Hybrid Simulation of Complex Structural Systems

Gilberto Mosqueda, PhDq ,Associate Professor and Director of Graduate Studies

Department of Civil, Structural and Environmental EngineeringUniversity at Buffalo

Outline• Failure of Bridges during Past

Earthquakes• Need for Advanced Experimental

Simulation Capabilities• Hybrid Simulation

– Capabilities and ChallengesCapabilities and Challenges– Numerical Integration Procedures– Monitoring of Experimental Errors– Monitoring of Experimental Errors – Distributed Testing Capabilities

Bridge Failures in Past Earthquakes

nisee.berkeley.edu

Bridge Failures in Past Earthquakes

Bridge Failures in Past Earthquakes

Bridge Failures in Past Earthquakes

Bridge Failures in Past Earthquakes

Bridge Failures in Past Earthquakes

Need for Experimental Research in Earthquake EngineeringEngineering

• Provide an improved understanding of structural behaviorbehavior

• Verify numerical modeling• Proof-of-concept testing of new materials and protectiveProof of concept testing of new materials and protective

systems• Provide laboratory test data for developing structural

fragilities from initial loading to collapse

9

Experimental Facilities in the U.S.

• Network for Earthquake Engineering Simulation (NEES) is a shared national network of 14 experimental ( ) pfacilities, collaborative tools, a centralized data repository, and earthquake simulation software.

10

Experimental MethodsSeismic Performance Assessment

of Structural Systems• Quasi-Static Testing • Shaking Table Testing • Effective Force Testing • Hybrid Simulation

11

Seismic Performance of Precast Segmental Bridges -University at Buffalo Shake Tables

• 1/2.4 scale single span b id i

y

bridge specimen • ABC (Accelerated Bridge Construction) techniquesConstruction) techniques•unbonded internal tendons•Simple friction-type connections

http://seesl.buffalo.edu/projects/accelbridge/default.asp

Seismic effects on Multi-span bridges with high degrees of horizontal curvature - University of Nevada Reno Shake TablesNevada, Reno Shake Tables

•2/5 scale model of a three-span bridge. •145 ft long with an 80 ft•145 ft long with an 80 ft radius at the centerline •Test on four shake tables in the laboratorytables in the laboratory •The superstructure consists of three steel girders and a 12 ft widegirders and a 12 ft wide concrete deck

http://nees.unr.edu/projects/curved_bridge.html

Hybrid Simulation Test Method

• Equation of motion for prototype structure

• Hybrid simulation combines:

frcvma Hybrid simulation combines: – Physical models of structural resistance– Computer models of structural damping and

inertiainertia

• Enables seismic testing of large- or full-scale structural models

14• Solve equation of motion using numerical

integration algorithms

Test ProcedureStartStart

Step 1:compute di+1

Step 2:command actuator

to impose di+1

Step 1:compute di+1

Step 2:command actuator

to impose di+1

Newmark time-stepping integration algorithm i

Step 4:compute other

Step 3:measure

force ri+1 at di+1

i

Step 4:compute other

Step 3:measure

force ri+1 at di+11 1 1 1

1i i i ima cv r f

g g

response quantities: such as vi+1 and ai+1

Step 5:

response quantities: such as vi+1 and ai+1

Step 5:

Experimental substructure

21

12

1

i i i id d tv t a

Step 5:increment counter i

i<Nyes

Step 5:increment counter i

i<Nyes

substructure 1 112i i i iv v t a a

15Stop

no

Stop

no

Methods of Hybrid Simulation• Conventional pseudodynamic testp y

– Ramp and hold loading procedure• Continuous pseudodynamic test

– Specimen is loaded continuously at slow rates to avoid the holdSpecimen is loaded continuously at slow rates to avoid the hold phase and relaxation in specimen

• Real-time pseudodynamic testSpecimen is loaded at correct velocities to account for rate– Specimen is loaded at correct velocities to account for rate-dependent behavior

– Dynamic inertial forces are modeled numerically• Real time dynamic hybrid testing• Real-time dynamic hybrid testing

– Dynamic inertial loads included in experiment– Shake table substructures

G hi ll di t ib t d t t16

• Geographically distributed tests– One or more remote substructures

Implementation IssuesI t ti Al ith

Central Difference

Newmark’s Method• Integration Algorithms

– Implicit or explicit– Integration time step

• Rate of testing

1 1 1 1

21

12

i i i i

i i i i

ma cv r f

d d tv t a

actuator position• Rate of testing

– Time scaling– Pseudo-dynamic vs. dynamic– Continuous vs. ramp-hold load

1 1

212i i i iv v t a a

di+1

steps 3-5 step 2step 1 steps 3-5

phistory

– Material strain rate effects– Observation of damage

E i t l E1.3

1.35en

t (in

)DesiredCommandMeasured

actual time

di

ti (simulation time step)

• Experimental Errors– Actuator tracking errors– Propagation of errors

1.2

1.25

Dis

plac

eme

1713.42 13.44 13.46 13.48 13.5 13.52 13.54 13.56 13.58

1.15

Time (s)

Structural Model• Modeling Issues

– Selection of experimental substructures –t f t t th t diffi lt t d lcomponents of structure that are difficult to model

– Interface boundary conditions between physical and numerical modelnumerical model

– Scale of experimental substructure limited by equipment capabilities

12 34 56 78 910 1112 1314E1 E2 E3 E4 E5 E6

N1N2 N4 N5 N6N3

18

Modeling Issues• Assume force release at boundary to simplify experimental setup• Consider available equipment in laboratory

12 34 56 78 910 1112 1314E1 E2 E3 E4 E5 E6

N1N2 N4 N5 N6N3

Assume pin connection

19

Holistic Simulation• Substructures at different length scales

12 34 56 78 910 1112 1314E1 E2 E3 E4 E5 E6E1 E2 E3 E4 E5 E6

N1N2 N4 N5 N6N3

Shake table substructurereduced scale

Soil ContainerReaction wallFull scale

20

ShakeTable 1 ShakeTable 2Full scale

Hybrid Testing of a Bridge –NEES/E-Defense Collaborative Research

Simulates seismic response of a continuous bridge by a distributedbridge by a distributed hybrid simulation with OpenFresco and OpenSees.The bridge consists of a RC C-bent column, a RC single column, a steel single column steel girdersingle column, steel girder and elastomeric bearings.

http://nees.berkeley.edu/Projects/reports/nees-edefensePresentation.pdf

Hybrid Testing of a Bridge –NEES/E-Defense Collaborative Research

http://nees.berkeley.edu/Projects/reports/nees-edefensePresentation.pdf

Multi-Site Soil-Structure-Foundation Interaction Test (MISST)

University of Illinois at Urbana-Champaign (UIUC), Rensselaer Polytechnic Institute (RPI), and Lehigh University (Lehigh)

( )

http://nees.uiuc.edu/research/MISST_Report_Final_Web.pdf

Multi-Site Soil-Structure-Foundation Interaction Test (MISST)( )

Division of model structure

http://nees.uiuc.edu/research/MISST_Report_Final_Web.pdf

Multi-Site Soil-Structure-Foundation Interaction Test

http://nees.uiuc.edu/research/MISST_Report_Final_Web.pdf

Testing of Complex Structures• Most previous applications of hybrid simulation have been• Most previous applications of hybrid simulation have been

on simple structural models with few degrees of freedom– Lack of robust implicit integration algorithms– Sensitivity of the results to experimental errors for stiff systems of

higher modes

Discretization Condensation

(Shao 2007)

26

( )

Integration Algorithms• Fully implicit methods typically used in numerical

simulations are difficult to implement with experimental substructuressubstructures Iterations can cause erroneous damage or energy dissipation in

experimental substructures Tangent stiffness matrix is difficult to estimate Tangent stiffness matrix is difficult to estimate

Hybrid Simulation integration procedures are predominantly explicit, or use initial stiffness matrix approximations, e.g., Operator-Splitting Method (Nakashima et al. 1990)

Implicit integration with specialized implementation27

Implicit integration with specialized implementation schemes mainly focused on real-time testing

New Integration Procedures for Hybrid Simulation

• Develop integration procedures with improved stability and accuracy suitable for hybrid simulation– Combined Implicit and Explicit Integration Procedure

• Implicit procedure that limits communication between integrator and experiments

• Fail-safe procedures provides backup explicit solution in case numerical integrator does not convergeintegrator does not converge

– Modified Operator-Splitting Integration with Tangent Stiffness Estimation• Capture the instantaneous behavior of experimental substructure and

improves corrector step– Implementation procedure for fully implicit integration methods designed

for pure numerical simulations• Strategy for safe iterations and procedure to estimate tangent stiffness

implemented at element level

28

implemented at element level

Implicit Integration ProcedureA i li it t litti th d f l ti i d• An implicit -operator-splitting method formulation is used

• Determine the predictor displacement:2

1 1 12n n n ntt

d d v a

• Apply displacement and measure restoring force• Update the experimental tangent stiffness matrix, • Use the updated tangent stiffness to calculate new states:

2

Use the updated tangent stiffness to calculate new states:

t1 1

1 e1 1 1

1 1g n n n

n n n n n

u t t t

M ι C v a

a B Kd r M a

Iterate until convergence criteria is satisfied l l e,l l l,m

n n n n n r r K d d 21n n n nt d d a a 1 11n n n nt t v v a a

e 2 T e,l l,m11 n n n n n nt

r K K d a T K d

29

• Iterate until convergence criteria is satisfied

Iteration Strategy for Experimental SubstructuresI it ti ti t i t l t i f f• In iterations, estimate experimental restoring force for iterative displacements using fitted polynomials

• Note that for distributed test, iterative displacements do not d t b t t t itneed to be sent to remote sites

30

Convergence Issues• Convergence is not guaranteed, but simulation

must go on….• If the iterations do not converge:• If the iterations do not converge:

– Leave the displacement unchanged and use explicit expressions to update acceleration and velocity:

11 12

a a en g n n n n n

tu t

a A Mι C v a K d r

1 12n n n nt

v v a a

Or make a one step correction using initial stiffness or tangent

2

2a at

A M C

31

– Or make a one-step correction using initial stiffness or tangent stiffness (Operator-Splitting approach):

Use of sporadic explicit steps• Characteristics:

– Prevents the accumulation of errors as it may occur using a fully explicit algorithm:p g

CE

MEN

TD

ISP

LAC

FULLY IMPLICIT INTEGRATIONACTUATOR PATH IN COMBINED METHODEXPLICIT COMMAND PREDICTIONFULLY EXPLICIT INTEGRATION

32IMPLICIT DISPLACEMENT CORRECTION

TIME

Tangent Stiffness Matrix• Many popular integrators such as Operator Splitting• Many popular integrators such as Operator-Splitting

method use initial stiffness matrix for corrector step– Tangent stiffness better captures the actual behavior of the

experimental substructure and improves rate of convergence :

RC

E

OPERATOR-SPLITTING CORRECTED FORCE

IMPLICIT CORRECTED FORCE

FOR

EME

NT

CE

EM

NT

PREV. FORCE

IMPLICIT CORRECTED FORCE

MEASURED FORCEU

S D

ISP

L.

TOR

DIS

PLA

CE

CTO

R D

ISP

LAC

33

DISPLACEMENT

PR

EV

IO

PR

ED

ICT

CO

RR

EC

Estimation of Tangent Stiffness Matrix• Updating the Stiffness Matrix• Updating the Stiffness Matrix

– In each step, only one pair of force-displacement measurement is available per actuator need to decouple the stiffness matrix to reduce the number of unknowns and directly use experimental measurements

D fi i t i i di t t d l di t t i hi h– Define an intrinsic coordinate system or modal coordinate system in which stiffness matrix is diagonal:

with transformation from actuator (local) to global coordinate system being:

e,l Tn p n pK T P T

e e,lTn nK T K T

s2

rx22

11 12e,l

21 22n

k kk k

K 1

2

00n

ss

P

2 22

s1

rx11

34

Tangent Stiffness Estimation

• Experimental pverifications with 2DOF building model:

35

Experimental Studies

• Sample Experimental Results from hybrid simulation40

DOF 1

0

20

t, m

m

DOF 1DOF 2

-40

-20

Dis

plac

emen

0 5 10 15 20 25 30 35-80

-60

36Time, s

Experimental Studies

• Sample Experimental Results10

K11

5

N/m

m

11

K12

K21

K22

0Stiff

ness

, kN

0 5 10 15 20 25 30 35-5

37Time, s

Estimated Experimental Stiffness Matrix in Actuator Coordinate System

Experimental Studies• Sample Experimental Results

5.5

2000

2500

ad

Story 1 Story 2

4.5

5

Tim

e, s

500

1000

1500

2000

Stiff

ness

, kN

-m/ra

-1 -0.5 0 0.5 14

Rotation, Deg4 4.5 5 5.5

0

Time, s

20 20

-10

0

10

Mom

ent,

kN-m

-10

0

10M

omen

t, kN

-m

38-1 -0.5 0 0.5 1

-20

Rotation, Deg4 4.5 5 5.5

-20

Time, s

Estimated Experimental Stiffness Matrix in Diagonal Form – local element DOFs

Experimental Studies• Sample Experimental Results

20Actual Hysteresis

20Observed Hysteresis

20Converged Hysteresis

5

10

15

men

t, kN

-m

5

10

15

men

t, kN

-m

5

10

15

nt, k

N-m

-10

-5

0

Mea

sure

d M

om

-10

-5

0

Feed

back

Mom

-10

-5

0

Fina

l Mom

en

-2 -1 0 1-20

-15

Measured Rotation, Deg

M

-2 -1 0 1-20

-15

Desired Rotation, Deg

F

-2 -1 0 1-20

-15

Final Rotation, Deg

39Captured Experimental Hysteretic Behavior

Numerical Studies• Numerical Simulation Results

4

gy)

Initial Stiffness t = 10/1024s

2.5

3

3.5

of In

put E

nerg Initial Stiffness t 10/1024s

Initial Stiffness t = 20/1024sUpdated Stiffness t = 10/1024sUpdated Stiffness t = 20/1024s

Experiment Yield Displacement

1

1.5

2

ed E

nerg

y (%

0 10 20 30 40 50 60 700

0.5

1

Unb

alan

ce

40Yield Displacement (mm)

Energy Balance Error versus Ductility and Time Step – Use of Tangent Stiffness improves simulation accuracy

Numerical Studies• Numerical Simulation with Highly Nonlinear Experimental

Substructure

1 5Actual Hysteresis

1 5Observed Hysteresis

1 5Converged Hysteresis

0 5

1

1.5

kN-m

0 5

1

1.5kN

-m

0 5

1

1.5

N-m

-0.5

0

0.5

sure

d M

omen

t,

-0.5

0

0.5

back

Mom

ent,

-0.5

0

0.5

nal M

omen

t, kN

2 0 2 4-1.5

-1

0 5

Mea

s

2 0 2 4-1.5

-1

0 5

Feed

2 0 2 4-1.5

-1

0 5

Fin

41

-2 0 2 4Measured Rotation, Deg

-2 0 2 4Desired Rotation, Deg

-2 0 2 4Final Rotation, Deg

Conventional Operator-Splitting Method

Numerical Studies• Numerical Simulation with Highly Nonlinear Experimental

Substructure1 5

Actual Hysteresis1 5

Observed Hysteresis1 5

Converged Hysteresis

0.5

1

1.5

, kN

-m

0.5

1

1.5

, kN

-m

0.5

1

1.5

N-m

-0.5

0

sure

d M

omen

t

-0.5

0

dbac

k M

omen

t

-0.5

0

nal M

omen

t, kN

2 0 2 4-1.5

-1Mea

s

2 0 2 4-1.5

-1

Feed

2 0 2 4-1.5

-1

Fin

42

-2 0 2 4Measured Rotation, Deg

-2 0 2 4Desired Rotation, Deg

-2 0 2 4Final Rotation, Deg

Improved Operator-Splitting Method with Experimental Tangent Stiffness

Errors in Hybrid Simulations

integrator l

hydraulic supply

D/A

dcintegrator

signal generation

on-line computer

PIDController

servo-valveactuator

h d li

D/A

servo-hydraulic system

A/D dmrm

da

specimentransducers

experimental substructureA/D

da = actual imposed displacementdc = command displacementd = measured displacement

43

dm = measured displacementrm = measured restoring force

Effects of actuator delay on measured specimen responsep p

Loading and unloading of linear-elastic element

resisting force resisting force

energyabsorbed

energyadded

displacement displacement

OvershootingUndershooting

44

OvershootingUndershooting(lag)

Effects of actuator delay on measured specimen responsespecimen response

resisting forceBest Estimate of energy in

Loading and unloading of linear-elastic element

energyadded )(BE ddE

Best Estimate of energy in experimental element

measured disp (dm)command disp (dc)

)( mmBE ddrE

Energy introduced into

displacement

)( cmE ddrE

numerical simulation

45

Numerical Errors• Objective is to solve equation of motion using time

stepping integration procedure – e.g., Newmark’s Method in explicit forme.g., Newmark s Method in explicit form

1 1 1 1

21i i i ima cv r f

d d t t

21 2

1

i i i id d tv t a

v v t a a

• Satisfy dynamic equilibrium • Satisfy kinematics relations derivatives of

1 12i i i iv v t a a

46

• Satisfy kinematics relations – derivatives of displacement and computed velocity and acceleration

Numerical Errors• Comparison of integration methods (t=0 05) for 2DOF shear buildingComparison of integration methods (t=0.05) for 2DOF shear building

(T=0.6,0.13 sec),

Operator Splitting

Newmark Explicit

47

Numerical ErrorsHo can res lts be erified hen the “e act” ans er is not kno n?• How can results be verified when the “exact” answer is not known?

• Unbalance error between input energy from earthquake excitation and internal energy stored and dissipated by structural model (Filiatrault et al 1994)(Filiatrault et al 1994)

10

15

Ener

gy

Operator SplittingNewmark Explicit

5

10

ror,

% o

f Inp

ut E Newmark Explicit

-5

0

rgy

Bala

nce

Err

480 5 10 15 20 25 30-10

Time, s

Ener

Monitoring Errors in Hybrid SimulationAlthough equilibrium is satisfied in each step, need to examine relationships between displacement, velocity and acceleration

gu Ma Cv Ku r Mι

K D S E ICE E E E E

Equation of Motion

Integrated over Displacement

acceleration.

Use time derivative of displacement in place of velocity to include their kinematic relationship.

; v u a u

This is the energy observed by the numerical simulation based on command displacement;

T1E v M v

TtI i gE u t M duInput Energy

Kinetic EnergT1E u Mu

Displacement p ;

But actual experimental displacements may be modified by delay compensation, and forces may be corrected for actuator tracking errors.

K 2E v M v

TDE v Cdu

Kinetic Energy

Damping Energy

K 2E u Mu

TDE u Cdu

Kinetic and Damping Energies Based

g

Use actual energy dissipated by or stored in the experimental substructure.

TSE u K du

C TEE r du

Strain Energy

Experimental Energy Tm mEE r du

Kinetic and Damping Energies Based on Displacement

49

Actual Experimental Energy

Relation between displacement and velocity

• Computing velocity as derivative of displacement in numerical simulation

112n n n u u u 12n n n

300(b)

Velocity

Explicit Newmark Operator-splitting300

(a)

Velocity

0

100

200

ity, m

m/s

Displacement Derivative

0

100

200

ty, m

m/s

Displacement Derivative

-200

-100Vel

oci

-200

-100Vel

oci

500 5 10 15

-300

Time, s

0 5 10 15

-300

Time, s

Overall Energy Error in Hybrid Simulation

• Effect of integration time step on displacement history and error indicator for numerical simulation– Explicit Newmark method

0

10 20

30 Exact 5 ms 10 ms 20 ms 50 ms 100 ms

-40

-30

-20

-10

% o

f Inp

ut E

nerg

y

-10

0

10

acem

ent,

mm

0 5 10 15-70

-60

-50

-40

EEI,

%

5 ms 10 ms 20 ms 50 ms 100 ms

0 5 10 15-40

-30

-20Dis

pla

51

0 5 10 15Time, s

0 5 10 15Time, s

Overall Energy Error in Hybrid Simulation

• Effect of integration time step on displacement history and error indicator for numerical simulation– Operator Splitting Methodp p g

20

30 Exact 5 ms 10 ms 20 ms 50 ms 100 ms

0

10

-10

0

10

plac

emen

t, m

m

-40

-30

-20

-10

% o

f Inp

ut E

nerg

y

0 5 10 15-40

-30

-20Dis

0 5 10 15-70

-60

-50

Ti

EEI,

5 ms 10 ms 20 ms 50 ms 100 ms

52

Time, s Time, s

Overall Energy Error in Hybrid Simulation• Unbalance energy measure also captures difference between

observed and measured behavior of experimental substructure (experimental errors)

5

10Actual Hysteresis

5

10Observed Hysteresis

5

10Converged Hysteresis

0

5

ed F

orce

, kN

0

5

ck F

orce

, kN

0

5

Forc

e, k

N

-5Mea

sure

-5Feed

bac

-5

Fina

l

53-40 -20 0 20-10

Measured Displacement, mm-40 -20 0 20

-10

Desired Displacement, mm-40 -20 0 20

-10

Final Displacement, mm

Experimental Simulation• Monitoring of energy unbalance during

actual hybrid simulation can indicate large errors in a simulation and possiblelarge errors in a simulation and possible instability

• Provide early warning of instability4

1

2

3

4

nt, m

m

DOF 1DOF 2

40

-20

0

ror,

% o

f Inp

ut

2

-1

0

1

Dis

plac

emen

-80

-60

-40

nerg

y B

alan

ce E

rr

15% Energy Error

540 5 10 15

-3

-2

Time, s

0 5 10 15-100

Time, s

En

Towards Collapse Simulation of Structures• Develop advanced hybrid testing methods that can• Develop advanced hybrid testing methods that can

simulate seismic response to collapse– Implicit numerical integration algorithms– Substructuring techniques, how to partition structure and apply

boundary conditions– Compensation of experimental errorsp p

• Apply hybrid simulation to complex structural models– Evaluate seismic response of realistic buildings models

V if bilit t t f il t ll• Verify capability to trace failure to collapse– Compare response of hybrid simulation to shake table test of

full-scale steel moment frame building

55

Four story steel moment resisting frame tested to collapse at E-Defense Japan,Sept. 2007

6m10m

3.5m

VIDEO

75m

3.5m

14.37

3.5m

3.875m

YX

YZ

11/15/2010 56

Internationally Distributed Test, July 2009Half-scale experimentalHalf-scale experimental substructures of lower 1 ½ stories – collapse mechanism

Reproduce E-Defense shake table collapse using hybrid simulation

Buffalo, USA Kyoto, Japan

Coordinator

Proxy PCProxy

Hardware architecture

StationUS with Matlab

Socket

Proxy Socket

Kyoto FacilitiesP

roxy

S

ocke

t Socket

CP

/IP

(Local Socket)

Coordinatord N i l M d l xPC

Kyoto FacilitiesThrough GPBIB TC

and Numerical Model xPC

Buffalo Facilities through ScramnetKyoto Buffalo

Selection of substructuresT t fi t t i t ll l i l d h lf f d tTest first story experimentally, also include half of second story

to simplify boundary with assumed hinges at center of beams and columns

Internationally Distributed Test July 2009Internationally Distributed Test July 2009Internationally Distributed Test, July 2009Internationally Distributed Test, July 2009

T f fi t t t l

Comparison of shake table and hybrid test

Top of first story center column

61

20304050

(mm

)

Shaking TableOnline Test

10152025

mm

)

Shaking TableOnline Test

-30-20-10

010

0 200 400 600 800 1000

Dis

plac

emen

t

-15-10-505

0 200 400 600 800 1000

Dis

plac

emen

t (

-50-40

Steps-25-2015

Steps 20% 40%

-200-100

0100

0 5 10 15 20

t (m

m)

0

20

40

60

nt (m

m)

Shaking Table

Online Test

-600-500-400-300

Dis

plac

emen Shaking Table

Online Test

-60

-40

-20

00 500 1000 1500

Dis

plac

emen

-800-700

Time (s)

-80

60

Steps 100%60%

First story force-displacement response for 60% TakatoriComparison of shake table and hybrid test

Fi S H i B h iFirst Story Hysteretic Behavior

1500

2000 E‐Defense Distributed Test

500

1000

1500

ear (kN

)

‐500

0‐0.05 ‐0.04 ‐0.03 ‐0.02 ‐0.01 0 0.01 0.02 0.03 0.04 0.05St

ory  She

‐1500

‐1000

Drift Angle (rad)

First story force-displacement response for 100% Takatori - CollapseComparison of shake table and hybrid test

First Story Hysteretic Behavior

1500

2000 E‐Defense Distributed Test

500

1000

1500

ar (kN)

‐1000

‐500

0‐0.05 0 0.05 0.1 0.15

Story  She

‐2000

‐1500

Drift Angle (rad)

SummaryI t ti d id i d t bilit• Integration procedure provides improved stability and accuracy as a step towards testing large and complex structural systems– Use of general implicit integration algorithms designed for

pure numerical simulations– Procedure to estimate tangent stiffness matrix for

experimental substructuresexperimental substructures– Safe iteration strategy for experimental substructures

• These procedures are being implemented in O SEES/O f f k i t lOpenSEES/Openfresco framework as experimental substructure element

• Framework can be applied to real-time simulations 65

and provide significant advantages for fast distributed testing

SummaryV ifi d ff ti f h b id t ti f li ti• Verified effectiveness of hybrid testing for realistic collapse simulation by comparison with shake table test results of full scale frame

• Demonstrate that hybrid testing is a safe and economical alternative for collapse simulation

• Use of international geographically distributedUse of international geographically distributed testing for large scales testing of structural systems

• Use of advanced numerical modeling (FEM, implicit integration) to capture degradation of numericalintegration) to capture degradation of numerical model

• Examined substructuring techniques and effects of b d diti tiboundary condition assumptions

Acknowledgements

• Research funded by – NSF CAREER Award CMMI-0748111

NSF Award CMS 0402490 for shared use access of nees@buffalo– NSF Award CMS 0402490 for shared use access of nees@buffalo• Graduate Student Researchers

– Mehdi Ahmadizadeh, Assistant Professor, Shiraz UniversityM i C t D l d PhD t d t U i it t B ff l– Maria Cortez-Delgado, PhD student, University at Buffalo

• International Collaborators– Masayoshi Nakashima, Professor, Kyoto University, Director, E-

DefenseDefense– Tao Wang, Senior Researcher, Institute of Engineering

Mechanics, Beijing, China

67

THANK YOU!

Questions?

68

QuestionsWh t th d t f h b id i l ti ?• What are the advantages of hybrid simulation?

• What additional difficulties are encountered in implementing implicit methods in a hybrid simulationimplementing implicit methods in a hybrid simulation compared to a numerical simulation?

• Why is there a need to compute the tangent stiffness matrix for experimental substructures?

• In addition to those errors found in numerical simulations what additional sources of errors aresimulations, what additional sources of errors are present in a hybrid simulation?

• What are the effects of errors in a hybrid simulation and how can errors be measured in a hybrid test?