OpenSees Workshop

http://opensees.berkeley.edu/OpenSees/workshops/OpenSeesWorkshop.pdf

Frank McKenna
UC Berkeley
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 What is Purpose of Simulation?

To develop a model capable of producing a

credible prediction of the behavior of an
existing/proposed structure.
And Just How Good are we
Today at predicting this
response?
source: Prof. B. Stojadinovic
source: Prof. B. Stojadinovic
 Current Status (simulation codes)
•  Individual models (materials/elements) are typically
well verified.
•  They are typically validated against few
experimental tests over a narrow performance range.
•  Computer simulations of systems do not necessarily
provide credible predictions and typically only
provide a single deterministic response.

“The uncertainty is as important a part of the result as the

estimate itself… . An estimate without a standard error is
practically meaningless.” [Jeffreys (1967)]
What Was/Is Wrong With Existing Software

New Element
New Material

•  Embedding of computational procedures in codes makes it difficult to

experiment (integration schemes, algorithms, solvers) and take
advantage of computing technology (Parallel & Grid Computing)
•  “Closed-source” was/is the norm, whereas other fields have adopted
“open-source” software for communities of users. Closed source is an
impediment to new research. No sharing of code, building upon others
ideas.
•  I started writing code in 1995 so I
could do my research.
•  It has a very modular design.
•  OpenSees has been under http://opensees.berkeley.edu
development by PEER since 1998.
NEES supported since 2005.
•  Windows application downloaded
over 10,000 times a year.
•  Parallel Applications utilize over
1,000,000 CPU hours on NSF
XSEDE compute resources yearly.
•  Open-source and royalty free
license for non-commercial use
and and internal commercial use.
•  License must be obtained for
software developers including
OpenSees code in their
applications.
•  Written in C++, C and Fortran
(C++ being the main language)
 Numerical Computation
Algorithms & Solvers Models
Material, Element

Open-Source - Leave it out there for community

Information Technology
Database, Visualization, Frameworks,
Building Blocks for Modern Simulation Code

Parallel & Grid/Network libraries

 PEER: OpenSees Goals (1998):
1.  To use modern software techniques to evolve an
extensible open-source finite element software platform
for earthquake engineering that would encompass both
structural & geotechnical engineering. Provost Gregory Fenves

2.  To provide a common analytical research framework UT Austin

for PEER researchers to educate students & share new
knowledge.
3.  To foster a mechanism whereby new research developed
through PEER could be disseminated to industry for
testing and implementation.
 Has It Worked:
Used Worldwide (2013)
 Example Usage

Interior Pedro Arduino

Gravity
Frame

350

Total execution time (minute)

300

250

200

150

100
Panagiotis Galanis & Jack Moehle 50

0
0 2 4 6 8 10 12 14 16 18
Number of processors
 As-
built

M.Talaat & K.Mosalam

A. Usmani et al. , University of Edinburgh
OpenSees C-bent (RC)
Model

RC
Steel Column

17

Kyoto/Berkeley
 New Directions:
1. Optimization
J. Conte & P.Gill (UCSD), Q.Gu (Xiaman)

2. Fluid Structure Interaction

M.Scott, Oregon State
 SO What is OpenSees?
•  OpenSees is a software framework for
building finite element applications in
structural and geotechnical systems.
•  These applications run on both sequential,
parallel, and distributed computer systems.
 OpenSees is a Software
Framework
•  A framework is NOT an executable.
•  A framework IS a set of cooperating software components for
building applications in a specific domain.
•  The OpenSees framework is written primarily in the object-
oriented language C++; though other languages namely C and
Fortran are also used.
•  The abstract classes in the OpenSees framework define the
interface. The concrete subclasses that exist in the framework
provide the implementations.
•  Other classes can be provided to extend the capabilities of the
framework by developers using DLL’s or providing the
source code to the OpenSees repository.
•  Currently over 1000 classes in the OpenSees framework.
 Main Abstractions in OpenSees
Framework

Holds the state of the model

i
at time t and (t + dt)
(500 classes)

ModelBuilder Domain Analysis

Constructs the objects Moves the model
in the model and adds from state at time t to
them to the domain. state at time t + dt
(5 classes) Recorder (200 classes)

Monitors user defined

parameters in the
model during the
analysis
(20 classes)
 Recorder Options
Recorder

ElementRecorder DataOutputHandler
NodeRecorder
EnvelopeNodeRecorder
EnvelopElementRecorder
DatabaseRecorder
StandardStream
FileStream
XML_FileStream
TCP_Stream
DatabaseHandler Database

File
MySQL
Oracle
 What is in a Domain?
Domain
Aggregation/Collection-of

Element Node MP_Constraint SP_Constraint LoadPattern TimeSeries

Plain
Truss Uniform
ZeroLength MultiSupport
ElasticBeamColumn
NonlinearBeamColumn(force, displacement)
BeamWithHinges Constant
Quad(std, bbar, enhanced, u-p)
ElementalLoad NodalLoad SP_Constraint
Linear
Shell Rectangular
Brick(std, bbar, 20node, u-p, u-p-U) Sine
Joint Path
GenericClient
BeamPointLoad
(>100 element classes) BeamUniformLoad
BeamTempLoad
 Some Other Classes associated with Elements:

Material GeomTransformation

Uniaxial nD Section Linear

Pdelta
Corotational

Elastic Elastic Element in Global System

ElasticPP Elastic Fiber
Hardening J2
Concrete DruckerPrager
Steel TemplateElasto-Plasto U
Hysteretic
PY-TZ-QZ
FluidSolidPorous Geometric Transformation
PressureMultiYield(dependent, independent)
Parallel v
Series q
Gap
Fatigue

(over 250 material classes) Element in Basic System

 What is an Analysis?
Analysis

AnalysisModel
StaticAnalysis
TransientAnalysis

CHandler Numberer CTest SolnAlgorithm Integrator SystemOfEqn

Plain Plain NormDispIncr EquiSolnAlgo StaticIntegrator BandGeneral

Penalty RCM NormUnbalance Linear LoadControl BandSPD
Lagrange AMD NormEnergy NewtonRaphson DispControl ProfileSPD
ArcLength
Transformation RelativeNormDispIncr ModifiedNewton SparseGeneral
…
RelativeNormUnbalance Broyden SparseSymmetric
TransientIntegrator
RelativeNormEnergy BFGS CentralDifference
KrylovNewton
Newmark
NewtonLineSearch HHT
… GeneralizedAlhpa
(25 classes) NewmarkExplicit
TRBDF2
(35 classes)
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 How Do People Use the
OpenSees Framework?
•  Provide their own main() function in C++ and
link to framework.

•  Use OpenSees interpreterS. These are

extensions of the Tcl interpreters, tclsh and
wish, for performing finite element analysis.
1.  OpenSees.exe
2.  OpenSeesTk.exe
3.  OpseseesSP.exe
4.  OpenSeesMP.exe
 Tcl Interpreters
•  wish and tclsh are tcl interpreters.
•  Interpreters (Perl, Matlab, Ruby) are programs that execute
programs written in a programming language immediately.
•  There is no separate compilation & linking.
•  An interpreted program runs slower than a compiled one.
puts “sum of 2 and 3 is [expr 2 + 3]”

sum of 2 and 3 is 5
 What is Tcl
•  Tcl is a dynamic programming language
•  It is a string based command language.
•  Variables and variable substitution
•  Expression evaluation
•  Basic control structures (if , while, for, foreach)
•  Procedures
•  File manipulation
•  Sourcing other files.
 Tcl Syntax Rules
(rules that define combinations that
give a correctly structured program)

•  A Tcl Script is a sequence of Tcl Commands

•  Commands in script are separated by newlines or ;
•  The words of a command are separated by white spaces
•  The first word is the command name
•  The remaining words are the command arguments

commandName $arg1 $arg2 $arg3

•  The number of arguments depends on the command
 Comments
•  Code that is skipped by the computer, but
allows you/ someone else to understand what is
happening in the code.

# This is a comment
•  Some people suggest writing comments
before you write any code.
•  Judicious use of comments, try to avoid to
comment trivial things, like:

set a 5; # setting a to 5
 Variables & Variable Substitution
•  A variable is a symbolic name used to refer to
some location in memory that has a value; the
separation of name and value allows the value
to be used independently of exact value.
•  In Tcl to create a variable use set command.
set a 2.0
•  To use the value of the variable use a $
set b $a
•  Use descriptive names
set PI 3.14159
 puts
•  puts is the command to produce output.
•  The last argument is string to be output.
•  Result sent to screen, unless the optional file id
is provided.
puts <$fileID> string

puts $a >2

puts “value of a is: $a” > value of a is: 2

 expr
•  expr command is used to evaluate expressions
•  Pretty much any mathematical expression is
allowed
expr sqrt(($x*$x)+($y*$y))
•  Typically you set some variable value equal
to result of expression.
set length [expr sqrt(($x*$x)+($y*$y))]
•  Watch out for integer math.
puts [expr 5/2] >2

puts [expr 5/2.] > 2.5

 if
•  The if command has following general form
if expr1 body1 <elseif expr2 body2 elseif ... > <else bodyN>
•  The else and elseif are optional
•  The expr must return a boolean value
•  The body is a set of commands enclosed in {}, use
{ on same line as the expression if {$a == 2} {
if {$a == 2} { set b 2
set b 2 } elseif {$a == 3} {
if {$a == 2} { set b 3
set b 2 } else {
set b 3 } else {
} set b 4
}
}
 while
•  The while command has the following form
while expression body
•  The while command executes the body of the loop
each time the expression evaluates to true.
set sum 0
set i 1
while {$i < 10} {
set sum [expr $sum + $i]
incr i 1
}
puts $sum Ø  45

•  An infinite loop will occur if expression always true

•  Body never evaluated if expression initially false
 for
•  The for command is used when #cycles is known
for {initiation} {expression} {increment} {body}
•  arg1 is set of commands executed at start, initiation
•  arg2 is expression checked at start of each loop, when
false for stops
•  arg3 is set of commands to do at end of each loop
•  arg4 is set of commands to do for body of the for loop
for {set i 1; set sum 0.} {$i < 10} {incr i 1} {
set sum [expr $sum + $i]
}
puts $sum
Ø  45
 foreach
•  The foreach command simplifies looping over lists
foreach varName1 list1 <varName2 list2 …> {body}
•  The foreach command successively assigns the
values contained in the list to the variable named.
•  If multiple names and lists, the lists must be of same
size. set sum 0
foreach v {1.0 9.0} s {2. 6.} {
set sum 0 set sum [expr $sum + $v*$s}
foreach v {1 2 3 4 5} { }
set sum [expr $sum + $v]
} set sum 0
foreach {v s} {1.0 2. 9.0 6.}
set sum [expr $sum + $v*$s}
}
 lists
•  A list is an ordered collection of elements, of no fixed
length. The list elements can be any string values,
including numbers, variable names, other lists
•  A list consists of elements separated by white spaces
•  There are commands for operating on lists:
list lappend linsert llength lindex lsearch
lreplace lrange lsort concat foreach
set a “123 456” >123 456
lappend a 789 >123 456 789
llength $a >3
lindex $a 2 >789 Lists start numbering at 0
set a [linsert $a 1 9] >123 9 456 789
lsearch $a 789 >3
 array
•  An array is an associated collection of elements –
–  A collection of key-value pairs.
–  key any string or number
•  The array command provides several operations for
working on arrays. array option name $arg.
options: set exists get names size unset
>
array set c {eleven 11 two 2}
>11
puts $c(eleven)
>
set c(ten) 10
>two ten eleven
puts [array names c]
>
foreach {key value} [array get c] {
>two 2
puts “$key $value”
ten 10
}
eleven 11
puts [array get c eleven]
>eleven 11
 open & file
•  The open command is used to open files for reading
and writing. It returns the file descriptor.
open filename $mode

set inFile [open test.txt r]

?
set outFile [open test.out w]
set fileData [read $inFile]
puts $outFile $fileData
close $inFile; close $outFile;
•  The file command provides several operations for
working with the file system. Of form:
file option name $arg1 $arg2 ..

•  example options include

copy exists delete isdirectory mkdir
 proc
•  The proc command creates procedures (your own
commands)
–  First arg is procedure name.
–  Second arg defines the list of arguments
–  Third argument is body of the procedure
•  The return command in the body returns the result
and returns from the procedure
proc sum {a b} {
return [expr $a + $b]
}

puts “sum 3 4 = [sum 3 4]” Ø  sum 3 4 = 7

 proc
•  The special variable name args allows procedures to
take variable number of arguments
•  Each Tcl procedure invocation maintains its own
variables.Variables in a procedure have local scope.
•  The global command inside a procedure marks
variable as global
proc addSum {args} {
global sum; set localSum 0. set sum 0
puts [addSum 3 4 5]
foreach num $args {
puts [addSum 3 4 5]
set localSum [expr $localSum + $num]
}
set sum [expr $sum + $localSum] Ø  12 12
return “$localSum $sum” Ø  12 24
}
Example Tcl • procedures & control structures
> for {set i 1} {$i < 10} {incr i 1}
• comments • expression evaluation puts “i equals $i”
}
>expr 2 + 3
># this is a comment 5 …
>set b[expr 2 + $b] > set sum 0
• Variables 3 foreach value {1 2 3 4} {
>set a 1 set sum [expr $sum + $value]
• lists }
1
>set b a >set a {1 2 three} >puts $sum
a 1 2 three 10
>set b $a >set la [llength $a] >proc guess {value} {
1 3 global sum
>set start [lindex $a 0] if {$value < $sum} {
• file manipulation 1 puts “too low”
>set fileId [open tmp w] >lappend a four } else {
?? 1 2 three four
if {$value > $sum} {
>puts $fileId “hello”
• associative arrays puts “too high”
>close $fileID
} else { puts “you got it!”}
>type tmp >array set a {one 1 three 3}
hello >set $a(fifty) blah }
>array get a fifty }
• Load other files fifty blah > guess 9
too low
>source Example1.tcl
 OpenSees Interpreters

•  The OpenSees interpreters are tcl interpreters which

have been extended to include commands for finite
element analysis:
1.  Modeling – create nodes, elements, loads and constraints
2.  Analysis – specify the analysis procedure.
3.  Output specification – specify what it is you want to monitor
during the analysis.

•  Being interpreters, this means that the files you create

and submit to the OpenSees interpreters are not input
files. You are creating and submitting PROGRAMS.
 OpenSees.exe
• An interpreter that extends tclsh for FE analysis.
model Command
*Adds the modeling commands to the interpreter.
Domain

Element Node MP_Constraint SP_Constraint LoadPattern TimeSeries

ElementalLoad NodalLoad SP_Constraint

•  Basic Model Builder
model Basic –ndm ndm? <-ndf ndf?>

This command now adds the following commands to the interpreter:

node mass element equalDOF fix fixX fixY fixZ

pattern timeSeries load eleLoad sp
uniaxialMaterial nDMaterial section geomTransf
fiber layer patch block2D block3D
model Basic -ndm 2 -ndf 2
#node $tag $xCrd $yCrd
Truss example:
50 100
node 1 0.0 0.0
4
node 2 144.0 0.0
node 3 168.0 0.0 8’
node 4 72.0 96.0 (1) (2) (3)
#fix $nodeTag $xFix $yFix
fix 1 1 1 1 2 3
fix 2 1 1 6’ 6’ 2’
fix 3 1 1
E A
#uniaxialMaterial Elastic $tag $E
uniaxialMaterial Elastic 1 3000.0 1 3000 10
2 3000 5
#element truss $tag $iNode $jNode $A $matTag 3 3000 5
element truss 1 1 4 10.0 1 #pattern Plain $tag $tsTag
element truss 2 2 4 5.0 1 pattern Plain 1 1 {
element truss 3 3 4 5.0 1 #load $nodeTag $xFrc $yFrc
load 4 100.0 -50.0
timeSeries Linear 1 }
 When should you Use Variables
In a Program?

•  NOT to document the commands

(USE comments instead: i.e. more ‘#’ and less ‘set’)

•  When you have a variable that you might change at

some point later in time or in the script, or if value will
be repeatedly used.
Truss example using variables:
node 1 $xCrd1 $yCrd1
model Basic -ndm 2 -ndf 2 node 2 $xCrd2 $yCrd1
set xCrd1 0.0 node 3 $xCrd3 $yCrd1
set xCrd2 144.0 node 4 $xCrd4 $yCrd2
set xCrd3 168.0 fix 1 1 1
set xCrd4 62.0 fix 2 1 1
set yCrd1 0 fix 3 1 1
set yCrd2 96 uniaxialMaterial Elastic $matTag1 $E1
set matTag1 1
set timeSeriesTag 1 element truss 1 1 4 $A1 $matTag1
set patternTag1 element truss 2 2 4 $A2 $matTag1
set E1 3000. element truss 3 3 4 $A3 $matTag1
set nodeLoadTag 4 timeSeries Linear $tsTag1
set nodeLoadx 100.
set nodeLoadY -50; pattern Plain $patternTag1 $tsTag1 {
set A1 10 load 4 $nodeLoadX $nodeLoadY
set A2 5.0 }
Analysis Analysis

StaticAnalysis
TransientAnalysis

CHandler Numberer Ctest SolnAlgorithm Integrator SystemOfEqn

handler type? args…

numberer type? args…
test type? args…
algorithm type? args…
integrator type? args…
system type? args…
analysis type? args..
analyze args …
 Example Analysis:
• Static Nonlinear Analysis with LoadControl
constraints Transformation
numberer RCM
system BandGeneral
test NormDispIncr 1.0e-6 6 2
algorithm Newton
integrator LoadControl 0.1
analysis Static
analyze 10

• Transient Nonlinear Analysis with Newmark

constraints Transformation
numberer RCM
system BandGeneral
test NormDispIncr 1.0e-6 6 2
algorithm Newton
integrator Newmark 0.5 0.25
analysis Transient
analyze 2000 0.01
 Commands That Return Values:
• analyze command set ok [analyze numIter <Δt>]

• getTime command set currentTime [getTime]

• nodeDisp command set disp [nodeDisp $node <$dof>]

• nodeVel command set vel [nodeVel $node <$dof>]

• nodeAccel command set acc [nodeAccel $node <$dof>]

• nodeEigen command set eig [nodeEigen $node <$dof>]

• eleResponse command set resp [eleResponse $eleTag $arg1 $arg2 …]

3 Ways to Execute the commands
1. Interactively - the commands as we have
shown can be input directly at the prompt
3 Ways to Execute the commands
2. Sourced from File- the commands are
placed in a text file which is sourced in
3 Ways to Execute the commands
3. Batch Mode- the commands are placed in a
text file which are executed at startup.
if batch mode - useful default
variables: argv & argc
 OpenSees & Matlab
•  Calling matlab from an OpenSees script (mScript.m)
# invoke matlab !
if {[catch {exec matlab -nosplash -nodesktop -r ”mScript; quit"}]}
{ !
puts "Ignore this $msg" !
}!

•  Calling OpenSees from a matlab script

# invoke matlab !
!OpenSees opsScript.tcl!
 OpenSees Resources
http://opensees.berkeley.edu
•  Message Board - look for answers, post questions and ANSWERS
http://opensees.berkely.edu/community/index.php
•  Getting Started Manual - basic how to for getting started
http://opensees.berkeley.edu/wiki/index.php/Getting_Started

•  User Documentation - command documentation & theory!

http://opensees.berkeley.edu/wiki/index.php/Command_Manual
•  User Examples
http://opensees.berkeley.edu/wiki/index.php/OpenSees_User
http://opensees.berkeley.edu/wiki/index.php/Examples_Manual

•  Developers
http://opensees.berkeley.edu/wiki/index.php/OpenSees_Developer
http://opensees.berkeley.edu/cgi-bin/cvsweb2.cgi/OpenSees/SRC/
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 Output Options
When you run OpenSees:

3 ways to obtain output:

1. puts command
puts <$fileID> $string
2. print command
print <-file $fileName> <-node $nd1 $nd2 ..> <-ele $ele1 $ele2 …>
3. recorder command
recorder $type $arg1 $arg2 …
 Example using puts (sdofExample1.tcl)
# create model & analysis
…
# open output file
set nodeOut [open node.out w]
set forceOut [open ele.out w]
#perform analysis
while {$ok == 0 && $t < $maxT} {
set ok [analyze 1 $dT]
set time [getTime]
set d [nodeDisp 2 1]
set forces [eleResponse 1 material stress]
puts $nodeOut "$time $d"
puts $forceOut "$time $forces"
if {$d > $maxD} {
set maxD $d
} elseif {$d < [expr -$maxD]} {
set maxD [expr -$d]
}
set t [expr $t + $dT]
}
#close the files
close $nodeOut
close $forceOut
puts "record: $record period: $Tn damping ratio: $dampRatio max disp: $maxD"
 Recorder Options
Recorder

ElementRecorder
NodeRecorder DataOutputHandler
EnvelopeNodeRecorder
EnvelopElementRecorder
DatabaseRecorder

StandardStream
FileStream
XML_FileStream
TCP_Stream
DatabaseHandler Database

File
recorder $type $arg1 $arg2 $arg3 …. MySQL
Oracle
 Element/EnvelopeElement Recorders
• To monitor what’s happening in the elements.
recorder Element <-file $fileName> <-time> <-ele $tg1 $tg2 …> $arg1 $arg2 …
<-xml $fileName> <-eleRange $tgS $tgE>
<-binary $fileName> <-region $rTag>
<-tcp $inetAddr>

• The response you can ask vary from element to element. There are
of course some each element will respond to, e.g. forces.
recorder Element -file ele.out -ele 1 2 forces

recorder Element -file ele1sect1fiber1.out -ele 1 2 section 1 fiber 1stress

• The EnvelopeElement takes exactly same args

recorder EnvelopeElement <-file $fileName> <-time> <-ele $tg1 $tg2 …> $arg1 $arg2 …
<-xml $fileName> <-eleRange $tgS $tgE>
<-binary $fileName> <-region $rTag>
<-tcp $inetAddr>
 Node/EnvelopeNode Recorders
• To monitor what’s happening at the Nodes.
recorder Node <-file $fileName><-timeSeries $tsTag> <-time> <-node $tg1 $tg2 …> -dof $d1 $d2 .. disp
<-xml $fileName> <-nodeRange $tgS $tgE> vel
<-binary $fileName> <-region $rTag> accel
<-tcp $inetAddr> incrDisp
reaction

Example:
recorder Node -file nodeD.out -node 2 -dof 1 2 3 disp

recorder Node -file nodeA.out -temeSeries 1 -node 2 -dof 1 accel

recorder EnvelopeNode <-file $fileName><-timeSeries $tsTag> <-time> <-node $tg1 $tg2 …> -dof $d1 $d2 .. disp
<-xml $fileName> <-nodeRange $tgS $tgE> vel
<-binary $fileName> <-region $rTag> accel
<-tcp $inetAddr> incrDisp
reaction
Example using recorders(sdofExample2.tcl)
# create model & analysis
…
#create recorders
recorder Node -file node1.out -time -node 2 -dof 1 disp
recorder Element -file ele1.out -time -ele 1 material stress
#perform analysis
while {$ok == 0 && $t < $maxT} {
set ok [analyze 1 $dT]
set time [getTime]
set d [nodeDisp 2 1]
if {$d > $maxD} {
set maxD $d
} elseif {$d < [expr -$maxD]} {
set maxD [expr -$d]
}
set t [expr $t + $dT]
}
puts "record: $record period: $Tn damping ratio: $dampRatio max disp: $maxD"
wipe
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
To develop a model capable of producing a credible
prediction of the behavior of an existing/proposed
structure. How complicated a model is required
of our structure?
Nonlinear Structural Beam-Column Models

Source: Filip Filippou, UC Berkeley

 Beam-Column Models:
Concentrated Plasticity
•  Concentrated plasticity models =
one or more rotational springs at each end +
elastic element
–  Advantages:
relatively simple, good(?) for interface effects
(e.g. shear sliding, rotation due to bar pull-
out)
–  Disadvantages:
properties of rotational spring depend on
N geometry and moment distribution; relation to
M strains requires “plastic hinge length”;
interaction of axial force, moment and
shear ????;
generality??? numerical robustness???

Source: Filip Filippou, UC Berkeley

 iNode2 jNode5

iNode jNode

Zero Length elements

Elastic Beam Column elements (rotational springs)
With Modified Stiffness (PEER/ATC 2010)
(Ibarra and Krawinkler, 2005) Hysteretic Material
Beam-Column Models: Distributed
x
Inelasticity
•  Distributed inelasticity models (1d FE model) =
consistent integration of section response at specific
“control” or monitoring points
–  Advantages:
versatile and consistent;
section response from integration of material
response thus N-My-Mz interaction (Bernoulli)
(shear and torsion?? Timoshenko, …)
thus numerical robustness is possible
–  Disadvantages:
can be expensive (what is the price $$$$) with
“wasted sections” for localized inelasticity
y inaccuracy of local response (localization)
thus better understanding of theory for
interpretation of local response and damage is
z necessary
Source: Filip Filippou, UC Berkeley
 2 Element Types to Choose From:
1.  dispBeamColumn – displacement based
•  Follows standard finite element procedures where we
interpolate deformations at sections (integration points)
using an approximate displacement field (constant axial
deformation and linear curvature distribution)
•  Like in typical finite element analysis, mesh refinement (h
refinement) is needed to capture higher order distributions

2.  forceBeamColumn – force based element

•  Uses fact that we do know what the force distribution is
along the element. No approximation.
•  Using the force approach means iteration to determine
compatible forces given nodal displacements (does not
always converge).
Which is more ‘accurate’ ?
“Economic” Distributed inelasticity models for
Columns •  beamWithHinges
x
•  2 monitoring points at element ends
(inelastic zones), elastic section in middle
-  Good for columns and girders with low
gravity loads
-  N-My-Mz interaction straightforward
-  shear and torsion ???
-  Consistent location of integration point?
-  Value of fixed length of inelastic zone?
y
-  Good for softening response
z (Fenves/Scott, ASCE 2006)
-  Hardening response à Spreading
inelastic zone element SIZE (Lee/
Filippou, ASCE 2009 to appear)
Source: Filip Filippou, UC Berkeley
 Good Distributed inelasticity
models for Girders

-  For girders with significant gravity loads

-  4-5 integration points are advisable (“good plastic hinge
length value with corresponding integration weights)
-  One element per girder -> avoid very high local deformation
values
Source: Filip Filippou, UC Berkeley
KISS is an acronym for "Keep it simple,
stupid” as a design principle noted by the U.S.
Navy in 1960. The KISS principle states that
most systems work best if they are kept simple
rather than made complex; therefore simplicity
should be a key goal in design and unnecessary
complexity should be avoided. source: wikipedia

source: wikipedia
 50 100
model Basic -ndm 2 -ndf 2 4
#node $tag $xCrd $yCrd 8’
node 1 0.0 0.0 (1) (2) (3)
node 2 144.0 0.0
node 3 168.0 0.0 1 2 3
node 4 72.0 96.0 6’ 6’ 2’
#fix $nodeTag $xFix $yFix E A
fix 1 1 1 1 3000 10
fix 2 1 1 2 3000 5
fix 3 1 1 3 3000 5
#uniaxialMaterial Elastic $tag $E timeSeries Linear 1
uniaxialMaterial Elastic 1 3000.0 #pattern Plain $tag $tsTag
pattern Plain 1 1 {
#element truss $tag $iNode $jNode $A $matTag #load $nodeTag $xForce $yForce
element truss 1 1 4 10.0 1 load 4 100.0 -50.0
element truss 2 2 4 5.0 1 }
element truss 3 3 4 5.0 1
The SCRIPTS you are submitting
to OpenSees
are PROGRAMS
you are submitting to a powerful
INTERPRETER ..

SO LETS START
PROGRAMMING!
THINK Before You Type
 Steel W Sections &
Regular Grid
col line col line
1 2 3 4 5 6
Floor 4
24
Floor 3
43

42 52 Floor 2
4252
5152 Floor 1
11

Nodes # $col$floor (if more than 10 col lines or floors,

Elements # $iNode$jNode start numbering at 10,
if > 100, at 100, ….)
 model Basic –ndm 2 –ndf 3
source Steel2d.tcl MRF1.tcl
# set some lists containing floor and column line locations and nodal masses
set floorLocs {0. 204. 384. 564.}; # floor locations in inches
set colLocs {0. 360. 720. 1080. 1440. 1800.}; #column line locations in inches
set massesX {0. 0.419 0.419 0.430}; # mass at nodes on each floor in x dirn
set massesY{0. 0.105 0.105 0.096} ; # “ “ “ “ “ “ in y dirn

# add nodes at each floor at each column line location & fix nodes if at floor 1
foreach floor {1 2 3 4} floorLoc $floorLocs massX $massesX massY $massesY {
foreach colLine {1 2 3 4 5 6} colLoc $colLocs {
node $colLine$floor $colLoc $floorLoc -mass $massX $massY 0.
if {$floor == 1} {fix $colLine$floor 1 1 1}
}
}
#uniaxialMaterial Steel02 $tag $Fy $E $b $R0 $cr1 $cr2
uniaxialMaterial Steel02 1 50.0 29000. 0.003 20 0.925 0.15; ; # material to be used for steel elements
# set some list for col and beam sizes
set colSizes {W14X370 W14X370 W14X211}; #col sizes stories 1, 2 and 3
set beamSizes {W33X141 W33X130 W27X102}; #beams sizes floor 1, 2, and 3
# add columns at each column line between floors
geomTransf PDelta 1
foreach colLine {1 2 3 4 5 6} {
foreach floor1 {1 2 3} floor2 { 2 3 4} {
set theSection [lindex $colSizes [expr $floor1 -1]]; # obtain section size for column
ForceBeamWSection2d $colLine$floor1$colLine$floor2 $colLine$floor1 $colLine$floor2 $theSection 1 1 –nip 5
}
}
#add beams between column lines at each floor
geomTransf Linear 2
foreach colLine1 {1 2 3 4 5} colLine2 {2 3 4 5 6} {
foreach floor {2 3 4} {
set theSection [lindex $beamSizes [expr $floor -2]]; # obtain section size for floor
ForceBeamWSection2d $colLine1$floor$colLine2$floor $colLine1$floor $colLine2$floor $theSection 1 2
}
}
Steel2.tcl – contains a library of procedures
#WinXlb/f "Area(in2) d(in) bf(in) tw(in) tf(in) Ixx(in4) Iyy(in4)"
array set WSection {
W44X335 "98.5 44.0 15.9 1.03 1.77 31100 1200 74.7"
W44X290 "85.4 43.6 15.8 0.865 1.58 27000 1040 50.9"
W44X262 "76.9 43.3 15.8 0.785 1.42 24100 923 37.3"
W44X230 "67.7 42.9 15.8 0.710 1.22 20800 796 24.9"
W40X593 "174 43.0 16.7 1.79 3.23 50400 2520 445"
W40X503 "148 42.1 16.4 1.54 2.76 41600 2040 277”
…
}
proc ElasticBeamWSection2d {eleTag iNode jNode sectType E transfTag {Orient XX}} {
global WSection
global in
set found 0
foreach {section prop} [array get WSection $sectType] {
set propList [split $prop]
set A [expr [lindex $propList 0]*$in*$in]
set Ixx [expr [lindex $propList 5]*$in*$in*$in*$in]
set Iyy [expr [lindex $propList 6]*$in*$in*$in*$in]
if {$Orient == "YY" } {
element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iyy $transfTag
} else {
element elasticBeamColumn $eleTag $iNode $jNode $A $E $Ixx $transfTag
}
}
}
proc ForceBeamWSection2d {eleTag iNode jNode sectType matTag transfTag args} {

global FiberSteelWSection2d
global ElasticSteelWSection2d

set Orient "XX"

if {[lsearch $args "YY"] != -1} {
set Orient "YY"
}
set nFlange 8
if {[lsearch $args "-nFlange"] != -1} {
set loc [lsearch $args "-nFlange"]
set nFlange [lindex $args [expr $loc+1]]
}

set nWeb 4
if {[lsearch $args "-nWeb"] != -1} {
set loc [lsearch $args "-nWeb"]
set nWeb [lindex $args [expr $loc+1]]
}

set nip 4
if {[lsearch $args "-nip"] != -1} {
set loc [lsearch $args "-nip"]
set nip [lindex $args [expr $loc+1]]
}

if {[lsearch $args "-elasticSection"] != -1} {

set loc [lsearch $args "-elasticSection"]
set E [lindex $args [expr $loc+1]]
ElasticSteelWSection2d $eleTag $sectType $E $Orient
} else {
FiberSteelWSection2d $eleTag $sectType $matTag $nFlange $nWeb $Orient
}

element forceBeamColumn $eleTag $iNode $jNode $nip $eleTag $transfTag

}
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 Why Nonlinear Analysis
• Geometric Nonlinearities - occur in model when
applied load causes large displacement and/or rotation, large
strain, or a combo of both

• Material nonlinearities - nonlinearities occur

when material stress-strain relationship depends on load
history (plasticity problems), load duration (creep
problems), temperature (thermoplasticity), or combo of all.

• Contact nonlinearities - occur when structure

boundary conditions change because of applied load.
 Nonlinear Analysis is Harder
• It requires much more thought when setting up the model
• It requires more thought when setting up the analysis
• It takes more computational time.
• It does not always converge.
• It does not always converge to the correct solution.

BUT if you are using a Finite element

code the Problem probably Requires a
Nonlinear Analysis
 CHECK YOUR MODEL

CHECK YOUR MODEL

CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL

99% Probability: if Fails in First Step THERE IS A PROBLEM IN YOUR MODEL

 Analysis

Solver
Static
Transient
VariableTransient

CHandler Numberer ConvergenceTest SolnAlgorithm Integrator SystemOfEqn

Penalty RCM NormDisIncr EquiSolnAlgo StaticIntegrator BandGeneral

Lagrange MinDegree NormUnbalance Linear LoadControl BandSPD
Transformation RelNormDispInc NewtonRaphson DispControl ProfileSPD
ModifiedNewton ArcLength SparseGeneral
constraints type? args… Broyden MinUnbalDispNorm SparseSymmetric
numberer type? args… BFGS
KrylovNewton
TransientIntegrator
Diagonal

algorithm type? args… Newmark

NewmarkExplicit
integrator type? args… HHT
system type? args… GeneralizedAlhpa
CentralDifference
analysis type? args…WilsonTheta
analyze args … TRBDF2
test command:
- to specify when convergence has been achieved
all look at system: KU = R
• Norm Unbalance
R^R < tol test NormUnbalance tol? numIter? <flag?>

• Norm Displacement Increment

U^U < tol test NormDispIncr tol? numIter? <flag?>
• Norm Energy Increment
½ (U^R) < tol
test NormEnergyIncr tol? numIter? <flag?>
• Relative Tests
test RelativeNormUnbalance tol? numIter? <flag?>
test RelativeNormDispIncr tol? numIter? <flag?>
test RelativeNormEnergyIncr tol? numIter? <flag?>
numberer command:
- to specify how the degrees of freedom are numbered

• Plain Numberer
nodes are assigned dof arbitrarily numberer Plain

• RCM Numberer
nodes are assigned dof using the numberer RCM
Reverse Cuthill-McKee algorithm

• AMD Numberer
nodes are assigned dof using the numberer AMD
Approx. MinDegree algorithm

•  numbering has an impact on performance of banded and profile solvers.

The sparse solvers all use their own optimal numbering schemes.
algorithm command:

•  Algorithm specifies the trial steps taken to solve the nonlinear

equation for each step.
•  Number of options (ALL have their place)
 theIntegrator->formUnbalance();

algorithm Linear theIntegrator->formTangent();

theSOE->solve()
theIntegrator->update(theSOE->getX());
 theIntegrator->formUnbalance();
do {

algorithm Newton
theIntegrator->formTangent();
theSOE->solve()
theIntegrator->update(theSOE->getX());
theIntegrator->formUnbalance();
(Newton-Raphson) } while (theTest->test() == fail)

BUT REQUIRES ITERATION

 theIntegrator->formUnbalance();
theIntegrator->formTangent();
do {
algorithm ModifiedNewton theSOE->solve()
theIntegrator->update(theSOE->getX());
theIntegrator->formUnbalance();
(Modified Newton-Raphson) } while (theTest->test() == fail)

MORE ITERATIONS
BUT ONE FACTOR
algorithm NewtonLineSearch
•  Adds line search algorithm to the search algorithm

algorithm KrylovNewton
•  A quasi-newton method – in which
approximations of the inverse matrix are made
from displacement vectors of previous trial
steps. "Nonlinear Finite Element Procedures” K.J.Bathe
 DISCLAIMER
All those functions were nice smooth continuous
functions. We model with material discontinuities,
contact, … and thus are NOT SMOOTH ..
CONVERGENCE IS NOT GAURANTEED ..
CONVERGENCE TO CORRECT SOLUTION IS
NOT GAURANTEED.
constraints command:
- to specify how the constraints are enforced
Uc = Crc Ur
CU=0 [Cr Cc]^[Ur Uc] = 0
T Ur = [Ur Uc]^
• Transformation Handler
K*=T^KT constraints Transformation
K* Ur = R*
R*=T^R
in OpenSees currently don’t allow retained node in one
constraint to be a constrained node in another constraint

• Lagrange Handler
K C^ U R
constraints Lagrange
C 0 λ = Q

• Penalty Handler
[K + C^αC] U = [R + C^αQ] constraints Penalty αsp?αmp?
system command:
- to specify how matrix equation KU = R is stored and solved
• Profile Symmetric Positive Definite (SPD)

system ProfileSPD
• Banded Symmetric Positive Definite
system BandSPD

• Sparse Symmetric Positive Definite

....
... system SparseSPD

• Banded General
system BandGeneral

• Sparse Symmetric system SparseGeneral

....
If you .. ... a large system
. .have
Use one of these system Umfpack
integrator command:
- determines the predictive step for time t+δt
- specifies the tangent matrix and residual vector at any iteration
- determines the corrective step based on ΔU

1. Static Integrators for Use in Static Analysis

Nonlinear equation of the form:

R(U, λ) = λP* – FR(U)

2. Transient Integrators for Use in Transient Analysis

Nonlinear equation
. .. of the form:
.. .
R(U, U, U) = P(t) – FI(U) – FR(U, U)
 Static Integrators
R(U, λ) = λP* – FR(U)
at each step solving for λ
§ Load Control
λn = λ n-1 + Δλ
integrator LoadControl Δλ

*does not require a reference load, i.e. loads in load patterns
with Linear series and all other loads constant.
§ Displacement Control
Ujn = Uj n-1 + ΔUj

integrator DisplacementControl node dof ΔU

§ Arc Length
2 2 integrator ArcLength α Δs
ΔUn^ΔUn + αΔλ n = Δs
λ
λ
λ

Δλ

U U
U
ΔU
 Transient Integrators
•  Explicit:
Dn+1 = f(Pn, Dn, Vn, An, Dn-1, Vn-1, An-1, …)
integrator CentralDifference
integrator NewmarkExplicit $gamma
integrator HHTExplicit $alpha
….
1. all Need Linear Algorithm
2. in absence of damping all require Positive Definite mass matrix.

•  Implicit
Dn+1= f(Vn+1,An+1, Dn, Vn, An , Dn-1, Vn-1, An-1, …)
integrator Newmark $gamma $beta
integrator HHT $alpha
integrator TRBDF2
…
 Stability & Linear Systems
•  Stability (bounded solution) and Accuracy are the most talked
about properties of transient integration schemes.
•  For most integration schemes, the stability and accuracy provisions
you read about are provided FOR LINEAR DYNAMICAL
SYSTEMS.
•  Conditionally Stable: numerical procedure leads to a BOUNDED
solution if time step is smaller than some stability limit.
Conditional stability requires time step to be inversely proportional
to highest frequency.
•  Unconditionally Stable: solution is bounded regardless of the time
step.
 Stability Limits Common
Integrators
Central Difference is conditionally stable if:

(.318)
Newmark is unconditionally stable if:

Average Acceleration Unconditionally Stable

(Trapezoidal)
Linear Acceleration

But Conditionally stable if: 0.55

 Example
(see “Dynamics of Structures” A.K. Chopra, section 5.5)
dT/Tn = 0.32 (ex1.tcl)
dT/Tn = 0.1 (ex1.tcl)
dT/Tn = 0.01 (ex1.tcl)
 Stability & Nonlinear Systems
•  Algorithms that are stable for linear dynamical systems ARE NOT
NECESSARY STABLE in nonlinear case.
“.. even with Newton–Raphson iterations carried out to very tight convergence
tolerances, a scheme that is unconditionally stable in linear analysis may become
unstable in a nonlinear solution.”
Source: “On a composite implicit time integration procedure for nonlinear dynamic systems” ,Klaus-Jurgen Bathe, Mirza M. Irfan Baig

•  A sufficient condition in non-linear systems for stability is the

conservation of total energy within a step, expressed:
Un+1 - Un + Kn+1 -K n <= Wext
where U = strain energy and K = kinetic energy
•  There are 3 groups of algorithms which ATTEMPT to satisfy this
criterion:
1.  Numerical Dissipation

}
Neither Types
2.  Enforced Conservation of Energy
3.  Algorithmic Conservation of Energy Are Available
in OpenSees
 Dissipation Algorithms
•  They were developed for large linear systems where
typically only the low modes of response are of interest
and the engineer wants to remove the high frequency noise
(sometimes you don’t want to do this!)
•  These controlled dissipation of high frequency modes is
used in an ATTEMPT to conserve energy.
•  For nonlinear systems they do not guarantee the dissipation
of enough energy to always satisfy the conservation of
energy.
•  EXAMPLES: Newmark (γ > 0.5), HHT, TRBDF2,
TRBDF3
Numerical Dissipation: dT/Tn = 0.01 (ex2.tcl)
Numerical Dissipation: dT/Tn = 0.1 (ex2.tcl)
Numerical Dissipation: dT/Tn = 0.25 (ex2.tcl)
 Example
(see “Dynamics of Structures” A.K. Chopra, section 3.1)
T/Tn = 0.1; dT/Tn = 0.01 (ex3.tcl)
T/Tn = 0.1; dT/Tn = 0.1 (ex3.tcl)
T/Tn = 0.1; dT/Tn = 0.3 (ex3.tcl)
 Remember
•  Rayleigh Damping will can also be used to provide numerical damping

•  When using dissipation to damp out higher frequencies, the choice of

dT is as important as choice of integrator parameters.

•  Why damp out higher frequencies?

1.  Not interested in spurious modes
2.  Contact
3.  (I know I am repeating but again) In nonlinear problems try to
remove energy and hopefully allow conservation of energy (not
guaranteed)
 EXAMPLE
(Andreas Schellenberg, Rutherford and Chekenne)
 RESULTS
Periods Start: 0.50 sec to 0.0015 sec
Periods Just Before Impact: 380590.94 sec to 0.0045 sec
Periods if successful Analysis: 1.29 sec to 0.0015

Just before At end of

point of successful
failure analysis

For a dT=0.001
Newmark Average Acceleration and HHT 0.9 failed
HHT 0.6, TRBDF2, and Newmark 0.6 0.3025 worked
Max recorded roof displacements: 6.03, 5.88, 5.87 respectively
analysis command:
• Static Analysis analysis Static
• Transient Analysis analysis Transient
- both incremental solution strategies

StaticAnalysis TransientAnalysis

analyze() analyze()

for (int i=0; i<numIncr; i++) { for (int i=0; i<numIncr; i++) {
theIntegrator->newStep(); theIntegrator->newStep(dt);
theAlgorithm->solveCurrentStep(); theAlgorithm->solveCurrentStep();
theModel->commit(); theModel->commit();
} }

• Eigenvalue
§ general eigenvalue problem
(K-λM)Φ=0 eigen numModes? -general
§ standard eigenvalue problem
(K-λ)Φ=0 eigen numModes? -standard
analyze command:
- to perform the static/transient analysis

• Static Analysis

StaticAnalysis for (int i=0; i<numIncr; i++) {

theIntegrator->newStep();
analyze() theAlgorithm->solveCurrentStep();
theModel->commit(); analyze numIter?
}

• Transient Analysis

TransientAnalysis for (int i=0; i<numIncr; i++) {

theIntegrator->newStep(dt);
analyze() theAlgorithm->solveCurrentStep();

}
theModel->commit(); analyze numIter? Δt?
 Example Static Analysis:
• Static Nonlinear Analysis with LoadControl
constraints Transformation
numberer RCM
system BandGeneral
test NormDispIncr 1.0e-6 6 2
algorithm Newton
integrator LoadControl 0.1
analysis Static
analyze 10
StaticAnalysis

Transformation RCM NormDispIncr Newton LoadControl BandGeneral

 Example Dynamic Analysis:
• Transient Nonlinear Analysis with Newmark
constraints Transformation
numberer RCM
system BandGeneral
test NormDispIncr 1.0e-6 6 2
algorithm Newton
integrator Newmark 0.5 0.25
analysis Transient
analyze 2000 0.01

DirectIntegrationAnalysis

Transformation RCM NormDispIncr Newton Newmark BandGeneral

Remember that nonlinear
analysis does not always
converge
CHECK YOUR MODEL

CHECK YOUR MODEL

CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
CHECK YOUR MODEL
 Commands that Return Values
• analyze command
The analyze command returns 0 if successful.
It returns a negative number if not
set ok [analyze numIter <Δt>]
• getTime command
The getTime command returns pseudo time in Domain.

set currentTime [ getTime]

• nodeDisp command
The nodeDisp command returns a nodal displacement.
set disp [ nodeDisp node dof]
Example Usage – Displacement Control
set maxU 15.0; set dU 0.1
constraints transformation
numberer RCM
system BandGeneral
test NormDispIncr 1.0e-6 6 2
algorithm Newton
integrator DispControl 3 1 $dU
analysis Static
set ok 0
set currentDisp 0.0
while {$ok == 0 && $currentDisp < $maxU} {
set ok [analyze 1]
if {$ok != 0} {
test NormDispIncr 1.0e-6 1000 1
algorithm ModifiedNewton –initial
set ok [anal;yze 1]
test NormDispIncr 1.0e-6 6 2
algorithm Newton
}
set currentDisp [nodeDisp 3 1]
}
Example Usage – Transient Analysis
set tFinal 15.0;
constraints Transformation
numberer RCM
system BandGeneral
test NormDispIncr 1.0e-6 6 2
algorithm Newton
integrator Newmark 0.5 0.25
analysis Transient
set ok 0
set currentTime 0.0
while {$ok == 0 && $currentTime < $tFinal} {
set ok [analyze 1 0.01]
if {$ok != 0} {
test NormDispIncr 1.0e-6 1000 1
algorithm ModifiedNewton –initial
set ok [analyze 1 0.01]
test NormDispIncr 1.0e-6 6 2
algorithm Newton
}
set currentTime [getTime]
}
 Still Not Working!
1.  Search the Message Board
2.  Post Problem on the Message Board
 Segmentation Faults, etc:

• Email: fmckenna@ce.berkeley.edu

NOTE: Zip up your files in 1 directory and send them to us

 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
Spring Example - Load Control a.tcl
(1) F
1 2 Fy (60) 0.1E (3000)
P (100)
E (30000)
# create the model builder U
model Basic -ndm 1 -ndf 1 # create an analysis
# create 2 nodes constraints Plain
node 1 0.0 numberer RCM
node 2 0.0 test NormDispIncr 1.0e-6 6 0
algorithm Newton
# fix node 1 system ProfileSPD
fix 1 1
integrator LoadControl 0.1
# create material analysis Static
set Fy 60.0
set E 30000.0 # perform the analysis
set b 0.1 analyze 10
uniaxialMaterial Steel01 1 $Fy $E $b
# Output
# create element print node 2
element zeroLength 1 1 2 -mat 1 -dir 1
set exact [expr $Fy/$E + (100-$Fy)/($b*$E)]
# create time series and load pattern set res [lindex [nodeDisp 2] 0]
set P 100.0 if {$exact == $res} {
timeSeries Linear 1 puts "Exact ($exact) EQUALS Result ($res)"
pattern Plain 1 1 { } else {
load 2 $P puts "Exact ($exact) NOT EQUAL Result ($res)"
} }
Computers cannot represent all numbers exactly
and
Computer math involves roundoff
 F b.tcl
(1)
1 2 Fy (60) -0.1E (-3000)
P (100)
E (30000)
# create the model builder
U
model Basic -ndm 1 -ndf 1 # create an analysis
# create 2 nodes constraints Plain
node 1 0.0 numberer RCM
node 2 0.0 test NormDispIncr 1.0e-6 6 0
# fix node 1 algorithm Newton
fix 1 1 system ProfileSPD
integrator LoadControl 0.1
# create material analysis Static
set Fy 60.0
set E 30000.0 # perform the analysis
set b -0.1 analyze 10
uniaxialMaterial Steel01 1 $Fy $E $b
# create element # Output
element zeroLength 1 1 2 -mat 1 -dir 1 print node 2
# create time series and load pattern
set P 100.0
timeSeries Linear 1
pattern Plain 1 1 {
load 2 $P
}
Another common situation for which the solve fails message occurs:
NOT ENOUGH BOUNDARY CONDITIONS!

50

change system ProfileSPD to system BandGen

change LoadControl 0.1 to LoadControl 0.0999999

 F c.tcl
(1)
1 2 Fy (60) -0.1E (-3000)
P (100)
E (30000)
# create the model builder
U
model Basic -ndm 1 -ndf 1 # create an analysis
# create 2 nodes constraints Plain
node 1 0.0 numberer RCM
node 2 0.0 test NormDispIncr 1.0e-6 6 0
# fix node 1 algorithm Newton
fix 1 1 system BandGen
integrator LoadControl 0.09999
# create material analysis Static
set Fy 60.0
set E 30000.0 # perform the analysis
set b -0.1 analyze 10
uniaxialMaterial Steel01 1 $Fy $E $b
# create element # Output
element zeroLength 1 1 2 -mat 1 -dir 1 print node 2
# create time series and load pattern
set P 100.0
timeSeries Linear 1
pattern Plain 1 1 {
load 2 $P
}
 F
Fy (60) -0.1E (-3000)

E (30000)

With a Yield Strength of 60

This is as far as we can push the
Model using LoadControl

We can go further using a Displacement Control scheme

Spring Example - Displacement Control d.tcl
(1) F
1 2 Fy (60) -0.1E (-3000)
P (100)
E (30000)
# create the model builder U
model Basic -ndm 1 -ndf 1 # create an analysis
# create 2 nodes constraints Plain
node 1 0.0 numberer RCM
node 2 0.0 test NormDispIncr 1.0e-12 6 0
# fix node 1 algorithm Newton
fix 1 1 system BandGen
integrator DisplacementControl 2 1 0.001
# create material analysis Static
set Fy 60.0
set E 30000.0 # perform the analysis & print results
set b -0.1 for {set i 0} {$i < 10} {incr i 1} {
uniaxialMaterial Steel01 1 $Fy $E $b
analyze 1
# create element set factor [getTime]
element zeroLength 1 1 2 -mat 1 -dir 1
puts "[expr $factor*$P] [lindex [nodeDisp 2] 0]"
# create time series and load pattern }
set P 100.0
timeSeries Linear 1
pattern Plain 1 1 { print node 2
load 2 $P
}
Truss Example - Displacement Control e.tcl
stress
1 (1) 2 Fy (60) -0.1E (-3000)
P (100)
# create the model builder E (30000) strain
model Basic -ndm 1 -ndf 1
# create 2 nodes # create an analysis
node 1 0.0 constraints Plain
node 2 1.0 numberer RCM
# fix node 1 test NormDispIncr 1.0e-12 6 0
fix 1 1 algorithm Newton
system BandGen
# create material integrator DisplacementControl 2 1 0.001
set Fy 60.0 analysis Static
set E 30000.0
set b -0.1 # perform the analysis & print results
uniaxialMaterial Steel01 1 $Fy $E $b for {set i 0} {$i < 10} {incr i 1} {
# create element analyze 1
set A 1.0 set factor [getTime]
element Truss 1 1 2 $A 1
puts "[expr $factor*$P] [lindex [nodeDisp 2] 0]"
# create time series and load pattern }
set P 100.0
timeSeries Linear 1
pattern Plain 1 1 { print node 2
load 2 $P
}
 Truss Example - Push & Pull f.tcl
stress
1 (1) 2 Fy (60) -0.1E (-3000)
P (100)
# create the model builder E (30000) strain
model Basic -ndm 1 -ndf 1
# create 2 nodes # create an analysis
node 1 0.0 constraints Plain
node 2 1.0 numberer RCM
# fix node 1 test NormDispIncr 1.0e-12 6 0
fix 1 1 algorithm Newton
system BandGen
# create material integrator DisplacementControl 2 1 0.001
set Fy 60.0 analysis Static
set E 30000.0
set b -0.1 # perform the analysis & print results
uniaxialMaterial Steel01 1 $Fy $E $b foreach numIter {10 20 10} dU {0.001 -0.001 0.001} {
# create element integrator DisplacementControl 2 1 $dU
set A 1.0 analyze $numIter
element Truss 1 1 2 $A 1 set factor [getTime]
# create time series and load pattern puts "[expr $factor*$P] [lindex [nodeDisp 2] 0]"
set P 100.0 }
timeSeries Linear 1
pattern Plain 1 1 {
load 2 $P print node 2
}
 Truss Example - Uniform Excitation j.tcl
# create the uniform excitation pattern
1 (1) 2 stress set record el_centro
source ReadRecord.tcl
M K ReadRecord $record.AT2 $record.dat dT nPts
strain timeSeries Path 1 -filePath $record.dat -dt $dT -factor $g
# set some variables pattern UniformExcitation 1 1 -accel 1
set Tn 1.0 # create the analysis
set K 4.0 constraints Plain
set dampR 0.02 integrator Newmark 0.5 [expr 1.0/6.0]
#set some constants system ProfileSPD
set g 386.4 test NormUnbalance 1.0e-12 6 0
set PI [expr 2.0 * asin(1.0)] algorithm Newton
#derived quantaties numberer RCM
set Wn [expr 2.0 * $PI / $Tn] analysis Transient
set M [expr $K / ($Wn * $Wn)]
set c [expr 2.0*$M*$Wn*$dampR] # perform analysis
set t 0.0; set ok 0.0; set maxD 0.0;
# create the model set maxT [expr (1+$nPts)*$dT];
model basic -ndm 1 -ndf 1 while {$ok == 0 && $t < $maxT} {
node 1 0.0 set ok [analyze 1 $dT]
node 2 1.0 -mass $M set t [getTime]
fix 1 1 set d [nodeDisp 2 1]
uniaxialMaterial Elastic 1 $K 0.0 if {$d > $maxD} {
uniaxialMaterial Elastic 2 0.0 $c set maxD $d
uniaxialMaterial Parallel 3 1 2 } elseif {$d < [expr -$maxD]} {
element truss 1 1 2 1.0 3 set maxD [expr -$d]
set dT 0.0; }
set nPts 0; }
puts "record: $record period: $Tn damping ratio: $dampR max d
Simply Supported Beam # create nodes
set nodeTag 1
n.tcl
set yLoc 0.0;
for {set i 0} {$i < $nY} {incr i 1} {
set xLoc 0.0;
for {set j 0} {$j < $nX} {incr j 1} {
node $nodeTag $xLoc $yLoc
set xLoc [expr $xLoc+ $L/($nX-1.0)]
incr nodeTag
}
set yLoc [expr $yLoc+ $H/($nY-1.0)]
}
# boundary conditions
fix 1 1 1
fix $nX 1 1
# create elements
set eleTag 1
for {set i 1} {$i < $nY} {incr i 1} {
set iNode [expr 1+($i-1)*$nX];
set jNode [expr $iNode+1];
set kNode [expr $jNode+$nX]
set lNode [expr $iNode+$nX]
for {set j 1} {$j < $nX} {incr j 1}
element quad $eleTag $iNode $jNode $kNode $lNode \
# some problem parameters $thick "PlaneStress" 1
set L 40.0 incr eleTag; incr iNode; incr jNode; incr kNode; incr lNode
set H 10.0 }
set thick 2.0 }
set P 10 # apply loads
set nX 9; # numNodes x dirn set midNode [expr ($nX+1)/2]
set nY 3; # numNodes y dirn timeSeries Linear 1
# model builder pattern Plain 1 1 {
model Basic -ndm 2 -ndf 2 load $midNode 0 -$P
load [expr $midNode + $nX*($nY-1)] 0 -$P
# create material }
nDMaterial ElasticIsotropic 1 1000 0.25 3.0 analysis Static;
analyze 1; print node $midNode
Simply Supported Beam o.tcl
# use block command
set cmd "block2D [expr $nX-1] [expr $nY-1] 1 1 \
quad \" $thick PlaneStress 1\" {
1 0 0
2 $L 0
3 $L $H
4 0 $H
}"
eval $cmd
# apply loads
set midNode [expr ($nX+1)/2]
timeSeries Linear 1
pattern Plain 1 1 {
load $midNode 0 -$P
load [expr $midNode + $nX*($nY-1)] 0 -$P
# some problem parameters }
set L 40.0 analysis Static;
set H 10.0 analyze 1;
set thick 2.0 print node $midNode
set P 10
set nX 9; # numNodes x dirn
set nY 3; # numNodes y dirn
# model builder
model Basic -ndm 2 -ndf 2
# create material
nDMaterial ElasticIsotropic 1 1000 0.25 3.0
 Cantilevered Circular Column # mesh generation
p.tcl
set sqrtR [expr sqrt($R/2.0)]
set P 1.0 set cmd "block3D $nx $ny $nz 1 1 $element
set L 20.0 1 -$sqrtR -$sqrtR 0
set R 1.0 2 $sqrtR -$sqrtR 0
set E 1000.0 3 $sqrtR $sqrtR 0
set nz 20 4 -$sqrtR $sqrtR 0
set nx 6 5 -$sqrtR -$sqrtR $L
set ny 6 6 $sqrtR -$sqrtR $L
7 $sqrtR $sqrtR $L
set PI [expr 2.0 * asin(1.0)] 8 -$sqrtR $sqrtR $L
set I [expr $PI*pow((2*$R),4)/64.0] 13 0 -$R 0
puts "PL^3/3EI = [expr $P*pow($L,3)/(3.0*$E*$I)]" 14 $R 0 0
15 0 $R 0
# Create ModelBuilder with 3 dimensions and 6 DOF/node 16 -$R 0 0
model Basic -ndm 3 -ndf 3 18 0 -$R $L
19 $R 0 $L
# create the material 20 0 $R $L
nDMaterial ElasticIsotropic 1 $E 0.25 1.27 21 -$R 0 $L
23 0 -$R [expr $L/2.0]
24 $R 0 [expr $L/2.0]
set eleArgs "1" 25 0 $R [expr $L/2.0]
set element bbarBrick 26 -$R 0 [expr $L/2.0]
}"
set nn [expr ($nz)*($nx+1)*($ny+1) + (($nx+1)*($ny+1)+1)/2]
set n1 [expr ($nz)*($nx+1)*($ny+1) +$nx] eval $cmd
# boundary conditions
fixZ 0.0 1 1 1
# Constant point load
pattern Plain 1 Linear {
load $nn 0.0 $P 0.0
}
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 Numerical Computation
Algorithms & Solvers

Models
Material, Element

Information Technology
Database, Visualization, Frameworks,
Parallel & Grid/Network libraries
Building Blocks for Simulation
 Bell’s Law
Bell's Law of Computer Class formation
was discovered about 1972. It states that
technology advances in semiconductors,
storage, user interface and networking advance
every decade enable a new, usually lower
priced computing platform to form. Once
formed, each class is maintained as a quite
independent industry structure. This explains
mainframes, minicomputers, workstations and
Personal computers, the web, emerging web
services, palm and mobile devices, and
ubiquitous interconnected networks.

Gordon Bell, http://research.microsoft.com/~GBell/Pubs.htm

 Technology is Changing
Intel Processor Speed
XeonE7Server 72Gflop
i7Desktop 55GFlop
i7Mobile 30GFlop
i5Desktop 40GFlop
i5Mobile 22GFlop
Core2 Quad 48GFlop
Core2 Duo 25GFlop
CHIP/Socket

GPU &
CO-Processors
STEVE JOBS KEYNOTE WWDC 2011
Some people think the cloud is just
A hard drive in the sky!

Cloud computing is internet-based computing ,

whereby shared resources, software, IT’S
and NOTinformation
are provided to computers and other devices on
demand, like the electricity grid. source: wikipedia

“..PC and Mac Demoted to a Device”

 Cloud Computing Compute
Resources
•  Commercial

•  Research
–  All of the above PLUS
–  Dedicated High Performance Computers
–  Grid (BOINC, OPEN SCIENCE GRID, ….)
–  NEEShub (http://nees.org)
 What is a Parallel Computer?
•  A parallel computer is a collection of processing
elements that cooperate to solve large problems fast.

File
CPU CPU CPU System

communication

File
System
Memory Memory
 HPC Performance
Projections 10e6 to 100e6
Cores!
1 Eflop/s

N=500

8-10 years

2019
page 163
Source:Jack Dongarra, 2011
 Why should you care?
•  They will save you time
•  They will allow you to solver larger problems.
•  They are here whether you like it or not!
HPC available through NEEShub
§  Kraken (Tennessee)
§  Nodes: 9,408
§  Cores: 112,896
§  Memory: 142TB
§  Peak: 1.17PFlops
§  Disk: 3.3PB
§  Stampede (Texas)
§  Nodes: 6,400
§  Cores: 102,400
§  Memory: 205TB
§  Peak: 9.5PFlops
§  Disk: 14PB
 BEFORE YOU GET ALL EXCITED
Speedup & Amdahl’s Law
Time(1)
speedupPC ( p ) =
Time( p )

T1 1
SpeedupPC = → as n → ∞
(1 − α )T 1 α
αT 1 +
n

Portion of sequential # of processors

 Improving Real Performance
Peak Performance grows exponentially,
a la Moore’s Law
●  In 1990’s, peak performance increased
100x; in 2000’s, it will increase 1000x 1,000

But efficiency (the performance relative to Peak Performance

the hardware peak) has declined
100
●  was 40-50% on the vector supercomputers
of 1990s

Teraflops
●  now as little as 5-10% on parallel Performance
10
supercomputers of today Gap
Close the gap through ...
●  Mathematical methods and algorithms that 1
achieve high performance on a single
Real Performance
processor and scale to thousands of
processors 0.1
1996 2000 2004
●  More efficient programming models and tools
for massively parallel supercomputers Source: Jim Demmell, CS267
166"
Course Notes
 What is OpenSees?

•  OpenSees is an Open-Source Software Framework written in C

++ for developing nonlinear Finite Element Applications for
both sequential and PARALLEL environments.
 Domain Classes
MovableObject Domain
sendSelf(Channel, ..)
recvSelf(Channel, ..)

PartitionedDomain

TimeSeries LoadPattern SP_Constraint MP_Constraint Element

NonlinearBeamColumn
BeamWithHinges Subdomain
Quad (std, bbar,)
ElementalLoad NodalLoad SP_Constraint Brick (std, bbar)
Shell

GraphPartitioner DomainPartitioner

Metis LoadBalancer
 Analysis Classes
MovableObject Analysis

sendSelf(Channel, ..)
recvSelf(Channel, ..)
StaticAnalysis DomainDecompAnalysis
TransientAnalysis

SubstructuringAnalysis StaticDDAnalysis TransientDDAnalysis

CHandler Numberer AnalysisModel SolnAlgorithm Integrator SystemOfEqn Solver

RCM EquiSolnAlgo BandGeneral Lapack(Gen, Band, ..)

Linear BandSPD ProfileSPD
ParallelNumberer
NewtonRaphson ProfileSPD SuperLU
ModifiedNewton SparseGeneral Umfpack
Broyden SparseSymmetric SparseSym
BFGS DistributedSuperLU
DistributedSparse
KrylovNewton Mumps
 The OpenSees Interpreters
•  OpenSees.exe, OpenSeesSP.exe and
OpenSeesMP.exe are applications that
extend the Tcl interpreter for finite element.

So What are OpenSeesSP.exe

and OpenSeesMP.exe ?
 Parallel OpenSees Interpreters

–  OpenSeesSP: An application for large models which

will parse and execute the exact same script as the
sequential application. The difference being the
element state determination and equation solving are
done in parallel.
–  OpenSeesMP: An application for BOTH large
models and parameter studies.
 OpenSeesSP:
An application for Large Models
P0
Single interpreter running on P0
interpreting the input file

Actor objects sitting on other processes

waiting to receive instructions

P1 P2 Pn-1
 Modified Commands
•  System command is modified to accept new
parallel equation solvers
system Mumps
system Diagonal
Model Built and Analysis Constructed in
P0 #build the model
source model.tcl
#build the analysis
system Mumps
constraints Transformation
numberer Plain
test NormDispIncr 1.0e-12 10 3
Single interpreter running on P0 algorithm Newton
integrator LoadControl
Interpreting the input file analysis Static

P0 P1
LoadControl
Domain Newton
Analysis P2
Mumps

P3
 #build the model
source modelP.tcl
#build the analysis
system Mumps
constraints Transformation
numberer Plain
test NormDispIncr 1.0e-12 10 3
algorithm Newton
integrator LoadControl
analysis Static
analyze 10

P0 P1
Analysis
P1
P2 =
P3 Analysis
P3
 Example Results:
Humboldt Bay Bridge Model
350

Total execution time (minute)

300

250

200

150

100

50

0
0 2 4 6 8 10 12 14 16 18
100,000+ DOF Model Number of processors

Implicit Integration
Mumps Direct Solver
 Effect of Shape of Elimination
Tree on Performance:

50,000 DOF+ Models

Implicit Integration
Direct Solver

* Note the fatter the elimination tree, the better the parallel
performance of the direct solver.
 OpenSeesMP: An application for
Large Models and Parameter Studies
pid = 0 pid = 1 pid = n-1
np = n np = n np = n

# source in the model and analysis procedures

set pid [getPID]
set np [getNP]
Each process is running an # build model based on np and pid
interpreter and can determine it’s source modelP.tcl
doModel {$pid $np}
unique process number and the total
# perform gravity analysis
number of processes in computation system Mumps
constraints Transformation
numberer Parallel
test NormDispIncr 1.0e-12 10 3
algorithm Newton
integrator LoadControl 0.1

Based on this script can do different analysis Static

things set ok [analyze 10]

return $ok
New Commands added to OpenSeesMP:
•  A Number of new commands have been added:
1.  getNP returns number of processes in computation.
2.  getPID returns unique pocess id {0,1, .. NP-1}
3.  send -pid pid? data pid = { 0, 1, .., NP-1}
4.  recv -pid pid? variableName pid = {0,1 .., NP-1, ANY}
5.  barrier
6.  domainChange
•  These commands have been added to ALL interpreters
(OpenSees, OpenSeesSP, and OpenSeesMP)
ex2.tcl Example
set pid [getPID]
set np [getNP]
if {$pid == 0 } {
puts ”Random:"
for {set i 1 } {$i < $np} {incr i 1} {
recv -pid ANY msg
puts "$msg"
}
} else {
send -pid 0 "Hello from $pid"
}
barrier
if {$pid == 0 } {
puts "\nOrdered:"
for {set i 1 } {$i < $np} {incr i 1} {
recv -pid $i msg
puts "$msg"
}
} else {
send -pid 0 "Hello from $pid"
}
set pid [getPID]
set np [getNP]
set recordsFileID [open "peerRecords.txt" r]
set count 0;
Steel Building Study
foreach gMotion [split [read $recordsFileID] ¥n] {
if {[expr $count % $np] == $pid} {

source model.tcl
7200 records
source analysis.tcl 2 min a record
240 hours or 10 days
set ok [doGravity]
Ran on 2000 processors
loadConst -time 0.0 on teragrid in less than 15 min.
set gMotionList [split $gMotion "/"]
set gMotionDir [lindex $gMotionList end-1]
set gMotionNameInclAT2 [lindex $gMotionList end]
set gMotionName [string range $gMotionNameInclAT2 0 end-4 ]

set Gaccel "PeerDatabase $gMotionDir $gMotionName -accel 384.4 -dT dT -nPts nPts"
pattern UniformExcitation 2 1 -accel $Gaccel

recorder EnvelopeNode -file $gMotionDir$gMotionName.out -node 3 4 -dof 1 2 3 disp

doDynamic [expr $dT*$nPts] $dT

wipe
}

incr count 1;
}
Concrete Building Study
113 records, 4 intensities
3 hour a record, 1356
hours or 56.5 days.

Ran on 452 processors

On XSEDE in less than 5
hours.
ATC-63/2 Project

3 buildings, 2 config a building, 44

records, 12 intensities, 5 hour a
record, would have, taken 15840
hours or 660 days or 1.8 years.
Ran on 44 processors of a XSEDE
Ranger in less than 7 days.
(ATC-63/2 project using NEEShub)
Example Results Parameter Study:
Moment Frame Reliability Analysis
100+ DOF Model
Explicit Integration,
Mumps Direct Solver
8000 Earthquake Simulations

* If more simulations
than processors
SpeedUp
With “Load Balancing”
will be “Linear”
 Modified Commands
•  Some existing commands have been modified to allow analysis of
large models in parallel:
1.  numberer

numberer ParallelPlain

numberer ParallelRCM
2.  system

system Mumps <-ICNTL14 %?>

3.  integrator

integrator ParallelDisplacementControl node? Dof? dU?

•  Use these ONLY IF PARALLEL MODEL

 Example Parallel Model:
ex4.tcl
set pid [getPID]
set np [getNP] 50 100
if {$np != 2} exit
4
model BasicBuilder -ndm 2 -ndf 2
uniaxialMaterial Elastic 1 3000
if {$pid == 0} { 8’
node 1 0.0 0.0 (1) (2) (3)
node 4 72.0 96.0
fix 1 1 1
element truss 1 1 4 10.0 1
1 2 3
pattern Plain 1 "Linear" {
load 4 100 -50
6’ 6’ 2’
}
} else { E A
node 2 144.0 0.0
node 3 168.0 0.0 1 3000 10
node 4 72.0 96.0
fix 2 1 1 2 3000 5
fix 3 1 1 3 3000 5
element truss 2 2 4 5.0 1
element truss 3 3 4 5.0 1
}
 Example Parallel Analysis:
#create the recorder
recorder Node -file node4.out.$pid -node 4 -dof 1 2 disp

#create the analysis

constraints Transformation
numberer ParallelPlain
system Mumps
test NormDispIncr 1.0e-6 6 2
algorithm Newton
integrator LoadControl 0.1
analysis Static

#perform the analysis

analyze 10

# print to screen node 4

print node 4
Parallel Displacement Control and
ex5.tcl domainChange!
source ex4.tcl

loadConst - time 0.0

if {$pid == 0} {
pattern Plain 2 "Linear" {
load 4 1 0
}
}

domainChange

integrator ParallelDisplacementControl 4 1 0.1

analyze 10
 Things to Watch For
1.  Deadlock (program hangs)
–  send/recv messages
–  Opening files for writing & not closing them
2.  Race Conditions (different results every
time run problem)
–  parallel file system.
3.  Load Imbalance
–  poor initial task assignment.
 Things to Watch For Using
Additional Commands
In addition to Load Imbalance:
1.  Deadlock (program hangs)
–  send/recv messages
–  Opening files for writing & not closing them
2.  Race Conditions (different results on re-
run)
–  parallel file system.
These I am not going to demonstrate
today .. But BE WARNED THEY DO
HAPPEN AND YOU PROBABLY WILL
COME ACROSS THEM!
 MRF_MP1.tcl
set np [getNP]
set pid [getPID]
set count 0
Parameter Study
# set some parameters & open some local files
….
if {$pid == 0} {
foreach Hazard $Hazards {
set dataDir [format "Oak-%i-50-Output" $Hazard]
file mkdir $dataDir/DriftAcceleration;
file mkdir $dataDir/DriftDeformation;
} To ensure only 1 processor
barrier
foreach Hazard $Hazards { does stuff to file system
foreach eqDir $eqDirections {
for { set i 1 } { $i <= $eqNum } { incr i} {
if {[expr $count % $np] == $pid} {
set tStart [clock clicks –milliseconds]
set GMdir [format "./GMfiles/Oak-%i-50/" $Hazard]
source buildModelWithGravity.tcl
source addRecorders.tcl
source Dynamic.EQ.tcl
source processResults.tcl
set tEnd [clock clicks -milliseconds]
puts $timeOut "DURATION: $i $eqDir $Hazard [expr ($tEnd-$tStart\)/1000.]”
}
incr count 1
}
}
}
set tEnd [clock clicks -milliseconds]
puts $timeOut "TOTAL DURATION: [expr ($tEnd-$tStartAll)/1000.]”
puts “PID: $pid DURATION: [expr ($tEnd-$tStartAll)/1000.]”
# close local files
….
 Results using 16 Processors

# Tasks Completed (pid vs # tasks) Duration (pid v time)

 Load Balancing Solutions:
The key question: When is information (task costs, task dependencies,
and task locality) about the load balancing problem known. Leads to
a spectrum of solutions:
•  Static scheduling. All information is available to scheduling
algorithm, which runs before any real computation starts.
–  Off-line algorithms, eg graph partitioning, DAG scheduling
(Pegasus)
•  Semi-static scheduling. Information may be known at program
startup, or the beginning of each timestep, or at other well-defined
points. Offline algorithms may be used even though the problem is
dynamic.
•  Dynamic scheduling. Information is not known until mid-execution. "

Source: Prof. Demmel, CS267, UC Berkeley

19
4!
 Dynamic Scheduling
(Dynamic Load Balancing)
In dynamic load balancing we Adjust Task Assignment as
Processing Takes Place. 2 Main Approaches:
•  Work Sharing: processors balance the
workload using a globally shared work
queue(s) that contain tasks to be computed.
If a task generates additional tasks, these
can be pushed back to task queue to share.
•  Work Stealing: processors keep own
queues, idle processors search among the
other processors in the computation in order
to find surplus work.
 Work Sharing
(Centralized Scheduling /Self
Scheduling)
•  Keep a queue of tasks waiting to be done
–  May be done by manager process
–  Or a shared data structure protected by locks

Source: Prof. Demmel, CS267, UC Berkeley

•  When free, Worker process requests some
tasks! worker
worker

Task
worker Queue worker

worker worker
 Work Sharing
MRF_MP2.tcl

set np [getNP] } else {

set pid [getPID] set done NOT_DONE;
while {$done != "DONE"} {
# set some parameters & open some local files
send -pid 0 $pid
….
recv -pid 0 task
if {$pid == 0} {
foreach Hazard $Hazards { set Hazard [lindex $task 0]

set dataDir [format "Oak-%i-50-Output" $Hazard] ; if {$Hazard == "DONE"} {

file mkdir $dataDir/DriftAcceleration; set done "DONE"
file mkdir $dataDir/ForceDeformation break;
}
foreach eqDir $eqDirections { set eqDir [lindex $task 1]
for {set i 1 } { $i <= $eqNum } { incr i} { set i [lindex $task 2]
recv -pid ANY pidWorker
set tStart [clock clicks -milliseconds]
send -pid $pidWorker "$Hazard $eqDir $i" set GMdir [format "./GMfiles/Oak-%i-50/" $Hazard];
} source buildModelWithGravity.tcl
} source addRecorders.tcl
} source Dynamic.EQ.tcl
# tell all processors we are done source processResults.tcl
for {set i 1} {$i < $np} {incr i 1} {
recv -pid ANY pidWorker set tEnd [clock clicks -milliseconds]
puts $timeOut "DURATION: $i $eqDir $Hazard [expr ($tEnd-$tStart)/1000.]”
send -pid $pidWorker "DONE"
}
}
}
} else { set tEnd [clock clicks -milliseconds]
puts $timeOut "TOTAL DURATION: [expr ($tEnd-$tStartAll)/1000.]”
puts “PID: $pid DURATION: [expr ($tEnd-$tStartAll)/1000.]”
# close local files
….
 Results using 16 Processors

# Tasks Completed (pid vs # tasks) Duration (pid v time)

 Variations on Work Sharing
•  Typically, don’t want to grab smallest unit of
parallel work, e.g., a single iteration
o  Too much contention at shared queue
•  Instead, choose a chunk of tasks of size K.
o  If K is large, access overhead for task queue is small
o  If K is small, we are likely to have even finish times
(load balance)
•  (at least) Four Variations:
o  Use a fixed chunk size
o  Guided self-scheduling
o  Tapering
Source: Prof. Demmel, CS267, UC Berkeley
o  Weighted Factoring
Variation 1: Fixed Chunk Size
•  Kruskal and Weiss give a technique for computing the optimal
chunk size (IEEE Trans. Software Eng., 1985)
•  Requires a lot of information about the problem characteristics
–  e.g., task costs, number of tasks, cost of scheduling
–  Probability distribution of runtime of each task (same for all)
–  Assumes distribution is IFR = “Increasing Failure Rate”"
•  Not very useful in practice
–  Task costs must be known at loop startup time
–  E.g., in compiler, all branches be predicted based on
loop indices and used for task cost estimates

Source: Prof. Demmel, CS267, UC Berkeley

 Variation 2: Guided Self-
Scheduling
•  Idea: use larger chunks at the beginning to
avoid excessive overhead and smaller chunks
near the end to even out the finish times.
–  The chunk size Ki at the ith access to the task pool
is given by
Ki = ceiling(Ri/p)
–  where Ri is the total number of tasks remaining and
–  p is the number of processors
•  See Polychronopoulos & Kuck, “Guided Self-
Scheduling: A Practical Scheduling Scheme for
Parallel Supercomputers,” IEEE Transactions
on Computers, Dec. 1987.
Source: Prof. Demmel, CS267, UC Berkeley
 Variation 3: Tapering
•  Idea: the chunk size, Ki is a function of not
only the remaining work, but also the task
cost variance
–  variance is estimated using history information
–  high variance => small chunk size should be
used
•  See– S.low variance
Lucco, => larger
“Adaptive Parallelchunks OK
Programs,” PhD Thesis,
UCB, CSD-95-864, 1994.
•  Gives analysis (based on workload distribution)
•  Also gives experimental results -- tapering always works
at least as well as GSS, although difference is often small

Source: Prof. Demmel, CS267, UC Berkeley

 Variation 4: Weighted
Factoring
•  Idea: similar to self-scheduling, but divide
task cost by computational power of
requesting node
•  Useful for heterogeneous systems
•  Also useful for shared resource clusters, e.g.,
built using all the machines in a building
–  as with Tapering, historical information is used
to predict future speed
–  “speed” may depend on the other loads currently
on a given processor
•  See Hummel, Schmit, Uma, and Wein, SPAA
‘96 Source: Prof. Demmel, CS267, UC Berkeley
 When is Work Sharing a Good
Idea?
Useful when:
•  A batch (or set) of tasks without
dependencies
–  can also be used with dependencies, but most
analysis has only been done for task sets without
dependencies

•  The cost of each task is unknown

•  Locality is not important
•  Shared memory machine, or at least number
Source: Prof. Demmel, CS267, UC Berkeley

of processors is small – centralization is OK

 Work Stealing
(Work Crews/Distributed Load
Balancing)
•  Each processor processes tasks in its queue
•  When finished, steals work from a processor that is busy
•  Requires asynchronous communication

Steal!
P P P P

Source: Prof. Demmel, CS267, UC Berkeley

 Work Stealing
MRF_MP3.tc

set np [getNP]
set pid [getPID]
# set some parameters & open some local files
# define some procedures for work stealing
….
if {$pid == 0} {

# create task queues

createTaskQueues $np

# add tasks to the different queus

set count 0
foreach Hazard $Hazards {
set dataDir [format "Oak-%i-50-Output" $Hazard] ;
file mkdir $dataDir/DriftAcceleration;
file mkdir $dataDir/ForceDeformation;

foreach eqDir $eqDirections {

for {set i 1 } { $i <= $eqNum } { incr i} {
set thePID [expr $count % $np]
addTask $thePID $Hazard $eqDir $i
incr count 1
}
}
}
}

barrier
 Work Stealing
MRF_MP3.tcl

#
# done with my own queue, start stealing from others
# #
# process my own tasks
# set numDone 1;
set done “NOTDONE”
set done NOT_DONE; while {$done == “NOTDONE”} {
while {$done != "DONE"} {
set task [getTask $pid] set task [stealTask]

if {[llength $task] == 0} { if {$task == ""} {

set done "DONE" set done “DONE”
break; break
} }

set Hazard [lindex $task 0] set Hazard [lindex $task 0]

set eqDir [lindex $task 1] set eqDir [lindex $task 1]
set i [lindex $task 2] set i [lindex $task 2]

set tStart [clock clicks -milliseconds] set tStart [clock clicks -milliseconds]

set GMdir [format "./GMfiles/Oak-%i-50/" $Hazard]; set GMdir [format "./GMfiles/Oak-%i-50/" $Hazard];
source buildModelWithGravity.tcl source buildModelWithGravity.tcl
source addRecorders.tcl source addRecorders.tcl
source Dynamic.EQ.tcl source Dynamic.EQ.tcl
source processResults.tcl source processResults.tcl

set tEnd [clock clicks -milliseconds] set tEnd [clock clicks –milliseconds]
puts $timeOut "DURATION: $i $eqDir $Hazard [expr ($tEnd-$tStart)/1000.]" puts $timeOut "DURATION: $i $eqDir $Hazard [expr ($tEnd-$tStart)/1000.]"
} }
 Work Stealing proc getRandomPID {np} {
if {$np == 0} {
return 0;
proc createTaskQueues {np} { }
# open some files to store tasks set maxFactor [expr $np + 1]
for {set i 0} {$i < $np} {incr i 1} { set value [expr int([expr rand() * 100])]
set taskFile [open tasks.$i w] set value [expr int([expr $value % $maxFactor])]
} return [expr $value % $np]
close $taskFile }
} proc stealTask {} {
global pid
proc addTask {thePID Hazard eqDir i} { global np
set taskFile [open tasks.$thePID a] global numDone
puts $taskFile "$Hazard $eqDir $i" global processesDone
close $taskFile set foundOne 0
} set task ””;
while {$foundOne == 0 && $numDone < $np} {
proc getTask {thePID} {
if {[file size tasks.$thePID] == 0} { set otherProcess [getRandomPID [expr $np-$numDone-1]]
return "" set task [getTask [lindex $processesDone $otherProcess]]
} if {[llength $task] == 0} {
set newProcessesDone {}
set taskFile [open tasks.$thePID r+]
for {set i 0} {$i < $np-$numDone} {incr i 1} {
seek $taskFile 0
if {$i != $otherProcess} {
gets $taskFile task
lappend newProcessesDone [lindex$processesDone $i]
set restData [read $taskFile]
}
chan truncate $taskFile 0
seek $taskFile 0 }
set data [split $restData "\n"] set numDone [expr $numDone+1]
foreach line $data { set processesDone $newProcessesDone
if {[llength $line] != 0} { } else {
set foundOne 1
puts $taskFile $line
}
}
}
}
return $task
close $taskFile
}
return $task
}
 Results using 16 Processors

# Tasks Completed (pid vs # tasks) Duration (pid v time)

 How to Select a Donor Processor
Three basic techniques:
1.  Asynchronous round robin
•  Each processor k, keeps a variable “targetk”
•  When a processor runs out of work, requests work from targetk
•  Set targetk = (targetk +1) mod procs
2.  Global round robin
•  Proc 0 keeps a single variable “target”
•  When a processor needs work, gets target, requests work from
target
•  Proc 0 sets target = (target + 1) mod procs
3.  Random polling/stealing
•  When a processor needs work, select a random processor and
request work from it
•  Repeat if no work is found
Source: Prof. Demmel, CS267, UC Berkeley
 How to Split Work
•  First question is number of tasks to split
–  Related to the work sharing variations, but total
number of tasks is now unknown
•  Second question is which one(s)
–  Send tasks near the bottom of the stack (oldest)
–  Execute from the top (most recent)
–  May be able to do better with information about
task costs Top of stack

Bottom of stack
Source: Prof. Demmel, CS267, UC Berkeley
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 NEEShub (First Release July 2010)

* The power behind NEES

 NEEShub Tools and Resources
Documents, Learning Objects, Series & TOOLS

Simulation

Data Management
 The OpenSeesLab tool:
http://nees.org/resources/tools/openseeslab

Is a suite of Simulation Tools powered by OpnSees for:

1.  Submitting OpenSees scripts (input files) to HUB resources
2.  Educating students and practicing engineers
OpenSees Interpreter Tool
Parallel Script Submission Tool
Full Path to main script
To Select Machine

To Select Application
 STRUCTURAL & Modeling
Uncertainties
* PEER Concrete Column Blind Prediction Contest 2010

How Can This Uncertainty Be Ignored in your Evaluation?

Moment Frame Reliability Analysis

http://nees.org/resources/tools/openseeslab
Roof Displacements
Roof Accelerations
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 Max Roof Displacement = ?
120 ft 72 ft
80.5 ft Dead Load: 95psf typical, roof 80psf
E=29,000, Fy=50.0, b =0.003
3% Rayleigh Damping 1st and 3rd Modes
Subjected to el_centro 1940 N-S (Peknold)

A Ixx
W14X193 56.8 2400
W14X159 46.7 1900 12.5 ft
W14X109 32.0 1240 24 ft
W30X173 51.0 8230
W27X146 43.1 5660
W24X104 30.6 3100
W30X99 29.1 3990 18 ft
W27X94 27.7 3270
W24X76 22.4 2100
This figure is taken from the first paper in the SAC 95-05 report: Hall, John F. "Parameter Study of Response of Moment-Resisting Steel Frame
Buildings to Near-Source Ground Motions”
 Basic Linux Commands:

•  mkdir dirname --- make a new directory

•  cd dirname --- change directory
•  pwd --- tells you where you currently are.
•  ls --- list files in current directory
•  cp origFile newFile --- copy a file
•  mv origFile newFile --- move a file
•  rm filename --- remove a file
•  wc –l filename ---- how many lines in a file
 To Get You Started – follow this:
•  Start batchsubmit tool
•  Type: cd ~
•  On 1 single line type :
•  svn co svn://opensees.berkeley.edu/usr/
local/svn/OpenSees/trunk/Workshops/
OpenSeesDays Examples
•  This will have created Examples directory
•  cd Examples and look at MRF1.tcl (spend some
time looking at other files)
•  Start OpenSeesLab tool and start
OpenSeesInterpreter
•  Go to editor, open MRF1.tcl and make changes
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 Traditional Finite Element
Software
•  Commercial fe codes are large complex
software containing over one million lines of code.
They are closed-source but do allow new
element and material routines to be added. (at
least the serious ones do)
•  They are slow to change as hardware changes
and they do not allow researchers to play with
other equally important aspects of the code.
They do not promote the active sharing of new
code.
 THE ADVANTAGE OF A
SOFTWARE FRAMEWORK
SUCH AS OPENSEES IS THAT
YOU DON’T HAVE TO
UNDERSTAND ALL OF IT TO
BUILD APPLICATIONS OR
MAKE CONTRIBUTIONS
YOU JUST NEED TO
UNDERSTAND THAT PART
THAT CONCERNS YOU
OPENSEES FEM ABSTRACT
CLASSES
 Framework Contains both Abstract
Classes & Concrete Subclasses

Material Element Integrator

Uniaxial nD Section StaticIntegrator

Truss
LoadControl
ZeroLength DispControl
ElasticBeamColumn ArcLength
ForceBeamColumn …
Elastic Elastic Elastic DispBeamColumn TransientIntegrator
ElasticPP J2 Fiber BeamWithHinges CentralDifference
Hardening DruckerPrager Quad (many forms) Newmark
Concrete FluidSolidPorous Shell HHT
Steel PressureMultiYield(dependent, Brick(many forms) GeneralizedAlhpa
Hysteretic independent) Joint NewmarkExplicit
PY-TZ-QZ Contact TRBDF2
Parallel AlphaOS
Series (>100 element classes) (>35 classes)
Gap
Fatigue
(over 250 material classes)
 Unknown Class Type
When OpenSees.exe is running and it comes
across a class type it knows nothing about
BEFORE GIVING AN ERROR IT WILL
TRY AND LOAD A LIBRARY OF THAT
CLASSES NAME. If it cannot find
a library of the appropriate name or the
procedure of the appropriate name in the
library it will FAIL.
Commands/Script

Output
 To Add a New Class you must:
1) Provide Code that meets the Interface
of the appropriate super-class
2) you must BUILD THE LIBRARY
3) make it accessible to the program.

WHILE C++ IS THE GLUE LANGUAGE

THAT HOLDS OPENSEES TOGETHER
YOUR CODE DOES NOT HAVE TO BE
WRITTEN IN C++.
C and FORTRAN OPTIONS ARE ALSO
AVAILABLE
class UniaxialMaterial : public Material Must be overridden by
{
public:
UniaxialMaterial(int tag, int classTag);
subclass, “pure virtual”
virtual ~UniaxialMaterial();

virtual int setTrialStrain(double strain, double strainRate = 0.0) = 0;

virtual double getStrain(void) = 0;
virtual double getStress(void) = 0;
virtual double getTangent(void) = 0;
virtual double getInitialtangent(void) =0;

virtual int commitState(void) = 0;

virtual int revertToLastCommit(void) = 0;
virtual int revertToStart(void) = 0;

virtual UniaxialMaterial *getCopy(void) = 0;

Can be overridden by subclass
virtual Response *setResponse(const char **argv, int argc,OPS_Stream &theOutput);
virtual int getResponse(int responseID, Information &info);
virtual void Print(OPS_Stream &s, int flag =0);

virtual int sendSelf(int commitTag, Channel &theChannel)=0;

virtual int recvSelf(int commitTag, Chanel &theChannel, FEM_ObjectBroker &theBroker)=0;
// THERE ARE SOME OTHERS .. BUT THESE ARE PURE VIRTUAL ONES THAT MUST BE PROVIDED
protected:
private:
};
 Adding New Code
For those new to Programming NEVER EVER NEVER START
WITH AN EMPTY FILE .. TAKE SOMETHING SIMILAR THAT
WORKS AND MAKE CHANGES TO THAT FILE.

We provide C++, C and Fortran examples on-line using svn

svn://opensees.berkeley.edu/usr/local/svn/OpenSees/trunk/DEVELOPER
TortoiseSVN for Windows Users

your
 Source Code Tree in
DEVELOPER
Makefile
WindowsInstructions
UnixInstructions

core integrator recorder material element element …

Trapezoidal.h
Trapezoidal.cpp cpp c fortran cpp c fortran

ElasticPPcpp.h elasticPPc.c elasticPPf.f

ElasticPPcpp.cpp example1.tcl example1.tcl
example1.tcl …
 class ElasticPPcpp: public UniaxialMaterial {
public:
Material ElasticPPcpp(int
ElasticPPcpp();
tag, double e, double eyp);

material input

properties
Name ~ ElasticPPcpp();
int setTrialStrain(double strain, double strainRate=0.0);


double getStrain(void);
double getStress(void);
double getTangent(void);
double getInitialTangent(void);

int commitState(void);
int revertToLastCommit(void);
int revertToStart(void);
UniaxialMaterial *getCopy(void);
int sendSelf(int commitTag, Channel &theChannel);
int recvSelf(int commitTag, Channel &theChannel, FEM_ObjectBroker &theBroker);
void Print(OPS_Stream &s, int flag = 0);
private:
double fyp, fyn; // pos & neg yield stress
data unique to
double ezero, E,ep; // init strain, elastic mod material includes:
double ep; // plastic strain at last commit Material parameters,
double trialStrain, trialStress, trialTangent;
double commitStrain, commitStress, commitTangent;
& State variables
};
ElasticPPcpp::ElasticPPcpp(int tag, double e, double eyp)
:UniaxialMaterial(tag, 0),
ezero(0), E(e), ep(0.0) trialStrain(0.0),trialStress(0.0),trialTangent(e),
commitStreain(0.0),commitStress(0.0),commitTangent(e)
{
fyp=E*eyp;
fyn = -fyp;
}
ElasticPPcpp::ElasticPPcpp()
:UniaxialMaterial(tag, 0)
fyp(0),fyn(0),ezero(0), E(0),ep(0),
trialStrain(0.0),trialStress(0.0),trialTangent(0),
commitStrain(0.0),commitStress(0.0),commitTangent(e){
}
ElasticPPcpp::~ElasticPPcpp
{
// does nothing .. No memory to clean up
}
UniaxialMaterial *ElasticPPcpp::getCopy(void)
{
ElasticPPcpp *theCopy = new ElasticPPcpp(this->getTag(), E, fyp/E);
return theCopy;
};
 Hardest Method to Write
ElasticPPcpp::setTrialStrain(double strain, double strainRate)
{
if (fabs(trialStrain - strain) < DBL_EPSILON)
return 0;
trialStrain = strain;
double sigtrial; // trial stress
double f; // yield function
// compute trial stress
sigtrial = E * ( trialStrain - ezero - ep );
// evaluate yield function
if ( sigtrial >= 0.0 )
f = sigtrial - fyp;
else
f = -sigtrial + fyn;
double fYieldSurface = - E * DBL_EPSILON;
if ( f <= fYieldSurface ) {
// elastic
trialStress = sigtrial;
trialTangent = E;
} else {
// plastic
if ( sigtrial > 0.0 ) {
trialStress = fyp;
} else {
trialStress = fyn;
}
trialTangent = 0.0;
}

return 0;
}
double
ElasticPPcpp::getStrain(void)
{
return trialStrain;
}

double
ElasticPPcpp::getStress(void)
{
return trialStress;
}

double
ElasticPPcpp::getTangent(void)
{
return trialTangent;
}

int
ElasticPPcpp::revertToLastCommit(void)
{
trialStrain = commitStrain;
trialTangent = commitTangent;
trialStress = commitStress;

return 0;
}
 Interpreter looking
OPS_Export for* this function in lib
void
OPS_ElasticPPcpp()
{ You can give yourself some
if (numElasticPPcpp == 0) {
opserr << "ElasticPPcpp unaxial material KUDOS, - Writtene.g. please
by fmk
reference
UC Berkeley\n”;
numElasticPPcpp =1; … if you used
this
}
// Pointer to a uniaxial material that will be returned
UniaxialMaterial *theMaterial = 0;
int iData[1];
double dData[2];
int numData; parse the script for
numData = 1;
three material parameters
if (OPS_GetIntInput(&numData, iData) != 0) {
opserr << "WARNING invalid uniaxialMaterial ElasticPP tag" << endln;
return 0;
}
numData = 2;
if (OPS_GetDoubleInput(&numData, dData) != 0) {
opserr << "WARNING invalid E & ep\n";
return 0;
} Function returns new material
theMaterial = new ElasticPPcpp(iData[0], dData[0], dData[1]);

return theMaterial;
}
 C & Fortran Procedural
Languages Can Also Be Used
OPS_Export void
elasticPPc (matObj *thisObj, SUBROUTINE ELASTICPPF(matObj,model,strain,tang,stress,isw,erro
modelState *model,
double *strain, !DEC$ IF DEFINED (_DLL)
double *tang, !DEC$ ATTRIBUTES DLLEXPORT :: ELASTICPPF
double *stress, !DEC$ END IF
int *isw, use materialTypes
int *result) use materialAPI
{ implicit none
*result = 0; IF (isw.eq.ISW_INIT) THEN

if (*isw == ISW_INIT) { c get the input data - tag? E? eyp?

double dData[2]; numData = 1

int iData[1]; iPtr=>iData;
/* get the input data - tag? E? eyp? */ err = OPS_GetIntInput(numData, iPtr)
int numData = 1; numData = 2
OPS_GetIntInput(&numData, iData); dPtr=>dData;
numData = 2; err = OPS_GetDoubleInput(numData, dPtr)
OPS_GetDoubleInput(&numData, dData);
c Allocate the element state
/* Allocate the element state */ matObj%tag = idata(1)
matObj%nparam = 2
thisObj->tag = iData[0];
thisObj->nParam = 2; /* E, eyp */ matObj%nstate = 2
What Follows are the Steps
required to Build
ElasticPPcpp.dll on a
Windows Machine with
Visual Studio 2010 Installed
 We Will Build the
ElasticPPcpp.dll

Source code and example are in

/DEVELOPER/material/cpp
Create Project

1)  File  -­‐>  New  -­‐>Project  

 4.  Select  Win32  Project  

3.  Select  Win32  

1.  Give  DLL  name  ElasAcPPcpp  

5.  Select  OK  
2.  Give  LocaAon  
Select  ApplicaAon  SeGngs  
 1.  Select  DLL  

2.  Select  DLL  

3.  Select  Finish  
Add Files To Project

1.  Right  Click  on  Source  Files  

2.  Select  Add  ExisAng  
3.  Navigate  to  DEVELOPER/material/cpp  directory  
4.  Select  the  ElasAcPPcpp.cpp  and  .h  file  
5.  Select  Add  
1)  Select  Build  -­‐>  SoluAon  
1.  Right  Click  on  ElasAcPPcpp  Project  
2.  Select  ProperAes  
3.  Select  C/C++  

IT FAILS!
 4.  Include  core  in  addiAonal  include  directories  

3.  Select  All  ConfiguaraAons  from  Pull  Down  Menu  

1.  Select  C/C++    

2.  Select  General  
1)  Select  Build  -­‐>  SoluAon  

IT FAILS!
1.  Right  Click  on  Source  Files  
2.  Select  Add  ExisAng  
3.  Navigate  to  DEVELOPER/core  directory  
4.  Select  the  All  .cpp  and  .h  file  
5.  Select  Add  
1.  Select  Build  -­‐  SoluAon  
 Copy ElasticPPcpp.dll from
location into current directory

Now run Example

What Follows are the Steps
required to Build
ElasticPPcpp.so on a Linux
Machine with gcc installed

NOTE: We Will use

NEEShub
for this demonstration
(http://nees.org)
 3 Simple Steps!
1. Download code
svn co svn://opensees.berkeley.edu/usr/local/svn/OpenSees/trunk/OpenSees/Developer Developer

2. cd DEVELOPER/material/cpp
3. type make
if you type ls you should see the .so and you
Can test it using >OpenSees example1.tcl

NOTE: mac users must have xcode installed and

must open DEVELOPER/Makefile.def and switch
comments on lines 1 and 2 before step 3.
1: Download Source Code
2/3: cd to Directory & Type make
 Outline of Workshop
•  Introduction
•  OpenSees & Tcl Interpreters
•  Output
•  Modeling in OpenSees
•  Nonlinear Analysis
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Adding Your Code to OpenSees
•  Conclusion
 Add the current directory
to your LD_LIBRARY_PATH
Run It
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 Advanced Modeling is about
developing scripts that are easier
to generate, easier to modify and
debug, easier for others to
decipher (think your advisor!)
and less error prone
•  “There are two ways of constructing a
software design: one way is to make it so
simple that there are obviously no
deficiencies; the other way is to make it so
complicated that there are no obvious
deficiencies. The first method is far more
difficult.” C.A. Hoare, The Emperor’s Old Clothes, 1980

KISS is an acronym
for "Keep it simple,
stupid”
The SCRIPTS you are submitting
to OpenSees
are PROGRAMS
you are submitting to a powerful
INTERPRETER ..

SO START PROGRAMMING!
 Steel W Sections &
Regular Grid
col line col line
1 2 3 4 5 6
Floor 4
24
Floor 3
43

42 52 Floor 2
4252
5152 Floor 1
11

Nodes # $col$floor (if more than 10 col lines or floors,

Elements # $iNode$jNode start numbering at 10,
if > 100, at 100, ….)
 model Basic –ndm 2 –ndf 3
source Steel2d.tcl MRF1.tcl
# set some lists containing floor and column line locations and nodal masses
set floorLocs {0. 204. 384. 564.}; # floor locations in inches
set colLocs {0. 360. 720. 1080. 1440. 1800.}; #column line locations in inches
set massesX {0. 0.419 0.419 0.430}; # mass at nodes on each floor in x dirn
set massesY{0. 0.105 0.105 0.096} ; # “ “ “ “ “ “ in y dirn

# add nodes at each floor at each column line location & fix nodes if at floor 1
foreach floor {1 2 3 4} floorLoc $floorLocs massX $massesX massY $massesY {
foreach colLine {1 2 3 4 5 6} colLoc $colLocs {
node $colLine$floor $colLoc $floorLoc -mass $massX $massY 0.
if {$floor == 1} {fix $colLine$floor 1 1 1}
}
}
#uniaxialMaterial Steel02 $tag $Fy $E $b $R0 $cr1 $cr2
uniaxialMaterial Steel02 1 50.0 29000. 0.003 20 0.925 0.15; ; # material to be used for steel elements
# set some list for col and beam sizes
set colSizes {W14X370 W14X370 W14X211}; #col sizes stories 1, 2 and 3
set beamSizes {W33X141 W33X130 W27X102}; #beams sizes floor 1, 2, and 3
# add columns at each column line between floors
geomTransf PDelta 1
foreach colLine {1 2 3 4 5 6} {
foreach floor1 {1 2 3} floor2 { 2 3 4} {
set theSection [lindex $colSizes [expr $floor1 -1]]; # obtain section size for column
ForceBeamWSection2d $colLine$floor1$colLine$floor2 $colLine$floor1 $colLine$floor2 $theSection 1 1 –nip 5
}
}
#add beams between column lines at each floor
geomTransf Linear 2
foreach colLine1 {1 2 3 4 5} colLine2 {2 3 4 5 6} {
foreach floor {2 3 4} {
set theSection [lindex $beamSizes [expr $floor -2]]; # obtain section size for floor
ForceBeamWSection2d $colLine1$floor$colLine2$floor $colLine1$floor $colLine2$floor $theSection 1 2
}
}
Steel2.tcl – contains a library of procedures
#WinXlb/f "Area(in2) d(in) bf(in) tw(in) tf(in) Ixx(in4) Iyy(in4)"
array set WSection {
W44X335 "98.5 44.0 15.9 1.03 1.77 31100 1200 74.7"
W44X290 "85.4 43.6 15.8 0.865 1.58 27000 1040 50.9"
W44X262 "76.9 43.3 15.8 0.785 1.42 24100 923 37.3"
W44X230 "67.7 42.9 15.8 0.710 1.22 20800 796 24.9"
W40X593 "174 43.0 16.7 1.79 3.23 50400 2520 445"
W40X503 "148 42.1 16.4 1.54 2.76 41600 2040 277”
…
}
proc ElasticBeamWSection2d {eleTag iNode jNode sectType E transfTag {Orient XX}} {
global WSection
global in
set found 0
foreach {section prop} [array get WSection $sectType] {
set propList [split $prop]
set A [expr [lindex $propList 0]*$in*$in]
set Ixx [expr [lindex $propList 5]*$in*$in*$in*$in]
set Iyy [expr [lindex $propList 6]*$in*$in*$in*$in]
if {$Orient == "YY" } {
element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iyy $transfTag
} else {
element elasticBeamColumn $eleTag $iNode $jNode $A $E $Ixx $transfTag
}
}
}
proc ForceBeamWSection2d {eleTag iNode jNode sectType matTag transfTag args} {

global FiberSteelWSection2d
global ElasticSteelWSection2d

set Orient "XX"

if {[lsearch $args "YY"] != -1} {
set Orient "YY"
}
set nFlange 8
if {[lsearch $args "-nFlange"] != -1} {
set loc [lsearch $args "-nFlange"]
set nFlange [lindex $args [expr $loc+1]]
}

set nWeb 4
if {[lsearch $args "-nWeb"] != -1} {
set loc [lsearch $args "-nWeb"]
set nWeb [lindex $args [expr $loc+1]]
}

set nip 4
if {[lsearch $args "-nip"] != -1} {
set loc [lsearch $args "-nip"]
set nip [lindex $args [expr $loc+1]]
}

if {[lsearch $args "-elasticSection"] != -1} {

set loc [lsearch $args "-elasticSection"]
set E [lindex $args [expr $loc+1]]
ElasticSteelWSection2d $eleTag $sectType $E $Orient
} else {
FiberSteelWSection2d $eleTag $sectType $matTag $nFlange $nWeb $Orient
}

element forceBeamColumn $eleTag $iNode $jNode $nip $eleTag $transfTag

}
Now that you don’t have to spend
a lot of time creating our models
you should spend time studying
the effects of your modeling
and analysis choices!
 Now We Can Do Fun Stuff MRF2.tcl

How Many Fibers?

foreach nFlange {1 2 3 10 10 20 35} nWeb {4 4 4 5 10 20 30} {
puts ”nFlange: $nFlange nWeb: $nWeb"

wipe;
model BasicBuilder -ndm 2 -ndf 3;

….

….
# add columns at each column line between floors
geomTransf PDelta 1
foreach colLine {1 2 3 4 5 6} {
foreach floor1 {1 2 3} floor2 { 2 3 4} {
set theSection [lindex $colSizes [expr $floor1 -1]]; # obtain section size for column
ForceBeamWSection2d $colLine$floor1$colLine$floor2 $colLine$floor1 $colLine$floor2 $theSection 1 1 –nFlange $nFlange –nWeb $nWeb
}
}

#add beams between column lines at each floor

geomTransf Linear 2
foreach colLine1 {1 2 3 4 5} colLine2 {2 3 4 5 6} {
foreach floor {2 3 4} {
set theSection [lindex $beamSizes [expr $floor -2]]; # obtain section size for floor
ForceBeamWSection2d $colLine1$floor$colLine2$floor $colLine1$floor $colLine2$floor $theSection 1 2 –nFlange $nFlange –nWeb $nWeb
}
}
}
 # fibers flange- # fibers web

Results 10 % in 50year

Time
1-4 292sec
2-4 302sec
3-4 309sec
10-10 578sec
20-20 1001sec
35-30 1305sec
 # fibers flange- # fibers web

Results 2% in 50year

Time
1-4 254sec
2-4 265sec
3-4 272sec
10-10 506sec
20-20 879sec
35-30 1539sec
 PDelta Gravity Column
•  To include PDelta effects from rest of Gravity column
structure on lateral system •  Pinned base
•  Impact seen when axial forces are large •  Gravity Column Loads
(think medium & high-rise) •  Truss with Pdelta
•  Tied to lateral system
with MP Constraint

•  Biggest impact
possible at
bottom where
axial loads
largest.
•  The bigger
inter-story drift
the bigger the
impact.
geomTransf PDelta 3;
set Arigid 10000.0
set Irigid 100000.0
set Ismall 1.0e-1;
set gravityColsArea {806.7 806.7 477.7}; # half sum of area of gravity cols & orthogonal frame
columns

#nodes
set col6 6; set col7 7;
foreach floor {1 2 3 4} floorLoc {0 204. 384. 564.} {
node $col7$floor 1900. $floorLoc
if {$floor == 1} {fix $col7$floor 1 1 0}
} for Pdelta Truss response, I am using
#elements elastic beam with small I to get PDelta
foreach floor1 {1 2 3} floor2 { 2 3 4} {
set A [lindex $gravityColsArea [expr $floor1-1]]
element elasticBeamColumn 7$floor17$floor2 7$floor1 7$floor2 $A $Es $Ismall 3;
element Truss $col6$floor2$col7$floor2 $col6$floor2 $col7$floor2 $Arigid 3
# equalDOF $col6$floor2 $col7$floor2 1
}
Either Works, Just wanted to look
# loads At forces being transmitted to frame.
pattern Plain 3 “Linear” {
# loads on gravity PDelta column
load 72 0.0 -748.48 0.0; # Floor 2
load 73 0.0 -748.48 0.0; # Floor 3
load 74 0.0 -792.84 0.0; # Floor 4
}
 Results 10 % in 50year

Pdelta will only have an effect when

axial loads are high .. Think tall building
 When DONE with a Program

Critique It

(if you have the time this will make

you a better programmer)
 model Basic –ndm 2 –ndf 3
source Steel2d.tcl MRF1.tcl
# set some lists containing floor and column line locations and nodal masses
set floorLocs {0. 204. 384. 564.}; I did not like
# floor locations in inches
set colLocs {0. 360. 720. 1080. 1440. 1800.}; #column line locations in inches
set massesX {0. 0.419 0.419 0.430};
set massesY{0. 0.105 0.105 0.096} ; # “ “ “ “
having to
# mass at nodes on each floor in x dirn
“ “ in y dirn

# add nodes at each floor at each column line location & fixcalculate
nodes if at floor 1 floor
and col locations
foreach floor {1 2 3 4} floorLoc $floorLocs massX $massesX massY $massesY {
foreach colLine {1 2 3 4 5 6} colLoc $colLocs {
node $colLine$floor $colLoc $floorLoc -mass $massX $massY 0.
if {$floor == 1} {fix $colLine$floor 1 1 1}
}
}
#uniaxialMaterial Steel02 $tag $Fy $E $b $R0 $cr1 $cr2
uniaxialMaterial Steel02 1 50.0 29000. 0.003 20 0.925 0.15; ; # material to be used for steel elements
# set some list for col and beam sizes
While putting numbers
set colSizes {W14X370 W14X370 W14X211}; #col sizes stories 1, 2 and 3
set beamSizes {W33X141 W33X130 W27X102}; #beams sizes floor 1, 2, and 3
# add columns at each column line between floors
in lists, e.g. 1 2 3 4 are
geomTransf PDelta 1
foreach colLine {1 2 3 4 5 6} {
easy to explain,
foreach floor1 {1 2 3} floor2 { 2 3 4} { changing model for
set theSection [lindex $colSizes [expr $floor1 -1]]; # obtain section size for column
ForceBeamWSection2d $colLine$floor1$colLine$floor2some other
$colLine$floor1 configuation
$colLine$floor2 $theSection 1 1 –nip 5
}
} involves more work
#add beams between column lines at each floor
geomTransf Linear 2 than necessary
foreach colLine1 {1 2 3 4 5} colLine2 {2 3 4 5 6} {
foreach floor {2 3 4} {
set theSection [lindex $beamSizes [expr $floor -2]]; # obtain section size for floor
ForceBeamWSection2d $colLine1$floor$colLine2$floor $colLine1$floor $colLine2$floor $theSection 1 2
}
}
source Steel2d.tcl
source ReadRecord.tcl; MRF3.tcl
# set some variables
set floorOffsets {204. 180. 180.}
set colOffsets {360. 360. 360. 360. 360.}
set massesX {0. 0.419 0.419 0.400}
set massesY {0. 0.105 0.105 0.096}
set colSizes {W14X370 W14X370 W14X211};
set beamSizes {W33X141 W33X130 W27X102};
set massesX {0. 0.419 0.419 0.430}; # mass at nodes on each floor in x dirn
set massesY{0. 0.105 0.105 0.096} ;
# set some calculated variables
set numFloor [expr [llength $floorOffsets]+1]
set numCline [expr [llength $colOffsets]+1]
set roofFloor [llength $numFloor]

wipe;
model BasicBuilder -ndm 2 -ndf 3
# build the nodes
for {set floor 1; set floorLoc 0} {$floor <= $numFloor} {incr floor 1} {
set massX [lindex $massesX [expr $floor-1]]
set massY [lindex $massesY [expr $floor-1]]
for {set colLine 1; set colLoc 0;} {$colLine <= $numCline} {incr colLine 1} {
node $colLine$floor $colLoc $floorLoc -mass $massX $massY 0.
if {$floor == 1} {fix $colLine$floor 1 1 1}
if {$colLine < $numCline} { set colLoc [expr $colLoc + [lindex $colOffsets [expr $colLine-1]]]}
}
if {$floor < $numFloor} { set floorLoc [expr $floorLoc + [lindex $floorOffsets [expr $floor-1]]]}
}
# define material
#uniaxialMaterial Steel02 $tag $Fy $E $b $R0 $cr1 $cr2 MRF3.tcl
uniaxialMaterial Steel02 1 50.0 29000 0.003 20 0.925 0.15

# build the columns

geomTransf PDelta 1
for {set colLine 1} {$colLine <= $numCline} {incr colLine 1} {
for {set floor1 1; set floor2 2} {$floor1 < $numFloor} {incr floor1 1; incr floor2 1} {
set theSection [lindex $colSizes [expr $floor1 -1]]
ForceBeamWSection2d $colLine$floor1$colLine$floor2 $colLine$floor1 $colLine$floor2 $theSection 1 1 -nip
}
}
#build the beams
geomTransf Linear 2
for {set colLine1 1; set colLine2 2} {$colLine1 < $numCline} {incr colLine1; incr colLine2 11} {
for {set floor 2} {$floor <= $numFloor} {incr floor 1} {
set theSection [lindex $beamSizes [expr $floor -2]]
ForceBeamWSection2d $colLine1$floor$colLine2$floor $colLine1$floor $colLine2$floor $theSection 1 2
}
}
 ?
Max Roof Displacement = 5.6in
120 ft 72 ft
80.5 ft
Dead Load: 95psf typical, roof 80psf
E=29,000, Fy=50.0, b =0.003
3% Rayleigh Damping 1st and 3rd Modes

Subjected to el_centro 1940 N-S (Peknold)

A Ixx
W14X193 56.8 2400
W14X159 46.7 1900 12.5 ft
W14X109 32.0 1240 24 ft
W30X173 51.0 8230
W27X146 43.1 5660
W24X104 30.6 3100
W30X99 29.1 3990 18 ft
W27X94 27.7 3270
W24X76 22.4 2100
This figure is taken from the first paper in the SAC 95-05 report: Hall, John F. "Parameter Study of Response of Moment-Resisting Steel Frame
Buildings to Near-Source Ground Motions”
source Steel2d.tcl
source ReadRecord.tcl; Solution2014.tcl
# set some variables
set motion el_centro; set Fy 50.0; set E 29000; set b 0.003
set in 1.0;
set g 386.4;
set roofWeight [expr 80*120.*72./1000.]; # 80psf * 120 long * 72 wide in kips
set floorWeight [expr 95*120.*72./1000.]; # 95psf * 120 long * 72 wide in kips
set numFrameResisting 2.0; # number lateral load resisting frames
set percentLoadFrame [expr 15./120.]; # percent load carried by lateral frame
# set up my lists
set floorOffsets {216. 150. 150. 150. 150. 150.}
set colOffsets {288. 288. 288.}
set colSizes {W30X173 W30X173 W27X146 W27X146 W24X104 W24X104};
set colExtSizes {W14X193 W14X193 W14X159 W14X159 W14X109 W14X109};
set beamSizes {W30X99 W30X99 W27X94 W27X94 W24X76 W24X76};
#calculated properties
set numFloor [expr [llength $floorOffsets]+1]
set numCline [expr [llength $colOffsets]+1]
for {set i 0; set width 0;} {$i < [expr $numCline-1]} {incr i 1} {
set width [expr $width + [lindex $colOffsets $i]
}
set massAtFloorNode [expr $floorWeight/($g*$numFrameResisting*$numCline*1.0)]
set massAtRoofNode [expr $roofWeight/($g*$numFrameResisting*$numCline*1.0)]
set uniformRoofLoad [expr $roofWeight*$percentLoadFrame/$width]
set uniformFloorLoad [expr $floorWeight*$percentLoadFrame/$width]
DON”T TOUCH BELOW LINE
wipe;
model BasicBuilder -ndm 2 -ndf 3; Solution2014.tcl
# build the nodes
for {set floor 1; set floorLoc 0} {$floor <= $numFloor} {incr floor 1} {
if {$floor == $numFloor} {
set mass $massAtRoofNode
} else {
set mass $massAtFloorNode
}
for {set colLine 1; set colLoc 0;} {$colLine <= $numCline} {incr colLine 1} {
node $colLine$floor $colLoc $floorLoc -mass $mass $mass 0.
if {$floor == 1} {fix $colLine$floor 1 1 1}
if {$colLine < $numCline} {set colLoc [expr $colLoc + [lindex $colOffsets [expr $colLine-1]]]}
}
if {$floor < $numFloor} {set floorLoc [expr $floorLoc + [lindex $floorOffsets [expr $floor-1]]]}
}
# define material
uniaxialMaterial Steel02 1 $Fy $E $b 20 0.925 0.15
# build the columns
geomTransf PDelta 1
for {set colLine 1} {$colLine <= $numCline} {incr colLine 1} {
for {set floor1 1; set floor2 2} {$floor1 < $numFloor} {incr floor1 1; incr floor2 1} {
if {$colLine == 1 || $colLine == $numCline} {
set theSection [lindex $colExtSizes [expr $floor1 -1]]
} else {
set theSection [lindex $colSizes [expr $floor1 -1]]
}
ForceBeamWSection2d $colLine$floor1$colLine$floor2 $colLine$floor1 $colLine$floor2 $theSection 1 1 -nip
}
}
 Some Braced Frame
EXAMPLES:
Typical Configurations
 •  Beams pinned at column

W27X84

W14X176
HSS10X10X3/8
W30X116

3@15’
W14X176
HSS12X12X1/2
W36X210

W14X176
#number of beam elements HSS12X12X1/2
pinned at either end
30’
Imperfection so will buckle
proc HSSbrace $eleTag $iNode $jNode $secType $matTag $numSeg $imperfection $transfTag args
source Steel2d.tcl
# set up my structure
set in 1
CBFbase.tcl
set floorOffsets {180. 180. 180.}
set colOffsets {180. 180.}
set masses {0. 0.419 0.419 0.400} W27X84
set colSizes {W14X176 W14X176 W14X176};
set beamSizes {W36X210 W30X116 W27X84}; Floor 4
set braceSizes {HSS12X12X1/2 HSS12X12X1/2 HSS10X10X3/8}
# build colLocations and floorLocations & set some variables W14X176
set numFloor [expr [llength $floorOffsets]+1]
set numStory [expr $numFloor-1]
W30X116
set numCline [expr [llength $colOffsets]+1]
wipe; Floor 3

3@15’
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm = #dimension, ndf = #dofs
# Build the Nodes
for {set floor 1; set floorLoc 0.} {$floor <= $numFloor} {incr floor 1} { W14X176
set mass [lindex $masses [expr $floor-1]]
for {set colLine 1; set colLoc 0.} {$colLine <= $numCline} {incr colLine 1} {
W36X210
node $colLine$floor $colLoc $floorLoc -mass $mass $mass 0.
if {$floor == 1} { fix $colLine$floor 1 1 1} Floor 2
if {$colLine < $numCline} {set colLoc [expr $colLoc + [lindex $colOffsets [expr $colLine-1]]]}
}
if {$floor < $numFloor} {set floorLoc [expr $floorLoc + [lindex $floorOffsets [expr $floor-1]]]} W14X176
}
uniaxialMaterial Steel02 1 $Fy $Es $b 20 0.925 0.15 0.0005 0.01 0.0005 0.01
# add the columns
geomTransf PDelta 1
Floor 1 2@15’
for {set colLine 1} {$colLine <= $numCline} {incr colLine 2} {
for {set floor1 1; set floor2 2} {$floor1 < $numFloor} {incr floor1 1; incr floor2 1} { cline 1 cline 2 cline 3
set theSection [lindex $colSizes [expr $floor1 -1]]
ForceBeamWSection2d $colLine$floor1$colLine$floor2 $colLine$floor1 $colLine$floor2 $theSection 1 1 -nip 5
}
}
# add the beams, pinned connection at column end
geomTransf Linear 2
for {set floor 2} {$floor <= $numFloor} {incr floor 1} {
set colLine1 1; set colLine2 2; set colLine3 3;
set theSection [lindex $beamSizes [expr $floor -2]]
DispBeamWSection2d $colLine1$floor$colLine2$floor $colLine1$floor $colLine2$floor $theSection 1 2 -release1
DispBeamWSection2d $colLine2$floor$colLine3$floor $colLine2$floor $colLine3$floor $theSection 1 2 -release2
}
}
 CBF1.tcl
(Diagonal bracing)
source CBFbase.tcl

# define material for braces

set Fy_b
} 46.0;
set E0 0.095
set m -0.3
uniaxialMaterial Steel02 2 $Fy_b $Es $b 20 0.925 0.15 0.0005 0.01 0.0005 0.01
uniaxialMaterial Fatigue 3 2 -E0 $E0 -m $m -min -1.0 -max 0.04

set imperfection 0.001

# add the X braces

geomTransf Corotational 3
for {set story 1} {$story <= $numStory} {incr story 1} {
set colLine1 1; set colLine2 3;
set floor1 $story; set floor2 [expr $story +1];

set theSection [lindex $braceSizes [expr $story -1]

HSSbrace $colLine1$floor1$colLine2$floor2
}
$colLine1$floor1 $colLine2$floor2 $theSection$impe
}
 CBF2.tcl
(X bracing)
source CBFbase.tcl

# define material for braces

set Fy_b
}
46.0;
set E0 0.095
set m -0.3
uniaxialMaterial Steel02 2 $Fy_b $Es $b 20 0.925 0.15 0.0005 0.01 0.0005 0.01
uniaxialMaterial Fatigue 3 2 -E0 $E0 -m $m -min -1.0 -max 0.04

set imperfection 0.001

# add the X braces

geomTransf Corotational 3
for {set story 1} {$story <= $numStory} {incr story 1} {
set colLine1 1; set colLine2 2; set colLine3 3;
set floor1 $story; set floor2 [expr $story +1];
set theSection [lindex $braceSizes [expr $story -1]]
# proc HSSbrace {eleTag} iNode jNode secType matTag numSeg Im transfTag args}
HSSbrace $colLine1$floor1$colLine3$floor2 $colLine1$floor1 $colLine3$floor2 $theSection 3 4 $
HSSbrace $colLine3$floor1$colLine1$floor2 $colLine3$floor1 $colLine1$floor2 $theSection 3 4 $
}
 CBF3.tcl
(V bracing)
source CBFbase.tcl

# define
}
material for braces
set Fy_b 46.0;
set E0 0.095
set m -0.3
uniaxialMaterial Steel02 2 $Fy_b $Es $b 20 0.925 0.15 0.0005 0.01 0.0005 0.01
uniaxialMaterial Fatigue 3 2 -E0 $E0 -m $m -min -1.0 -max 0.04

set imperfection 0.001

# add the V braces

geomTransf Corotational 3
for {set story 1} {$story <= $numStory} {incr story 1} {
set colLine1 1; set colLine2 2; set colLine3 3;
set floor1 $story; set floor2 [expr $story +1];
set theSection [lindex $braceSizes [expr $story -1]]
HSSbrace $colLine2$floor1$colLine1$floor2
} $colLine2$floor1 $colLine1$floor2 $theSection 3 4 $
HSSbrace $colLine2$floor1$colLine3$floor2 $colLine2$floor1 $colLine3$floor2 $theSection 3 4 $
}
 Outline of Workshop
•  Introduction to OpenSees Framework
•  OpenSees & Tcl Interpreters
•  OpenSees & Output
•  Modeling in OpenSees
•  Nonlinear Analysis in OpenSees
•  Basic Examples
•  Parallel & Distributed Processing
•  OpenSees on NEEShub
•  Hands on Exercise
•  Adding Your Code to OpenSees
•  Advanced Model Development
•  Conclusion
 Conclusion
•  OpenSees is a powerful tool for performing FE analysis
•  It NEEDS contributions from others to grow
•  The scripting aspect is something “STUDENTS LEARN
TO LOVE”
•  OpenSees LIKE ANY simulation tool requires the user to
understand the theory and limitations
•  OpenSees (if features are fully utilized!) will allow you to
generate models faster and more accurately than you
could with a GUI and will allow you to obtain information
on the Uncertainty using parallel computing resources that
is the dominant computer architecture available today.