OpenSees dynamic_analysis
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Dynamic Analysis
ByDhanaji S. Chavan ,
Assistant Professor, TKIET, Warananagar
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Problem-1
4 m
-6.00E-01-4.00E-01-2.00E-010.00E+002.00E-014.00E-016.00E-01
0 1 2 3 4 5
acce
lera
tio
n
time
E= 2.1e8 kPa
C/s: 0.3mx0.3m
Input motion is given
500 kN
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……………..
• Objectives: to determine………
– Displacement at fee end & fixed end
– Reactions at free end & fixed end
– Local & global forces in the column
– Plot displacement time history at free end for first
2 second
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Coding starts……….
model basic -ndm 2 -ndf 3
node 1 0 0
node 2 0 4
fix 1 1 1 1
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To define mass
• In dynamic analysis it is must to define nodal or elemental mass
– Beacause Transient(earthquake) motion develops inertial force which is
f=m .a
Inertial force mass
Acceleration to which mass is subjected
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……..
mass $nodeTag (ndf $MassValues)
Node number at which mass to be defined
command
Mass for specific degree of motion
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…………
mass 2 50 00 0
command
Node number
Mass in x-direction
Mass in y direction
Mass in the direction of rotation
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……….
• while defining mass we have to be very careful.
• In present case earthquake motion is in x-direction, so we have to define mass in that direction
• If we defined mass in any other direction that will be
ineffective in analysis
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………….
geomTransf Linear 1
element elasticBeamColumn 1 1 2 .09 2.1e8 0.000675 1
recorder Node -file Rbase.out -time -node 1 -dof 1 2 reaction
recorder Node -file RFree.out -time -node 2 -dof 1 2 reaction
recorder Node -file Dbase.out -time -node 1 -dof 1 2 disp
recorder Node -file Dfree.out -time -node 2 -dof 1 2 disp
recorder Element -file ele_Lfor.out -time -ele 1 localForce
recorder Element -file ele_Gfor.out -time -ele 1 globalForce
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…………
pattern Plain 1 Constant {
load 2 000 -500.0 0.0}
– Remember that self weight of the super structure
has to be applied separately as a force. It won’t be
calculated automatically form mass .
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.............
system UmfPack
constraints Plain
test NormDispIncr 1.0e-5 10 0
algorithm Newton
numberer RCM
integrator LoadControl 1
analysis Static
analyze 10
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Quick review of integrator LoadControl
integrator LoadControl $dLambda1 <$Jd$minLambda $maxLambda>
$dLambda1:- first load-increment factor (pseudo-time step)
- Usually same is followed further
<$Jd: - must be integer
-factor relating load increment at subsequent time steps
minLambda, maxLambda:-decides minimum &maximum time increment bound
- optional, default: $dLambda1 for both
Dhanaji Chavan 12
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……….
loadConst -time 00.00
– This command is used to restart the time for the transient analysis
command keywordStart time
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……….
wipeAnalysis
– This command clears previously-defined analysis
parameters. i.e. parameters defined for static
analysis
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To define the input motion..
set accelSeries "Series -dt 0.01 -filePath INPUT_accl.dat -factor 1“
Set: command
accelSeries: variable name to which acceleration time history is to be assigned
• Portion in the box is a time Time Series
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Time Series
• Types of time series are :
i. Constant Time Series
ii. Linear Time Series
iii. Rectangular Time Series
iv. Sine Time Series
v. Path Time Series
• For the first four time series the load variation follows fixed pattern.
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………..
• When load pattern does not follow a fixedpattern i.e. earthquake load, we have to go forPath Time Series
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Ways to define Path Time Series
where the values are specified in a list included in the command & at constant time interval
Series -dt $dt -filePath $fileName <-factor $cFactor>
– In our case we have used this series
keyword
File name which contains the values e.g. accl, vel,load etc
keywordConstant time interval e.g 0.01
keyword
Load factor coefficient.Default value is 1
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………….
The load factor to be applied to the loads in the LoadPattern object is :
– load factor = $cFactor*(user-defined series)
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Ways to define Path Time Series
For a load path where the values are specified at constant time intervals:
Series -dt $dt -values {list_of_values} <-factor $cFactor>
keyword
Constant time interval e.g 0.01
keyword
List of values e.g. accl, vel, load etc
keyword
Load factor coefficient.Default value is 1
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…………
• For a load path where the values are specified at non-constant time intervals:
Series -time {list_of_times} -values {list_of_values} <-factor $cFactor>
• where both time and values are specified in a list included in the command:
Series -fileTime $fileName1 -filePath $fileName2 <-factor $cFactor>
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To define load pattern
pattern UniformExcitation $patternTag $dir -accel(TimeSeriesType arguments) <-vel0 $ver0>
• Pattern: command
• UniformExcitation: name/type of load pattern
• $patternTag: unit pattern tag/ number
• $dir: direction of excitation (1, 2, or 3) used in formulating the inertial loads for the transient analysis
• -accel: keyword to define acceleration history
• -vel0: keyword to define initial velocity $ver0 whose default value is zero
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……………
In our case…….
pattern UniformExcitation 2 1 -accel $accelSeries
Unique pattern tagDirection of excitation X-direction
A uniform acceleration history is imposed at all nodes constrained in the x-direction i.e. in our case node 1 only
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Defining Dynamic analysis commands………………
system ProfileSPD
test NormDispIncr 1.e-6 50 0
algorithm KrylovNewton
constraints Transformation
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To define integrator
• We can not use the integrator defined for static analysis
• We have to define the following integrator
integrator Newmark $gamma $beta
command
Name of the integrator
Newmarkparameter
Newmarkparameter
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…………
Integrator Newmark 0.5 0.25
numberer RCM
analysis Transient
analyze 4000 0.01
Thank u……………………………………
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Assignment -1.
1. Perform both static & dynamic analysis for given problem discretizing into one element only
2. Don’t define nodal mass & see what happens
3. Define the mass in y direction & see the results
4. Apply both vertical & lateral static loads at free end & perform the analysis
5. Don’t use the loadConst -time 00.00 & see what happens
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Assignment -2
• Discretize above model in 4 elements & perform the complete analysis
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Problem- 2
1(0,0) 2(1,0)
3(1,1)4(0,1)
E= 2.1e8 kPa, mass density = 1.6 ton/m3
input motion: sinusoidal acceleration at base
3.0
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………
Wipe
model basic -ndm 2 -ndf 2
nDMaterial ElasticIsotropic 1 2.1e8 0.3
node 1 0.000 0.000
node 2 1.000 0.000
node 3 1.000 1.000
node 4 0.000 1.000
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…………
element quad 1 1 2 3 4 1.0 "PlaneStrain" 1 0.0 0.0 0 -16
Surface pressure
Mass density
Body force in x direction
Body force in y direction
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………
fix 1 1 1
fix 2 1 1
system ProfileSPD
test NormDispIncr 1.e-12 25 0
constraints Transformation
integrator LoadControl 1 1 1 1
algorithm Newton
numberer RCM
analysis Static
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………………..
analyze 1
loadConst -time 0.000
wipeAnalysis
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Application of earthquake motion
pattern UniformExcitation 1 1 -accel "Sine 0 1000
1 -factor 10"
Sinusoidal variation
Start time
End timePeriod of sine wave
Load factor coefficient
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……………….
constraints Transformation; test NormDispIncr 1.e-12 25 0algorithm Newton numberer RCMsystem ProfileSPDintegrator Newmark 0.5 0.25 analysis Transient recorder Node -file disp.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 disprecorder Node -file acce.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 accelrecorder Element -ele 1 -time -file stress1.out -dT 0.01 material 1 stress recorder Element -ele 1 -time -file strain1.out -dT 0.01 material 1 strain recorder Element -ele 1 -time -file stress3.out -dT 0.01 material 3 stress recorder Element -ele 1 -time -file strain3.out -dT 0.01 material 3 strain analyze 2000 0.01
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……………
recorder Node -file disp.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 disp
recorder Node -file acce.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 accel
recorder Element -ele 1 -time -file stress1.out -dT 0.01 material 1 stress
recorder Element -ele 1 -time -file strain1.out -dT 0.01 material 1 strain
recorder Element -ele 1 -time -file stress3.out -dT 0.01 material 3 stress
recorder Element -ele 1 -time -file strain3.out -dT 0.01 material 3 strain
analyze 2000 0.01
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Assignment-3
1. Perform both static & dynamic analysis for given problem &………
Plot displacement time history plot for node 3 & 4
Plot acceleration time history plot for node 3 & 4
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Assignment-4
• Discretize domain in 4 elements & perform the complete analysis
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Assignment- 5
• Apply equal dof for node 3 & 4 , perform dynamic analysis and
Plot displacement time history plot for node 3 & 4
Plot acceleration time history plot for node 3 & 4
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………
equalDOF 3 4 1 2
Thank u............