A.flexural stresses of the extreme fibers :(FscFyand FstFy) or (FscFyand FstFy)Fsc: flexural stress of extreme fiber in compressionFst: flexural stress of extreme fiber in tensionFy : yield stress of steel 非非彈彈性梁的屈服強度性梁的屈服強度P (+)yzMy(+)Mz(+)Mcr: cracking momentP: axial force (positive for compression)k : coefficient for the cracking moment (ACI=7.5 in lb-in unit, AIJ=1.8 in kgf-cm unit)Z: elastic section modulusfck,cu : ultimate compressive stre