Time history analysis

[sgs]

Hi all;
I wanted to impose a dynamic force on one of the nodes of my structure and do dynamic time history analysis. But the velocity and acceleration that I get seems wrong. To figure it out, I defined a simple example. force.txt is the text file of function : F=10*sin(2*pi*t) with dt=1/20. I assumed that mass is negligible, so that I can compare the results with static analysis as well.
Could you help me plz?


model BasicBuilder -ndm 2 -ndf 3
set A1 1
set E 29000000
set mass1 .0001
set I1 1
node 1 0.0 0.0 -mass $mass1 $mass1 0.0
node 2 0.0 9.0 -mass $mass1 $mass1 0.0

fix 1 1 1 1

geomTransf Linear 10
element elasticBeamColumn 1 1 2 $A1 $E $I1 10

pattern Plain 1 "Series -dt 0.05 -filePath force.txt " {
load 2 1 0 0
}
recorder Node -file point_2_disp.out -node 2 -dof 1 disp
recorder Node -file point_2_vel.out -node 2 -dof 1 vel
recorder Node -file point_2_acce.out -node 2 -dof 1 accel

integrator Newmark 0.5 0.25
test EnergyIncr 1.0e-6 20 1
algorithm Linear
numberer Plain
constraints Transformation 1.0
system SparseGeneral

analysis Transient
for {set i 1} {$i <= 20} {incr i 1} {
analyze 1 0.05
}
wipe all

[vesna]

Your code looks good to me and does exactly what you want. Did you try computing accelerations and velocities manually to compare with the OpenSees results?

[sgs]

Yes, It looks fine but the results I get with this code is wrong.
I assumed the mass is negligible, so I found the displacement , velocity and acceleration by running a number of static analysis.
And also, since the force function is harmonic , I expect to get cosine function for velocity and sine function for acceleration.

Nodal displacements from time history analysis are the same from the static analysis(done iteratively).
but velocity and acceleration from time history analysis do not match the static case and the harmonic expectations as well!

What may be wrong in the integration or in my definition of time history analysis?

[sgs]

Do you have any suggestions?

[vesna]

Ok, here is an example from Prof. Chopra's book (Example 5.4) where at the top of the cantilever column I apply half-sine force. This way you can compare OpenSees results with the ones from the book.

wipe

model BasicBuilder -ndm 2 -ndf 3
set A1 1.0
set E [expr 10./3.]
set mass1 0.2533
set I1 1.0
set pi 3.14
node 1 0.0 0.0
node 2 0.0 1.0 -mass $mass1 0.0 0.0

fix 1 1 1 1

geomTransf Linear 10
element elasticBeamColumn 1 1 2 $A1 $E $I1 10

timeSeries Trig 1 0.0 0.6 1.2 -factor 10.0

pattern Plain 1 1 {
load 2 1.0 0. 0.
}
recorder Node -file point_2_disp.out -time -node 2 -dof 1 disp
recorder Node -file point_2_vel.out -time -node 2 -dof 1 vel
recorder Node -file point_2_acce.out -time -node 2 -dof 1 accel

set lambda [eigen -fullGenLapack 1]
set T [expr (2*$pi)/sqrt($lambda)]
puts "T = $T"
set freq [expr sqrt($lambda)]
set dampRatio 0.05
rayleigh 0. 0. 0. [expr 2*$dampRatio/$freq]


integrator Newmark 0.5 [expr 1./6.]
test EnergyIncr 1.0e-6 20 1
algorithm Linear
numberer Plain
constraints Plain
system BandGeneral

analysis Transient
analyze 10 0.1

print -node 2

[sgs]

Dear vesna,
Thanks for your help.
just another question, I decreased the mass in your example to model a massless system, this time if you check the acceleration data you see there is a stability problem, even with average acceleration method. Do you have any idea? Because I wanted to use this method in my project with assumption of very small mass, and I could not get the acceleration right!

[vesna]

All this numerical methods are sentive to (time increment)/(fundamental period). If it is a big number as in you case it won't work. If you are decreasing a period you have to decrease a time increment as well for analysis to work.

[sgs]

As I said, I am using average acceleration method and based on chapter 5 of Chopra's book with this method we dont expect to have instability in the response regardless of time step length! So, I dont understand what is happening here.

[vesna]

The problem you have is not stability issue. It is numerical error issue. It is advisable to start with a time increment of 0.1*(Tn) and to reduce it if necessary until you reach the solution.

[esi_opensees]

Dear vesna

You modeled example 5.4 from Prof. Chopra's book. When I run your script, opensees doesn’t give any error message. But output files are empty. I use opensees 2.2.2. would you please tell me what the problem is?

Thank you.

[susan]

i also have this problem. but if you consider the $numIncr=1000, then the output files are not empty. i do not know why this happens.
meanwhile the results of opensees is not coincident with those obtained by Chopra's book, exactly. in your opinion, what is caused the difference? Both opensees and example are using the linear acceleration method.

[vesna]

type "wipe" at the end of the file and you will see the results

[vesna]

When I run this program I am getting the exact same results as given in the book in Table E5.4.