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1、2002. 9. 2MIDAS IT 开发二组开发二组动力非线性边界分析动力非线性边界分析简介简介 Boundary Nonlinear Dynamic Analysis Damper type Nonlinear Link Modal Nonlinear Analysis : Equivalent Dynamic Load Base Isolator type Nonlinear LinkDynamic Nonlinear Analysis (2002. 9. 2.)Dynamic Nonlinear Analysis (2002. 9. 2.) Damper type Nonlinear
2、Link Visco-Elastic Damper (VED) Solid Type Fluid TypeHysteretic System(HYS) Metal Damper Friction DamperDynamic Nonlinear Analysis (2002. 9. 2.)Effectiveness of DamperPeriodDisplacementResponse SpectrumPeriod ShiftDampingDamping Increase Energy Dissipation by Damper Viscosity or Damper Plastic Behav
3、ior Building Damage ReductionVisco-Elastic Damper (VED)DisplacementForceHysteretic System (HYS)Area = A1Area = A0Equivalent DampingDisplacementForceDamperFEquivalent Damping by DamperDynamic Nonlinear Analysis (2002. 9. 2.)Dynamic Nonlinear Analysis (2002. 9. 2.)cdkbdddbffkdDamperBraceVisco-Elastic
4、Damper (VED)Input Variables cd : VED Damping Constant kd : VED Stiffness S : Damping Exponent kb : Bracing StiffnessDynamic Nonlinear Analysis (2002. 9. 2.)Damping Exponent (S)Linear (s=0.0)Nonlinear (0.0s1.0)Nonlinear (1.0s)Velocity of DeformationViscous Damping ForceDynamic Nonlinear Analysis (200
5、2. 9. 2.)Hysteretic System (HYS)ffdInput Variablesk : Initial StiffnessFy : Yield Strengthr : Post Yield Strength Ratio , : Loop Shape ParameterS : Bi-linear Transition ParameterDeformation(d)Force ( f )kr kFyDynamic Nonlinear Analysis (2002. 9. 2.)=0.1 , =0.9=0.9 , =-0.1=0.5 , =-0.5=0.25 , =0.75-2-
6、1.5-1-0.500.511.52-1-0.75-0.5-0.2500.250.50.751dDeformation(d)Internal variable (z)-2-1.5-1-0.500.511.52-5-4-3-2-1012345dzDeformation(d)Internal variable (z)-2-1.5-1-0.500.511.52-3-2-10123dDeformation(d)Internal variable (z)-2-1.5-1-0.500.511.52-1-0.75-0.5-0.2500.250.50.751dzDeformation(d)Internal v
7、ariable (z)Loop ShapeParameter (, )Dynamic Nonlinear Analysis (2002. 9. 2.)Bilinear Transition Exponent (S)00.20.40.60.81.01.21.41.61.82.000.20.40.60.81.01.2dzs = 1.0s = 10.0s = 2.0s =100.0Deformation(d)Internal variable (z)Dynamic Nonlinear Analysis (2002. 9. 2.)Visco-Elastic DamperSolid Type Visco
8、-elastic DamperImplementationFluid Type Visco-elastic DamperOrificeFluidImplementationDynamic Nonlinear Analysis (2002. 9. 2.)Visco-Elastic DamperDynamic Nonlinear Analysis (2002. 9. 2.)Hysteretic SystemMetal Damper : ADAS system(Added Damping and Added Stiffness)Dynamic Nonlinear Analysis (2002. 9.
9、 2.)Metal Damper : TADAS system (Triangular ADAS)Hysteretic SystemDynamic Nonlinear Analysis (2002. 9. 2.)Metal Damper : Unbonded Brace systemHysteretic SystemDynamic Nonlinear Analysis (2002. 9. 2.) Base Isolator type Nonlinear Link Lead Rubber Bearing (LRB)Friction Pendulum System(FPS)Dynamic Nonl
10、inear Analysis (2002. 9. 2.)Base Isolation :FundamentalsFixed BaseBase IsolationDynamic Nonlinear Analysis (2002. 9. 2.)Effectiveness of Base IsolationPeriod Shift Isolator Flexibility after Yielding Force Reduction : Building Damage Reduction Isolator Displacement IncreaseDamping Increase Energy Di
11、ssipation by Isolator Plastic Behavior Isolator Displacement Reduction Building Damage ReductionPeriodDisplacementResponse SpectrumPeriodPseudo-AccelerationResponse SpectrumPeriod ShiftDampingPeriod ShiftDampingDynamic Nonlinear Analysis (2002. 9. 2.)Lead Rubbr Bearing (LRB)Lead : Energy Dissipation
12、 Wind Resistance Deformation RecoveryRubber : Lateral FlexibilitySteel Plate : Vertical Load CapacityComposition of 3 Springs in LRBDynamic Nonlinear Analysis (2002. 9. 2.)Input Data of Axial SpringInput Data of Axial Spring kx : Elastic StiffnessInput Data of Shear SpringInput Data of Shear Spring
13、ky, kz : Initial Stiffness Fy,y, Fy,z : Yield Strength ry, rz : Post Yield Strength Ratio , : Loop Shape ParameterElastic Axial SpringNonlinear Shear Spring(Hysteretic System)kxxzyky, Fy,y, ry, , kz, Fy,z, rz , Dynamic Nonlinear Analysis (2002. 9. 2.)PPPPffRkShear Spring in FPSFriction Pendulum Syst
14、em (FPS)Spherical Concave Surface(Radius of Curvature = R)Friction Material(Friction Coefficient = )Dynamic Nonlinear Analysis (2002. 9. 2.)Before SlidingAfter SlidingColumnShear Stiffness (= k )fPfPffPPInitial Stiffness (= k )Shear Stiffness of Slider & Connected Member Before SlidingUsually Column
15、 Stiffness (in which isolator is installed) Before SlidingDynamic Nonlinear Analysis (2002. 9. 2.)Composition of 3 Springs in FPSxzyGAP type Axial SpringNonlinear Shear Spring(Friction Pendulum System)fast, yslow, yRyRzInput Data of Axial SpringInput Data of Axial Spring kx : Elastic Stiffness O : G
16、ap Opening = 0 (fixed)Input Data of Shear SpringInput Data of Shear Spring ky , kz : Initial Shear Stiffness Ry, Rz : Radius of Curvature of Friction Surface fast,y, fast,z : Friction coefficient at Fast deformation slow,y, slow,z : Friction coefficient at Slow deformation r y, r z : Friction coeffi
17、cient Transition Ratiokykzryfast, zslow, zrzkxDynamic Nonlinear Analysis (2002. 9. 2.)Implementation of Base IsolationDynamic Nonlinear Analysis (2002. 9. 2.)Implementation of Base IsolationDynamic Nonlinear Analysis (2002. 9. 2.)Implementation of Base IsolationDynamic Nonlinear Analysis (2002. 9. 2
18、.) Modal Nonlinear Analysis : Equivalent Dynamic LoadComposite Spring Link Spring Composition Spring LocationEquivalent Dynamic Load Mothod Effective Stiffness Equivalent Dynamic Load Choice of Effective Stiffness Modal Nonlinear Analysis Dynamic LoadDynamic Nonlinear Analysis (2002. 9. 2.)krykrzjoi
19、nt ikrxkdxkdykdzxzycyiLcyjLLcziLczjLjoint jNonlinear Link :Composite Spring LinkDynamic Nonlinear Analysis (2002. 9. 2.)NL-Link with Spring Location : Shear & Moment Couple Similar to Beam Elementrirjdr=rj - riLj rjLi riLiLjMjVjMiViMiMjViVjVMkrkuLMxVxdushear forcediagrambending momentdiagramuj-uirig
20、idrigidMoment of SpringDepends on Spring LocationDynamic Nonlinear Analysis (2002. 9. 2.)NL-Link without Spring Location : Shear & Moment DecoupleVjViMiMjViVjVMkuLshear forcediagrambending momentdiagramdu =uj-uirigidMirirjdr=rj - riMjkrrigidDynamic Nonlinear Analysis (2002. 9. 2.)Effective Stiffness
21、=+-()=NonlinearSpringElastic Spring withEffective StiffnessElastic Spring withEffective StiffnessNonlinearSpringNonlinearAnalysisLinearAnalysisEquation of Motion :fNfLfLppppfLfNfLfNfLfNEquivalent Dynamic Load MethodpfNfLfLfLfLfNDynamic Nonlinear Analysis (2002. 9. 2.)Modal Nonlinear AnalysispdNd1d3d
22、2=+Nonlinear Link Force :fN = function of dN (=d1+d2+d3)Effective Stiffness ModelChoice of Effective Stiffness Non-zero Value Mode Shapes depends on Effective StiffnessDynamic Nonlinear Analysis (2002. 9. 2.)UnstableUnstableStable Stable bybyEffective StiffnessEffective StiffnessStructure with Isola
23、tor Type Structure with Isolator Type Nonlinear LinkNonlinear LinkStable without Effective StiffnessStable without Effective StiffnessDynamic Nonlinear Analysis (2002. 9. 2.)Structure with Damper Type Structure with Damper Type Nonlinear LinkNonlinear LinkChoice of Effective Stiffness Zero Value Original Mode ShapeDynamic LoadFor Nonlinear AnalysisW Scale (=0 to 1)GA(g)ScaleGA1.0t1t0t2Gravity LoadEarthquake Loadt1t2Dynamic LoadImportant Case :FPS type IsolatorW Scale (=1)
