MERCURY Optimized Software for Hybrid Simulation;saouma/wp-content/...Optimized Software for Hybrid Simulation; from Pseudo-Dynamic to Hard Real Time V. Saouma D.H. Kang G. Haussmann

MERCURYOptimized Software for Hybrid Simulation;

from Pseudo-Dynamic to Hard Real Time

V. Saouma D.H. Kang G. Haussmann

University of Colorado, Boulder

September 6, 2010

V. Saouma et al.; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 1/37

Outline I

1 IntroductionGlobal ContextBackgroundNRC/NEESMercury Overview

2 AnalysisConstitutive ModelsElements

LibraryState Determination

Nonlinear Algorithms

3 HybridMatlabc++; Generalc++; Hybrid Elementc++; Coordinate Transformation

4 ImprovementsRTHS on a Shared Memory Computer


Outline II

RTHS on a Computer Cluster; AlgorithmRTHS on a Computer Cluster; Results

5 Scripting6 Interface

IntroductionHybrid PipeSCRAMNet PipeVirtual Spring PipeEnvironmental Variables

7 Xtras8 Documentation

Technical ManualUser’s manualsValidation Manual

9 RemarksCurrent DevelopmentGraphical Post ProcessorApplications


Outline III

Shake Table vs RTHS

10 Summary

11 Credit


Introduction Global Context

Global Context

Numerical simulation remains a major challenge to EQ engineering community.

We can simulate the explosion of a nuclear bomb, but we can not (“exactly”)simulate seismic response of structures.

Must rely on experiments of structural components, or systems to capturecomplex response.

Finite element modeling capabilities are sophisticated, but not yet “perfect”.

Many (hundreds of) laboratories

Are equipped with digitally controlled actuators/load frames (and LabView),and continue to operate under load/strain/stroke control only.Could benefit from a full nonlinear finite element code which can beplugged in LabView/Simulink to drive their tests


Introduction Background

Background

Existing software not ideally suited for single site pseudo dynamic (PsD)and RTHS.

Software may require support of a “facilitator” (such as OpenFresco orSIMCOR) to interact with hardware. Essential for distributed hybridsimulation, a handicap for single site HS.

The literature provides very little evidence of RTHS of structures(complexity of the numerical substructure, validation with shake tabletests).

Boulder embarked in a project to

Develop an optimized software for single site PsD and RTHS (not meant asan alternative to OpenSees, Sap2000, Midas, ...)Perform RTHS of a reinforced concrete frame previously tested on a shaketable, and compare results.


Introduction NRC/NEES

A Research Agenda for the Network for

Earthquake Engineering Simulation (NEES)

Committee to Develop a Long-Term Research

Agenda for the N etwork for Earthquake Engineering Simulation (N EES)

Board on Infrastructure and the Constructed Environment

Division on Engineering and Physical Sciences

Preventing Earthquake

DisastersTHE GRAND CHALLENGE IN EARTHQUAKE ENGINEERING

National Research Council

One of the primary goals of NEESis to foster a movement towardintegrated computer simulation andphysical testing.

Holy Grail: replace all testing bynumerical simulation. How can weachieve it?

1 Increase sophistication of real timehybrid simulation (RTHS).

2 Gradually replace/eliminate ST testsby RTHS.

3 Eliminate ST & RTHS


Introduction Mercury Overview

Mercury Overview

Two identical versions

Matlab (used for prototyping, and pedagogical purposes)c++ for deploymentStudents found it much easier to start with the Matlab version, and then runthe c++ version.

Has most of the key features likely to be required in a comprehensivenonlinear RTHS of steel or reinforced concrete structures.

Runs within LabView, Simulink/xPC, or real time Linux.

Optimized for speed and performance.

“Battle tested”

c++ version with a complex RTHS simulation.Matlab version in a new course (Nonlinear Structural Analysis)

Extensive documentation, and validation.

Will be supported by Boulder if you decide to adopt it.


Analysis Constitutive Models

Constitutive Models; fiber elements

Steel

Models with isotropic and kinematichardening

Bilinear with isotropic hardening

Modified Giuffre-Pinto

tanE

1 1C ( , )rev revε σ

1 10 0( , )ε σ

2 20 0B ( , )ε σ

2 2A ( , )rev revε σ

E

yε

Strain [mm/mm]

Stre

ss [

Mpa

]

-0.04 -0.02 0 0.02 0.04 0.06 0.08

-2000

-1000

0

1000

2000

(a)

(b)

Concrete

Modified Kent and Park

A

B C

1 1D( , )m mε σ

EF

G

H

2 2I( , )m mε σ

R( , )R Rε σ

1tε

2tε

1RE

2RE

20.5 RE⋅

20E

10.5 RE⋅

cE

cE

cε

cσ

Anisotropic damage model(LMT/Cachan)

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

-0.010 -0.008 -0.006 -0.004 -0.002 0.000 0.002

Str

ess

[kN

/mm

2]

Strain [mm/mm]

Strain-Strain Curve


Analysis Constitutive Models

Constitutive Models; Lumped Plasticity

Model of Ibarra, Medina and Krawinkler (2005)

1

0

2

37

4

5

6

8

F

y

!F

1

!F

1

"F

y

"F

0

! 1

!

0

" 1

"

0

"K

1

"K

K

1

!K

0

!K

Original Envelope Original Envelope

1

0

2

3

7

45

6

8

F

y

!F

,1ref

!F

y

"F

0

! 1

!

0

" 1

"

K

,1reK

,0ref

!F

,1ref

"F

,0ref

"F

Basic strength deterioration Post capping strength deterioration

1

0

2

3

7

4

5

6

F

y

!F

y

"F

K

1K

Original Envelope

K

2K

Interruption

(Disregard stiffness deterioration)

1

0

2

3

7

4

5

6

8

F

y

!F

y

"F

0

!

0

"

K

,1reK

Original Envelope

9

,1s

!#

,1s

"#

Unloading stiffness deterioration Accelerated reloading stiffness deterioration


Analysis Elements

Element Library

2D truss and beam-columns

Stiffness Based

Flexibility Based (with or withoutelement iterations)

x

y

z

x

, ( )e yw x

, ( )e xw x1 1,z zM θ��

2 2,x xN u� �

2 2,z zM θ��

1 1,z zM θ��

, ( )e yw x

, ( )e xw x ( ), ( )z zM x xφ

( ), ( )x zN x xε

eL

Layered (fiber) sections

x

z

y y

zifiby

ifibz

Zero length elements and sections


Analysis Elements

State Determination

Analysis

,tnP1

int

, ,

ext

t n t n P P?

8

a) Structure level; , u P b) Element level; , d f

,tnu

2

Element Nodal

Forces

intint

,, , enenff

Structure Tangent

Stiffness Matrix

tan

SK

Structure Nodal

Forcesint

,tnP7

c) Section level;

4Section

Deformations ,,senConstitutive Model

! "D# $ $ !f % &$

Section

Forces

Section

Forces , ,s e n#

Elem

ent N

odal

Disp

lacemen

ts,

en

d E

lemen

t

Nod

al

Fo

rces,

en

f

Element Nodal

Displacements ,e nd

3

int

,,sen

?5 int

, ,e n e n d d

Element Tangent

Stiffness Matrix

tan tan

, ,,e n e nk k

66

7


Analysis Nonlinear Algorithms

Nonlinear Analysis

Solution AlgorithmsLinear staticEigenvalue analysisInitial stiffnessNewton-RaphsonModified Newton-Raphson

Mixed User can specify automatic change of solution algorithm ifconvergence fails

Convergence CriteriaDisplacement normForce normEnergy norm

IntegratorsStatic

Load controlDisplacement controlArc length†

TransientNewmark βHilber-Hughes-Taylorα

Shing (IS, NR, or MNR)


Hybrid Matlab

Hybrid Capabilities; Matlab

Supports (non-real time) distributed hybridelement

Communication through TCP/IP,

“Physical element” can be another versionof Mercury.

Transfers nodal displacementshybrid2DBeamColumnNumerical

Slave node (if Mercury) can returnrestoring forces and nodal displacementshybrid2DBeamColumnPhysical.

For “debugging” (testing coordinate transformation) and teaching

♦ Defintion of hybrid element in Mercury_Master with IP address2

elements = {{eletag1, Hybrid2DBeamColumnNumerical , in, jn, sectag, IP address1 , port number}};

♦ Definition of physical element in Mercury_Slave with IP address1

hybrid = { Hybrid2DBeamColumnPhysical , IP address2 , port number, eletag2}

Hy

bri

d2

DB

eam

Co

lum

nN

um

eric

alw

ith

elet

ag1

clientdouble.m

clientdouble( IP address2,

port number,

number of retries)

Hy

bri

d2

DB

eam

Co

lum

nP

hy

sica

lw

ith

elet

ag2

serverdouble.m

serverdouble( ,

port number,

number of retries)

n

ed

TCP/IP Connection

serverdouble.m

serverdouble( ,

port number,

number of retries)

clientdouble.m


port number,

number of retries)

m

ef

serverdouble.m

serverdouble( ,

port number,

number of retries)

clientdouble.m


port number,

number of retries)

m

ed


Hybrid c++; General

Hybrid Capabilities; c++

Hybrid Element converts numerical values into physical space values

transfer interface shuttles data between Mercury and the hosting application thatcontrols the physical test.

Hybrid functionality has been exposed to a command-line program, NationalInstruments LabView, and Mathworks MATLAB/Simulink.

Transfer interface can be used to embed Mercury within other applications

Environment assigns a platform on which Mercury runs.

Mercury performs timestep/increment iteration internally vs. embedded analysis(Mercury performs a single step when triggered by the hosting application)


Hybrid c++; Hybrid Element

Hybrid Element

Appears as an element like any other element in the numerical model computes restoring

forces (finte ) in terms of nodal displacements (d

ne).

Uses physical measurements instead of computation to produce element restoring forces.

Measured quantities include all forces produced by the specimen: stiffness, damping, andinertial forces.

For nonlinear solution user must provide reasonable estimates of initial and tangentstiffness.

n

ed np

m

ef

m

ef

mpd

ed

d

ef


Hybrid c++; Coordinate Transformation

Coordinate Transformation

Element nodal displacements in structural model are converted into actuatordisplacements (pn) which are applied to the physical specimen

measured element restoring forces (fme ) and element nodal displacements (d

me ) from the

specimen are then converted into desired element restoring forces (fde ) and element nodal

displacements (dde ) used in the numerical model

1 1 1X , A , p

BL

nx

ny

nz

nx nxN , u

ny nyV ,v

nz nzM ,

p pxX , u 2 2 2X ,A , p

3 3 3X ,A , p

1

2

p pyY , v

p pz

Z ,


Improvements RTHS on a Shared Memory Computer

RTHS on a Shared Memory Computer

Multithreading based on Intel MKL library

Linear Solver: PARDISO (thread-safe,high-performance, robust, memoryefficient software for large sparsesymmetric matrices).

Force Recovery: is multi-threaded forparallel operations.

Test Problem to Assess benefit ofmulti-threading analysing a R/C frame ofincreasing size.

0

0.5

1

1.5

2

2.5

3

3.5

0 200 400 600 800 1000 1200 1400 1600 1800

Spe

edup

ove

r se

rial p

rogr

am

DOFs in model

Speedup of multithreaded Mercury vs. serial Mercury


Improvements RTHS on a Computer Cluster; Algorithm

RTHS on a Computer Cluster;Algorithm

K3-1

u11

u21

u1m...u1

2u2

2u2

m... u3

1u3

2u3

m...

K0-1

1 2 3

a) Initial stiffness; One processor; m=10

u11

u21

u1m...u1

2u2

2u2

m... u3

1u3

2u3

m...

K1-1

1 2 3

Incr.

Incr.

K2-1

b) Modified Newton-Raphson; m=10 (not feasible, K-1 computationally expensive)

Shared Memory Configuration (Multi-threaded)

1Incr.

SCRAMNet Card

2 3 4 5 6 7 8 9 10 11 12 13 14

K0-1

K0-1

K3-1

K7-1

K10-1

Cluster A (Real time)

Cluster B (Non-Real time) K3-1



Distributed Memory Configuration (MPI)

c) Saouma-Kang (Variable Initial Stiffness)

K7-1

Iter.

Iter.

Two clusters: A (real time) dedicated to hybrid simulation (multipleCPU for force recoveries); B (not real time) dedicated to evaluation ofK−1t . Swap inverse tangent matrix when completed.


Improvements RTHS on a Computer Cluster; Results

RTHS on a Computer Cluster; Results

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

1 2 3 4 5 6 7

Sp

eed

up

Number of processors

Speedup (Parallel program)

with inverse matrix & element state determination)

# of elements = 53 # of elements = 109 # of elements = 165 # of elements = 333

# of elements = 389 # of elements = 445 # of elements = 501


Scripting

Scripting Interface: LUA

Embedded in code

MATLAB like syntax (cell arrays), and can easily define functions andvariables

can use alphanumeric (as opposed to just numeric) tags

Listing 1: Example� �

b a r s l i p s e c t i o n f = ’ BSColDFSection ’ ; b a r s l i p s p r i n g f = ’BSColDFSS ’ ;columnsect ion = ’ ColDSection ; b a r s l i p s p r i n g = ’BSColDSS ’ ;b a r s l i p s e c t i o n = ’ BSColDSection ’ ; c o l u mn r i g i d s ec t io n = ’ Co lR ig idSec t ion ’ ;i f ( c o l f l o o r ==1) thennode1 = columnnodename( colbay , c o l f l o o r , 1 ) ;node2 = columnnodename( colbay , c o l f l o o r , 2 ) ;ba rs l ipbo t tom = { s t r i n g . format ( ’ columnbsb_%d_%d ’ , colbay , c o l f l o o r ) ,’ In ter faceElement2D ’ , node1 , node2 ,{ { b a r s l i p s p r i n g f , { 1 , 0 , 0 } } } , { { b a r s l i p s e c t i o n f } } , {0 ,1 ,0 } , { −1 ,0 ,0 } }p las t icco lumn1 = { s t r i n g . format ( ’ columnpl1_%d_%d ’ , colbay , c o l f l o o r ) ,’ StiffnessBased2DBeamColumn ’ , node2 , node3 , { columnsect ion , n I p _ s t i f } }f lexco lumn = { s t r i n g . format ( ’ co lumnf lx_%d_%d ’ , colbay , c o l f l o o r ) ,’ Flexibil ityBased2DBeamColumn ’ , node3 , node4 , { columnsect ion , n I p _ f l e x } ,f lexparams }p las t icco lumn2 = { s t r i n g . format ( ’ columnpl2_%d_%d ’ , colbay , c o l f l o o r ) ,’ StiffnessBased2DBeamColumn ’ , node4 , node5 , { columnsect ion , n I p _ s t i f } }b a r s l i p t o p = { s t r i n g . format ( ’ columnbst_%d_%d ’ , colbay , c o l f l o o r ) ,’ In ter faceElement2D ’ , node5 , node6 ,{ { b a r s l i p s p r i n g , { 1 , 0 , 0 } } } , { { b a r s l i p s e c t i o n } } , {0 ,1 ,0 } , { −1 ,0 ,0 } }r ig idco lumntop = { s t r i n g . format ( ’ co lumnrdt_%d_%d ’ , colbay , c o l f l o o r ) ,


Interface Introduction

Interface and Coupling to Hosting Application

Embedded in code

MATLAB like syntax

can easily define functions and variables

Embedded version of Mercury which runs within another application (thehosting application)

C/C++ code connects embedded Mercury to hosting application(LabView,Simulnk, etc.) which can

Transfer data quantities between embedded Mercury and externalapplicationAllows the hosting application to ’trigger’ embedded Mercury to perform asingle timestep or increment

Input files used for command-line based Mercury can be used byembedded Mercury with minimal changes


Interface Hybrid Pipe

Hybrid Pipe

Abstract interface which connects Mercury hybrid element to a physicalspecimen

Different hybrid pipes must be used/written depending on specificlaboratory hardware

Example: SCRAMNETpipe is specifically designed to work with MTSSCRAMNet-based actuators

Laboratory hardware differences are contained in the Hybrid Pipe code,without affecting other code

Two labs with differing actuator setups could use the same input file bychanging the Hybrid Pipe used


Interface SCRAMNet Pipe

SCRAMNet Pipe

Hybrid Pipe specifically written to work with SCRAMNet-driven MTSactuators

Displacements and Forces of a hybrid element are written/read from theproper SCRAMNet memory locations

Timestepping is synchronized from a SCRAMNet interrupt, lockingMercury’s timestep rate

Useful starting point for writing new Hybrid Pipe classes to handledifferent hardware


Interface Virtual Spring Pipe

Virtual Spring Pipe

A Hybrid pipe that simulates a physical specimen

Useful for testing and verifying simulation setup without actually runningactuators

Simple spring response: F = Kd

Can delay the response by N timesteps, to simulate actuator lag fortesting purposes


Interface Virtual Spring Pipe

Transient Recorders

[fragile]

transientrecorder will accumulateand record displacements and forces for alist of nodes and write them only aftersimulation is completed in order to avoidinterrupting the real-time simulation.

One should specify:

Number of values to record

Number of DOFs in the model

Filename to save the data into

Names/numbers of all the nodes torecord


Interface Environmental Variables

Environmental Variables

Describes which platform Mercuryis running on. There are severalpossible values:

1 CommandLine

2 CommandLineTriggered

3 LabView

4 Simulink

For the CommandLineenvironment, one should use thesolve method to perform analysis,specifying the number of timestepsto use. For any other environment,the user should set some variablesdescribing the model, analysis andloading to use; the environment willproperly trigger Mercury for thespecified number of timesteps.

� �i f ( Environment == "CommandLine " ) then

p r i n t ( " Er ro r : run mercury wi th the −−e x t e r n a l op t ion " )t r a n s i e n t a n a l y s i s : so lve (30000)

elseCommandLineTriggeredHook = t r a n s i e n t a n a l y s i sLabViewHook = t r a n s i e n t a n a l y s i sSimulinkHook = t r a n s i e n t a n a l y s i sModelRef = modelLoadingRef = ear thquakeloadingnumsteps = 30001rampsteps = 1000 −−[ [ ramp up i n i t i a l va lues ] ]

end� �


Xtras

Special Features

Speed

Shared memory: multithreaded with Intel MKL libraryDistributed memory: Two groups of processors (MPI)

Hybrid simulation in real time, element force recoveryspread in a cluster of n processorsContinuous update of tangent stiffness matrix in a “parallel”non real time computer cluster; Initial stiffness matrix iscontinuously overwritten

Refinements of Shing’s Method to allow 10n iterations per incrementof 0.01 sec.

Pushover Analysis Allows application of displacement over multipledof following application of vertical loads (single analysis).

High performance concrete model (Developed by LMT/Cachan)


Documentation Technical Manual

Technical Manual

Over 250 pages of detailed technical documentation for element formulations, constitutivemodels, integration schemes, hybrid elements.

DraftWith the section tangent flexibility matrices at end of the last convergence in structural

level given byctan,k=1,j=0s,e,n (x) = c

tans,e,n−1(x)

the linearization of the section force-deformation relation yields the incremental section defor-mation vectors.

δεεεk=1,j=1s,e,n (x) = ctan,k=1,j=0s,e,n (x) · δσσσ

k=1,j=1s,e,n (x)

The section deformation vectors are updated to the state that corresponds to point B inFig. 3.13(b), and the updated section deformation vector will be given by

εεεk=1,j=1s,e,n (x) = εεεk=1,j=0s,e,n (x) + δεεε

k=1,j=1s,e,n (x)

For the sake of simplicity we will assume that the section force-deformation relation is explic-itly known, then the section deformation vectors εεεk=1,j=1s,e,n (x) will correspond to internal section

force vectors σσσint,k=1,j=1s,e,n (x) and updated section tangent flexibility matrices ctan,k=1,j=1s,e,n (x) in

Fig. 3.13(b) can be defined.The residual section force vectors are then determined

σσσR,k=1,j=1s,e,n (x) = σσσk=1,j=1s,e,n (x)− σσσ

int,k=1,j=1s,e,n (x)

and are transformed into residual section deformation vectors εεεR,k=1,j=1s,e,n (x)

εεεR,k=1,j=1s,e,n (x) = ctan,k=1,j=1s,e,n (x) · σσσ

R,k=1,j=1s,e,n (x)

The residual section deformation vectors are thus the linear approximation of the deforma-tion error made in the linearization of the section force-deformation relation (Fig. 3.13(b)).While any suitable section flexibility matrix can be used to calculate the residual section defor-mation vector, the section tangent flexibility matrices offer the fastest convergence rate.

The residual section deformation vectors are integrated along the element using the com-plimentary principle of virtual work to obtain the residual element nodal displacement vector.

d̃R,k=1,j=1e,n =

∫ Le0

Nf,e(x)T· εεεR,k=1,j=1s,e,n (x)dx

At this stage the first iteration (j = 1) is completed. The final element and section states for

j = 1 correspond to pointB in Fig. 3.13. The residual section deformation vectors εεεR,k=1,j=1s,e,n (x)

and the residual element nodal displacement vector d̃R,k=1,j=1e,n were determined in the firstiteration, but the corresponding element nodal displacement vector have not yet been updated.Instead, they constitute the starting point of the remaining steps within iteration loop j.

The presence of residual element nodal displacement vector d̃R,k=1,j=1e,n will violate com-patibility, since elements sharing a common node would now have different element nodal dis-placement vector. In order to restore the inter-element compatibility, corrective force vector

56

Draftef%

A

D

B

C

, 1e n−f%

0, 0

, 1 ,

k j

e n e n

= =

−=d d% % 1, 1

,

k j

e n

= =d%

ed%

1, 2

,

k j

e n

= =d%1, 3,

k j

e n

= =d%

1, 1

,

1, 0 1, 1

,

k j

e n

k j k j

e e n

δ

δ

= =

= = = ==

f

k d

%

% %

int, 1, 1

,

k j

e n

= =f%

1, 1

,

k j

e nδ= =

d% , 1, 1,

R k j

e n

= =d%

, 1, 2

,

R k j

e n

= =d%

, 1, 3

, 0R k j

e n

= ==d%

tan, 1, 1

,

k j

e n

= =c%

tan, 1, 2

,

k j

e n

= =c%

36tan, 1, 3

,

k j

e n

= =c%

int, 1, 3

,

k j

e n

= =f%

in t, 1, 2

,

k j

e n

= =f%

1, 2

,

1, 1 , 1, 1

, ,

k j

e n

k j R k j

e n e n

δ= =

= = = ==

f

c d

%

%%

3

2

1

25

13

37

15

27

26

27

24

12

38

1, 3

,

1, 2 , 1, 2

, ,

k j

e n

k j R k j

e n e n

δ= =

= = = ==

f

c d

%

%%

A

D

B

C

1, 1

, , ( )k j

s e n xδ= =

εεεε

, ( )s e xσσσσ

, ( )s e xεεεε0, 0

, , 1 , ,( ) = ( )k j

s e n s e nx x= =

−ε εε εε εε ε

, , 1( )s e n x−σσσσ1, 1

, , ( )k j

s e n x= =

εεεε

int, 1, 1

, , ( )k j

s e n x= =

σσσσ

, 1, 1

, , ( )R k j

s e n x= =

σσσσ

tan, 1, 1

, ( )k j

s n x= =

c

, 1, 1

, , ( )R k j

s e n x= =

εεεε

1, 2

, , ( )k j

s e n x= =

σσσσ

1, 2

, , ( )k j

s e n xδ= =

εεεε

1, 2

, , ( )k j

s e n x= =

εεεε

tan, 1, 2

, , ( )k j

s e n x= =

c

, 1, 2

, , ( )R k j

s e n x= =

σσσσ

int, 1, 2

, , ( )k j

s e n x= =

σσσσ

, 1, 2

, , ( )R k j

s e n x= =

εεεε

1, 3

, ,

1, 3

, , ,

( )

( )

k j

s e n

k j

f e s e n

x

x

δ

δ

= =

= == N f%

σσσσ

1, 3

, , ( )k j

s e n xδ= =

εεεε

1, 3

, , ( )k j

s e n x= =

εεεε

tan, 1, 3

, , ( )k j

s e n x= =

c

, 1, 3

, , ( ) 0R k j

s e n x= =

=σσσσ

, 1, 3

, , ( ) 0R k j

s e n x= =

=εεεε

1, 1

, ,

1, 1

, ,

( )

( )

k j

s e n

k j

f e e n

x

x

δ

δ

= =

= == N f%

σσσσ

1, 3

, ,

int, 1, 3

, ,

( )

( )

k j

s e n

k j

s e n

x

x

= =

= ==

σσσσ

σσσσ

1, 1

, , ( )k j

s e n x= =

σσσσ1, 2

, ,

1, 2

, ,

( )

( )

k j

s e n

k j

f e e n

x

x

δ

δ

= =

= == N f%

σσσσ

18

116

7

30

23

3519

31

4

29 33

5

17

21

9 10

16

22

34

28

8 20

32

(a) Element state determination

(b) Section state determination

3a 5

4

A

B

Fig. 3.13 Element and section state determinations for flexibility-based 2D beam-column ele-

ment with Newton-Raphson iteration loop in element level

54


Documentation User’s manuals

User’s Manuals

One for Matlab version, and one for c++

Draft- Tol: Convergence criteria on the residuals

Example:FlexibilityBased2DBeamColumn in Sec. A.4, then we could have: StrMiter = 20; EleMiter= 50; Convergence = ‘ForceNorm’; ConvergenceEle = ‘EnergyNorm’; Tolerance = 1.0e-8

A.3 Geometry Block

The geometry block defines nodal coordinates and their constraints assuming a right handedcoordinate system.

A.3.1 Nodal coordinates

The nodcoord assigns coordinates of nodes.

nodcoord = { nodtag1, x1, y1 [z1] ;... ;nodtagi, xi, yi [zi] ;... ;nodtagn, xn, yn [zn] }

for example:

Node = { 1, 0.0, 0.0 ;2, 1.0, 3.0 ;3, 2.0, 0.0 }

A.3.2 Boundary condition

The constraint command assigns boundary conditions to the nodes. Each node has tohave as many constraint as d.o.f’s per node.

constraint = { nodtag1, id11, id1

2[ id1

3, id1

4, id1

5, id1

6] ;

... ;nodtagi, idi

1, idi

2[ idi

3, idi

4, idi

5, idi

6] ;

... ;nodtagn, idn

1, idn

2[ idn

3, idn

4, idn

5, idn

6] }

Where 0 corresponds to a free dof, and 1 to a fixed one. For example:constraint = { 3, 1, 1 ;

5, 1, 0 }

A.4 Element Block

The elements command defines element type, nodal connectivity, and basic sectional infor-mation. These may vary with the element type.

252

Chapter 1

MERCURY USER’S MANUAL

FOR C++

This document1 describes the input for C++ version of Mercury. The C++ version usesthe Lua scripting language2 (analogous to TCL in OpenSees).

1.1 nodes

The “nodes” command defines nodal coordinates, and nodal masses if material densities arenot in materials.

nodes = { { nodtag1, x1, y1 [, z1] [, ‘mass’, mx1, my1 [, mz1]] };{ . . . };{ nodtagi, xi, yi [, zi] [, ‘mass’, mxi, myi [, mzi]] };{ . . . };{ nodtagn, xn, yn [, zn] [, ‘mass’, mxn, myn [, mzn]] } };

• nodtagi: Tag of the ith node

• xi, yi, and zi are node coordinates of node i at each global coordinate.

• mxi, myi, and mzi are mass quantities of node i at each global coordinate.

1.2 elements

The “elements” command defines element type, nodal connectivity, and basic section infor-mation. These may vary with the element type.

elements = { { Definition of element1 };{ . . . };{ Definition of elementi };{ . . . };{ Definition of elementn } };

1In this preliminary version of Mercury, no attempt has been made to simplify (generate/automate) dataentry, and there is not (yet) a mesh generator for the program. Those are simple future developments.

2http://www.lua.org/

5


Documentation Validation Manual

Validation Manual

Over 30 examples used for validations. Each problem stored in a separate folder containing: a)Matlab input file; b)c++ (lua) input file; c) OpenSees (tcl) input file; and d) Excel/visio files forresults

Example Algorithm Element Section Material Analysis 1 Analysis 2

Ex01 Linear Simple truss General Elastic Static Newmark beta

Ex02 Linear Simple truss General Elastic Load control HHT

Ex03 Linear Simple truss General Elastic Load control

Ex04 Linear Simple truss General Elastic Disp control

Ex05 Mixed Simple truss General Elastic and Hardening Static Newmark beta

Ex06 Mixed Simple truss General Elastic and Hardening Load control HHT

Ex07 Mixed Simple truss General Elastic and Hardening Newmark beta

Ex08 Mixed Simple truss General Elastic and Hardening Disp control HHT

Ex09 Mixed Simple truss General Elastic and Bilinear Load control Newmark beta

Ex10 Mixed Simple truss General Elastic and ModGMP Load control HHT

Ex11 Mixed Simple truss General Damage2 Cyclic disp control

Ex12 Mixed Simple truss General ModKP Cyclic disp control

Ex13 Mixed Simple truss General Hardening Cyclic disp control



Ex16 Mixed Simple truss General Bilinear Cyclic disp control

Ex17 Mixed Simple truss General Bilinear Cyclic disp control

Ex18 Mixed Simple truss General ModGMP Cyclic disp control

Ex19 Mixed Simple truss General ModGMP Cyclic disp control

Ex20 Mixed SBC Layer Hardening Cyclic disp control HHT

Ex21 Mixed FBC1 Layer Hardening Cyclic disp control Shing

Ex22 Mixed FBC2 Layer Hardening Cyclic disp control

Ex23 Mixed SBC and zero-length General Elastic and Bilinear Load control

Ex24 Mixed SBC and zero-length section General Elastic and Bilinear Load control

Ex25 Mixed SBC Layer Hardening Multiple disp control

Ex26 Mixed FBC1 Layer Hardening Multiple disp control

Ex27 Mixed Ghanoumn single column Layer ModGMP and ModKP HHT

Ex28 Mixed Ghanoumn single column Layer ModGMP and Damage2 HHT

Ex29 Mixed Ghannoum 3 bay 3 floor Layer Mixed materials HHT/Shing


Remarks Current Development

Current Development

Timoshenko beam

Graphical (OpenGL based) post-processor

Geometric nonlinearity

Limit elements

Online tutorials

Mesh generator

Translator from Matlab to Lua

Improved documentation for integration with hybrid simulation


Remarks Graphical Post Processor

Graphical Post Processor

A Graphical Post Processor (written in Matlab) is under currentdevelopment. It will support both the Matlab and the C++ versions, andwill provide a GUI through which user could visualize various results.


Remarks Applications

Applications

Mercury has been “battle tested" through two major endeavors:

Research Real time Hybrid Simulation of a reinforced concreteframe with non-ductile columns, and comparison withshake table test results.

Education in a new course “Nonlinear Structural Analysis” in whichstudents first used the Matlab version to gently acquaintthemselves with basic concepts (including modifying thecode), and then with the c++ version for a comprehensiveproject on seismic rehabilitation.


Remarks Shake Table vs RTHS

Comparison between Shake Table and RTHS; The Video


st-rths-short-high-quality.wmvMedia File (video/x-ms-wmv)

Summary

Summary

Mercury

Is a full nonlinear structural dynamic finite element code which can beembedded inside LabView for pseudo-dynamic tests, or real time hybridsimulation.

Is more than a software for hybrid dynamic nonlinear analysis of civilengineering structures.

It is a concept of hardware in the loop which can be adapted to otherdisciplines such as automotive and aerospace engineering.


Credit

Credit

Prof. Victor Saouma Project DirectorDr. Dae-Hang Kang Development of Mercury Matlab, c++

Dr. Gary Haussmann Development of Mercury c++ &Hybrid capabilitiesLMT/Cachan Anisotropic model

State of Colorado Financial support


IntroductionGlobal ContextBackgroundNRC/NEESMercury Overview

AnalysisConstitutive ModelsElementsNonlinear Algorithms

HybridMatlabc++; Generalc++; Hybrid Elementc++; Coordinate Transformation

ImprovementsRTHS on a Shared Memory ComputerRTHS on a Computer Cluster; AlgorithmRTHS on a Computer Cluster; Results

ScriptingInterfaceIntroductionHybrid PipeSCRAMNet PipeVirtual Spring PipeEnvironmental Variables

XtrasDocumentationTechnical ManualUser's manualsValidation Manual

RemarksCurrent DevelopmentGraphical Post ProcessorApplicationsShake Table vs RTHS

SummaryCredit

Documents

MERCURY Optimized Software for Hybrid Simulation;saouma/wp-content/...Optimized Software for Hybrid Simulation; from Pseudo-Dynamic to Hard Real Time V. Saouma D.H. Kang G. Haussmann