下的非线形动力分析

1、 迈达迈达斯程序的非斯程序的非线线形形动动力力分析分析 Jong-Min KIM Analysis Tech., MIDASITModeling, Integrated Design & Analysis SoftwareMIDAS Information Technology Co., Ltd.MIDAS PROGRAMSHANGHAI 2008.04.252MidasIT China (Shanghai) Technical Seminar 介绍介绍边界非线性分析边界非线性分析隔震结构分析隔震结构分析243弹塑性动力分析弹塑性动力分析5内容内容11基础隔振控制基础隔振控制3Mida

2、sIT China (Shanghai) Technical Seminar Northridge Earthquake(1994, USA) 1994年年1月月17日日 04时时30分分- Magnitude : ML=6.7- 死亡人死亡人数数: 57人人- 受灾人受灾人数数: 约约20,000人人 - 财产损财产损失失: 400亿亿美元美元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桥桥墩墩采用采用1980之前老之前老规规范范采用新采用新规规范范(1980年年)的的桥桥墩墩1993竣工竣工RC建筑物（建筑物（5层层） 1995年年1月月17日日 05时时46分分- Magnitude : ML=7.2- 死亡人死亡人数数 : 5,373人人- 受灾人受灾人数数: 约约32,000人人- 财产损财产损失失: 9兆兆 9,630亿亿日元日元1. Introduction2. Ba

4、se Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis5MidasIT China (Shanghai) Technical Seminar 非弹性行为非弹性行为较易更换或不用更换较易更换或不用更换弹性行为弹性行为低维修成本或不需要维修低维修成本或不需要维修能力保护措施能力保护措施强度基基础础的隔离的隔离与与震震动动控制控制新抗震新抗震设计设计地震新地震新概概念念设计设计延性 + 对旧抗震规范提出安全性疑问

5、开发新抗震设计方法论 预测结构物确实效应 + 确保抗震性能 评测已有结构的抗震性能抗震性能抗震性能设计设计 为了能够精确计算出结构的实际地震效应，采用非线性地震分析 结构自身能力与抗震需求的比较结构物隔离装置 / 抑制装置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、响应响应分析分析等效等效静静力分析力分析地震地震响应响应分析分析设计设计反反应谱应谱Pushover分析分析静静力分析力分析 动动力分析力分析时时程分析程分析模模态态分析分析线形分析线形分析非线形分析非线形分析非非线线性性动动力分析力分析基基础础的隔离的隔离与与振振动动控制分析控制分析1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis7MidasIT China (

7、Shanghai) Technical Seminar MIDAS的非的非线线性性动动力分析力分析1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis 边界非线形分析非线性振型叠加法内内力作用力作用类类型的一般型的一般连连接接 黏黏弹弹性消能器性消能器 滞滞回系回系统统 铅铅芯橡芯橡胶胶支座支座 摩擦摩擦摆摆隔振系隔振系统统 油阻尼油阻尼(2007)非线性直接积分法

8、非非线线性性时时程分析程分析非线形直接积分法弹塑性梁-柱 集中铰类型 分布铰类型 纤维模型单元类型的一般连接非非弹弹性性墙墙: CRB, General Wall非弹性桁架8MidasIT China (Shanghai) Technical Seminar MIDAS下的非下的非线线性性动动力分析力分析1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis9Midas

9、IT China (Shanghai) Technical Seminar 基础隔震控制基础隔震控制2110MidasIT China (Shanghai) Technical Seminar 常常规规抗震抗震设计设计抗震建筑抗震建筑结构结构的常的常规设计规设计常常规规抗震抗震设计设计结构结构:塑性损坏塑性损坏高维修成本高维修成本损害满足要求损害满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 基基础础的隔离的隔离与与振振动动控制控制地震的隔离地震的隔离能量能量损损耗装置耗装置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础础隔离隔离与与振振动动控制控制隔离隔离 / 阻尼阻尼非弹性行为非弹性行为易更换或不需要更换易更换或不需要更换结构结构:近似弹性行为近似弹性行为低维修成本或不需要维修低维修成本或不需要维修能力保护措施能力保护措施基基础础隔离隔离被被动动振振动动控制控制1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis13MidasIT China (Shangh

12、ai) Technical Seminar 基基础础隔离隔离概概念念固定支座: 加速度响应响应基础础隔离后: 加速度响应响应1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis14MidasIT China (Shanghai) Technical Seminar 基基础础隔离基本原理隔离基本原理改变周期隔离器屈服后柔度 力减小: 建筑损失降低 隔离器位移增加阻尼增加

13、 隔离器塑性形变下的能量损耗 隔离器位移降低 建筑损失降低周期周期位移位移响应谱响应谱周期周期拟拟加速度反加速度反应谱应谱改改变变周期周期阻尼阻尼改改变变周期周期阻尼阻尼1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis15MidasIT China (Shanghai) Technical Seminar 铅芯橡胶支座铅芯橡胶支座(LRB)(LRB)铅芯 : 能量

14、损耗 抗风 变形恢复橡橡胶胶 : 横横向柔度向柔度钢钢板板: 竖竖向承向承载载力力1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4 Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis16MidasIT China (Shanghai) Technical Seminar 铅芯橡胶支座应用铅芯橡胶支座应用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 摩擦摆隔振摩擦摆隔振 (FPS) (FPS)摩擦摩擦摆动摆动系系统区统区凹球面(曲率半径= R)摩擦材料(摩擦系数 = )WMRM摆动摆动滑滑动摆动动摆动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应应用用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粘弹性阻尼滞滞回阻尼回阻尼 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响应谱响应谱改改变变周期周期阻尼阻尼阻尼增加 能量损耗 由黏性阻尼 或 塑性变形产生的阻尼 建筑损失降低1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis2

19、1MidasIT China (Shanghai) Technical Seminar 黏弹性阻尼黏弹性阻尼(Kelvin Model)(Kelvin Model)变形过程变形过程Maxwell Maxwell 模型模型液压黏弹性装置液压黏弹性装置1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis22MidasIT China (Shanghai) Technica

20、l Seminar 黏弹性阻尼黏弹性阻尼(Kelvin Model)(Kelvin Model)固体类型的黏弹性装置固体类型的黏弹性装置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 金属屈服阻尼金属屈服阻尼分离

21、支撑系统分离支撑系统1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis24MidasIT China (Shanghai) Technical Seminar 边界非线性分析边界非线性分析1325MidasIT China (Shanghai) Technical Seminar 【边界非线形分析简述边界非线形分析简述fN , fN :非非线线性性弹弹簧簧，非，非线

22、线性力性力 , fL :等效等效刚刚度度，等效力，等效力pfLfNfL应用振型叠加应用振型叠加p 适用于结构的一部分有非线性特性的情况 将非线性单元转换成线性弹性 非线性效果将非线性构件内力转换为外力来考虑1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis26MidasIT China (Shanghai) Technical Seminar 有效刚度有效刚度: :

23、 非线性弹簧替代非线性弹簧替代=+-()=非非线线形形弹弹簧簧弹弹性性弹弹簧簧弹弹性性弹弹簧簧非非线线形形弹弹簧簧非非线线形形时时程分程分析析线线形形静静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 等效等效动动力荷力荷载载 , fN :No

24、nlinearspring& force , fL :Effectivestiffness& forcefNfLfLppppfLfNfLfNfLfNpfNfLfLfL应应用振型用振型叠叠加法加法1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis28MidasIT China (Shanghai) Technical Seminar 振型叠加法分析简述

25、振型叠加法分析简述隔离器隔离器 / 阻尼器阻尼器: 非弹性行为非弹性行为结构结构: 近似近似 弹性行为弹性行为SMuCuFRLSLK uMuCuRFK u2( )( )2)( )TTTiPiNiNiiiiiTTTiiiiiiLNB p tBBq tq tq tMMtffMt + 杜哈梅积分1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis29MidasIT Chin

26、a (Shanghai) Technical Seminar 直接直接积积分法分法简简述述隔离隔离 器器/ 阻尼器阻尼器: 非弹性行为非弹性行为结构结构: 近似近似 弹性行为弹性行为. 有效刚度有效刚度 : 常量常量. 非线形恢复力非线形恢复力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 一般一般连连接接: 多多样弹样弹簧簧连连接接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 一般一般连连接接 : 多多样弹样弹簧簧连连接接1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis应用类型单元类型基本连接Forty Type General Link性能类型弹簧线形阻尼器弹簧和线形阻尼器线性特征刚度阻尼刚度阻尼刚度阻尼有效刚度有效阻尼静力分析弹性-弹性-弹

31、性-反应谱弹性-弹性-弹性-线形时程分析模态分析弹性-线性弹性线性1)弹性线性1)直接积分弹性-线性弹性线性2)弹性线性2)非线形时程分析模态分析弹性-线性弹性线性1)弹性(假想)线性1)直接积分弹弹性性-线性弹性线性2)弹性(假想)线性2)1) 应变能比2) 质量& 刚度比& 单元质量& 刚度比: 阻尼矩阵 应变能比 : 模态阻尼比34MidasIT China (Shanghai) Technical Seminar 一般一般连连接的接的节节点力点力1. Introduction2. Base Isolation & Vib. Control3. Bound

32、ary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis不不带线带线性有效阻尼性有效阻尼带线性有效阻尼35MidasIT China (Shanghai) Technical Seminar 力力类类型一般型一般连连接的有效接的有效刚刚度度不不稳稳定定结构结构有效有效刚刚度度下的下的稳稳定定带带隔离隔离类类型的非型的非线线性性连连接接结构结构有效有效刚刚度的度的测测定定 非零非零值值 有效有效刚刚度支撑下的度支撑下的样样式式1. Introduction2. Base Isolation

33、 & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis36MidasIT China (Shanghai) Technical Seminar kbkdcdffdddbN1N2MIDAS Civil中的被中的被动动振振动动控制控制黏黏弹弹性阻尼性阻尼 dddddbbdbfk dc sign ddk ddddS输输入入变变量量 cd : VED Damping Constant kd : VED 刚刚度度 S : 阻尼系阻尼系数数 k

34、b : 支撑支撑刚刚度度1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis37MidasIT China (Shanghai) Technical Seminar MIDAS Civil下的被下的被动动振振动动控制控制黏黏弹弹性阻尼性阻尼 阻尼系数(S)线线形形 (s=1.0)非非线线形形 (0.0s 边边界界条条件件 一般一般连连接特性接特性值值Applicati

35、on Type : 非非线线性性连连接接单单元的作用元的作用类类型型 Element Type:直接更新直接更新单单元元刚刚度矩度矩阵来阵来反映非反映非线线性。性。 Force Type:根据非根据非线线性的特性性的特性计计算出算出来来的的内内力力置置换换成外部荷成外部荷载载，间间接的考接的考虑虑非非线线性。性。Property Type Element Type : 弹弹簧簧 线线性阻尼器性阻尼器 弹弹簧簧与线与线形阻尼器形阻尼器 Force Type : 黏黏弹弹性消能器性消能器 滞滞后系后系统统 铅铅芯橡芯橡胶胶支座隔震装置支座隔震装置 摩擦摩擦摆摆隔震装置隔震装置 间间隙隙 钩钩一般一

36、般连连接特性接特性1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis54MidasIT China (Shanghai) Technical Seminar 1. Main 对话对话框框模型模型 边边界界条条件件 一般一般连连接特性接特性值值Linear Properties : 输输入入线线性性弹弹簧的簧的刚刚度以及阻度以及阻尼尼 Effective Stiffn

37、ess : 有效有效刚刚度度Effective Damping : 有效阻尼有效阻尼Nonlinear Properties : 定定义义非非线线性特性性特性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 隔离器建模隔离器建模: 线线形特性形特性- 有效有效刚刚度度1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis56MidasIT China (Shanghai) Technical Seminar 2. 非非线线性特性性特性对话对话框框Stiffness (k) 弹弹簧屈服之前的初始簧屈服之前的初始刚刚度度Yield Strength (Fy)

39、弹弹簧的屈服强度簧的屈服强度Post Yield Stiffness Ratio (r) 屈服后的切屈服后的切线刚线刚度除屈服前初始度除屈服前初始刚刚度的比度的比值值Hysteretic Loop Parameter () 决决定恢定恢复复力曲力曲线线形形状状的的参数参数Hysteretic Loop Parameter () 决决定恢定恢复复力曲力曲线线形形状状的的参数参数| + | = 1.0LRB Isolator Modeling: 非非线线性特性性特性1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonl

40、inear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis57MidasIT China (Shanghai) Technical Seminar , : 屈服后的屈服后的滞滞回曲回曲线参数线参数 + 0: 软软化体系化体系 + 结构类结构类型型 . 模型模型质质量量节节点点质质量量. 模型模型质质量量将将荷荷载转换载转换成成质质量量质质量量输输入入1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analys

41、is4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis60MidasIT China (Shanghai) Technical Seminar 时程函数时程函数: : 荷载荷载 时程分析数据时程分析数据 时程荷载函数时程荷载函数定义时程函数定义时程函数 1) 1) 用户定义用户定义 2) 2) 地震波数据库地震波数据库 : 32 : 32种地震荷载种地震荷载 3) 3) 导入导入 外部数据导入示例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时程函数时程函数#1#11. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis61MidasIT China (Shanghai) Technical Seminar 时时程函程函数数#21. Introduction2.

43、Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis重力荷载重力荷载62MidasIT China (Shanghai) Technical Seminar 1) Analysis Method Modal Analysis(振型振型叠叠加法加法) Direct Integration（直接（直接积积分法）分法）2) Time History Type Transient : （瞬（瞬态态）单单次加次加

44、载载，地震荷，地震荷载载 Periodic :（周期）（周期） 按周期重按周期重复复加加载载，机械振，机械振动动3) End Time : 分析分析时间时间4) Time Increment : 分析分析时间时间步步长长5) Step Number Increment for Output : 输输出出结结果的子步果的子步数数增量增量6) Order in Sequential Loading : 连续连续施加的施加的动动力荷力荷载载加加载顺载顺序序7) Damping Method （阻尼（阻尼计计算方法）算方法）时时程荷程荷载载工工况况#11. Introduction2. Base Is

45、olation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis63MidasIT China (Shanghai) Technical Seminar 时时程荷程荷载载工工况况#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 非非线线性分析控制性分析控制参数参数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 基基础础隔离隔离结构结结构结果果#1屋屋顶绝对顶绝对加速度加速度固定支座结构结构屋屋顶顶位移位移屋屋顶绝对顶绝对加速度加速度屋屋顶顶位移位移基础础隔离后结构结构1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic

48、 Analysis66MidasIT China (Shanghai) Technical Seminar 基基础础隔离隔离结构结结构结果果#2固定支座结构结构屋屋顶顶位移位移: 频频率率响应响应基础础隔离后结结果F=0.562Hz T=1.78secF=0.940Hz T=1.06sec屋屋顶顶位移位移: 频频率率响应响应特征特征值值分析分析结结果果特征特征值值分析分析结结果果1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Stru

49、c. 5. Inelastic Dynamic Analysis67MidasIT China (Shanghai) Technical Seminar 基基础础隔离隔离结构结结构结果果#3Story Drift固定支座固定支座结构结构隔离隔离结构结构1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis68MidasIT China (Shanghai) Techni

50、cal Seminar 基基础础隔离隔离结构结结构结果果#4固定支座结构结构1st 柱剪力柱剪力基础础隔离后结结果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 基基础础隔离隔离结构结结构结果果#5滞滞回曲线线: 铅铅芯橡胶胶支座1st Column Sh

51、ear Force1st Column Shear Force滞滞回曲线线: 摩擦摆摆隔震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程序程序边边界非界非线线形分析指形分析指导导方方针针执执行迭代行迭代非线性振型叠加法非线形直接积分时间时间步步长长: t 0.005sec一般一般连连接有效接有效刚刚度度特征值分析阻尼模型动力方程有效刚度1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated

53、Struc. 5. Inelastic Dynamic Analysis71MidasIT China (Shanghai) Technical Seminar 51非弹性动力分析非弹性动力分析72MidasIT China (Shanghai) Technical Seminar ,EfftttD ttS, FP=RMu +GMIDAS程序的直接程序的直接积积分法分法时时程分析程分析ttttttttD, S, MuGFREffttKuEffP21effttttKMKC 有效荷有效荷载载: : 有效有效刚刚度度: : ,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 非非线线性性动动力平衡方程力平衡方程线线性振性振动动非非线线性振性振动动非

55、非弹弹性振性振动动线线性性 :非非线线性性 :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 钢筋混凝土结构非线性响应分析钢筋混

56、凝土结构非线性响应分析. 自由集中度自由集中度整体模型整体模型离散有限元模型离散有限元模型. 集中铰模型集中铰模型. 分布铰模型分布铰模型 . 纤维模型纤维模型非非弹弹性性铰铰纤维区纤维区细细部分析的有限元模型部分析的有限元模型Smeared Crack Model有限元有限元网网格格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) 带带分布分布铰铰的非的非弹弹性梁性梁- 高斯积分点(1-20)- 精确的力分布函数- 没用到形函数（近视值）0( ) ( ) ( )FbfbLTxxx dx: 精确的截面力差精确的截面力差值值函函数数( )b x: x 处处的截面柔度矩的截面柔度矩阵阵 ( )f

58、 x: 单单元柔度矩元柔度矩阵阵Fdx1( )dxdx( )M xx. 柔度矩阵柔度矩阵1K = F. 刚度矩阵刚度矩阵1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis76MidasIT China (Shanghai) Technical Seminar 1FFFK = FBSI带带集中集中铰铰的非的非弹弹性梁性梁EIfAfBL21126tttmelastich

59、ingeABLEffIFFFAAtmBBddMddMFwhere. 柔度矩阵柔度矩阵. 刚度矩阵刚度矩阵ABBMAM1. Introduction2. Base Isolation & Vib. Control3. Boundary Nonlinear Analysis4. Analysis of Isolated Struc. 5. Inelastic Dynamic Analysis77MidasIT China (Shanghai) Technical Seminar 屈服强度的自屈服强度的自动计动计算算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 非非弹弹性梁的屈服强度性梁的屈服强度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