problem in uniaxial material in series

[zishendemi]

Hi,

I'm just trying to assign a material which consists of 2 uniaxial elastic material in series to a truss element. The truss element is simply supported and I applied an axial force at the roller but the analysis fails. It says my matrix is singular. Surprisingly, if I just change those 2 material from series to parallel, the analysis would work? Is it able to assign uniaxial material in series to a truss element?

Thanks a lot!


Below is the code:

wipe; # clear opensees model
model basic -ndm 2 -ndf 3; # 2 dimensions, 3 dof per node



# NODAL COORDINATES
node 1 0. 0.
node 2 100 0.


# Define MATERIALS and SECTIONS --------------------------------------------------
# set constants
set E 29000.0
set A .5

# Single point constraints -- boundary conditions
# $dof1 $dof2 $dof3 0 = unrestrained, 1 = restrained
fix 1 1 1 1

fix 2 0 1 1


set MatTag1 1
set MatTag2 2
uniaxialMaterial Elastic $MatTag1 $E
uniaxialMaterial Elastic $MatTag2 $E

set BrMatTag 3
uniaxialMaterial Series $BrMatTag $MatTag1 $MatTag2


element truss 1 1 2 $A $BrMatTag

#Apply the nodal Load
pattern Plain 1 Linear { load 2 1.0 0.0 0.0 }
#Recorder
recorder Node -file Node2.out -time -node 2 -dof 1 2 3 disp;
recorder Element -file ele1.out -time -ele 1 localForce;


#Static Analysis parameters
test EnergyIncr 1.0e-8 300 0
algorithm Newton
system UmfPack
numberer RCM
constraints Transformation
integrator LoadControl 0.1
analysis Static
analyze 10

[zishendemi]

I think this is a very series bug! Any one has any idea?

Thanks!

[vesna]

The problem with your model is not material but boundary conditions.

I made some changes to your code so it works now. With the boundary conditions you have your system is unstable and thus the only way to apply the load is by using "sp" command that sets constraint at node 2 of your element making it stable.


Here is the corrected model:

wipe; # clear opensees model
model basic -ndm 2 -ndf 3; # 2 dimensions, 3 dof per node



# NODAL COORDINATES
node 1 0. 0.
node 2 100 0.


# Define MATERIALS and SECTIONS --------------------------------------------------
# set constants
set E 29000.0
set A .5

# Single point constraints -- boundary conditions
# $dof1 $dof2 $dof3 0 = unrestrained, 1 = restrained
fix 1 1 1 1

fix 2 0 1 1

puts "a"
set MatTag1 1
set MatTag2 2
uniaxialMaterial Elastic $MatTag1 $E
uniaxialMaterial Elastic $MatTag2 $E

set BrMatTag 3
uniaxialMaterial Series $BrMatTag $MatTag1 $MatTag2


element truss 1 1 2 $A $BrMatTag
puts "b"
#Apply the nodal Load
pattern Plain 1 Linear {
#load 2 1.0 0.0 0.0
sp 2 1 1.0
}
#Recorder
recorder Node -file Node2.out -time -node 2 -dof 1 2 3 disp;
recorder Element -file ele1.out -time -ele 1 localForce;

puts "c"
#Static Analysis parameters
test EnergyIncr 1.0e-8 300 0
algorithm Newton
#system UmfPack
system BandGeneral
#numberer RCM
numberer Plain
#constraints Transformation
constraints Penalty 1.e14 1.e14
integrator LoadControl 0.1
analysis Static
analyze 10

[zishendemi]

Dear Dr. Terzic,

Thanks you very much for your reply! I have some follow up questions.

So basically you made 2 changes to my previous code:
1. apply sp at the dof1 at node 2 instead of load
2. use Penalty Constraints instead of Transformation

1st question
You said the structure in my previous is unstable due to boundary condition. I restrained all 3 dofs at node 1 and restrained vertical translation and rotation at node 2. See the code below
# $dof1 $dof2 $dof3 0 = unrestrained, 1 = restrained
fix 1 1 1 1

fix 2 0 1 1

So it's essentially a simply supported beam. I can't understand why it's unstable. Can you elaborate more?

2nd question
Why doesn't the code work when Transformation constraint is used? And also how do we choose the value for alphaS and alphaM as parameters for Penalty constraints?

Thanks a lot!

[vesna]

It is not simple supported beam but truss with one end fixed and the other one free.

To impose single point constraints you need to use Penalty constraint handler.

Penalty values need to be large but not too large as it can create problems associated with conditioning of the system of equations. If your first guess is not working you need to change the penalty values until you find the ones that work.