The file discusses the issues related with dynamic analysis in OpenSees with illustrative examples

1. Dynamic Analysis
By
Dhanaji S. Chavan ,
Assistant Professor, TKIET, Warananagar

2. Problem-1
4 m
-6.00E-01
-4.00E-01
-2.00E-01
0.00E+00
2.00E-01
4.00E-01
6.00E-01
0 1 2 3 4 5
acceleration
time
E= 2.1e8 kPa
C/s: 0.3mx0.3m
Input motion is given
500 kN

3. ……………..
• 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

4. Coding starts……….
model basic -ndm 2 -ndf 3
node 1 0 0
node 2 0 4
fix 1 1 1 1

5. 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

6. ……..
mass $nodeTag (ndf $MassValues)
Node number at
which mass to be
defined
command
Mass for specific degree
of motion

7. …………
mass 2 50 00 0
command
Node
number
Mass in x-
direction
Mass in y
direction
Mass in the
direction of rotation

8. ……….
• 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

9. ………….
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

10. …………
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 .

11. .............
system UmfPack
constraints Plain
test NormDispIncr 1.0e-5 10 0
algorithm Newton
numberer RCM
integrator LoadControl 1
analysis Static
analyze 10

12. 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

13. ……….
loadConst -time 00.00
– This command is used to restart the time for the
transient analysis
command keyword
Start time

14. ……….
wipeAnalysis
– This command clears previously-defined analysis
parameters. i.e. parameters defined for static
analysis

15. 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

16. 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.

17. ………..
• When load pattern does not follow a fixed
pattern i.e. earthquake load, we have to go for
Path Time Series

18. 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
keyword
Constant time
interval e.g 0.01
keyword
Load factor coefficient.
Default value is 1

19. ………….
The load factor to be applied to the loads in
the LoadPattern object is :
– load factor = $cFactor*(user-defined series)

20. 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

21. …………
• 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>

22. 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

23. ……………
In our case…….
pattern UniformExcitation 2 1 -accel $accelSeries
Unique pattern tag
Direction 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

24. Defining Dynamic analysis
commands………………
system ProfileSPD
test NormDispIncr 1.e-6 50 0
algorithm KrylovNewton
constraints Transformation

25. 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
Newmark
parameter
Newmark
parameter



26. …………
Integrator Newmark 0.5 0.25
numberer RCM
analysis Transient
analyze 4000 0.01
Thank u……………………………………

27. 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

28. Assignment -2
• Discretize above model in 4 elements &
perform the complete analysis

29. 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

30. ………
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

31. …………
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

32. ………
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

33. ………………..
analyze 1
loadConst -time 0.000
wipeAnalysis

34. 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

35. ……………….
constraints Transformation;
test NormDispIncr 1.e-12 25 0
algorithm Newton
numberer RCM
system ProfileSPD
integrator Newmark 0.5 0.25
analysis Transient
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

36. ……………
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

37. 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

38. Assignment-4
• Discretize domain in 4 elements & perform
the complete analysis

39. 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

40. ………
equalDOF 3 4 1 2
Thank u............