Call for explanation: a strange behavior of VABS results

[Wenbin Yu]

All,

Jose Blasques from Technical University of Denmark brought to me the following strange behavior of VABS results.

For a square section, splitting along x2 direction, mesh it with 100x100 elements. One half has material 1 (say E1=100, nu=0.2) while the other has material 2. Make it so that E2=E1/alpha (the same for nu). Evaluate the cross section stiffness matrix. Plot each of the entries of the stiffness matrix against alpha. Look specifically at the two diagonal entries corresponding to the shear stiffness. Compare them to the cross section stiffness matrix of only half the section. One would naturally expect the values of each entry should converge to the values of only half the section as alpha increases. However,  one can observe that S22 is decreasing along with increasing alpha, but S33 is reaches the minimum among the six values when alpha=10. Input file and the results are attached. I don't know how to explain it. Can any of you come up with a reasonable explanation or help debug this problem if this is a bug in VABS?

Wenbin

[Wenbin Yu]

Jimmy,

Thanks a lot for your thoughts and contribution. The original problem was keeping \nu of material 2 the same as material 1, only E get divided by \alpha. What I wrote was confusing.

We also know that when \alpha increases, the stiffness values will converge to those of the section without the other half. However, what I don't understand is than why the convergence is not monotonic. In other words, why S33 has a minimum at \alpha=10?


Wenbin
At 07:53 PM 12/1/2010, Jimmy Ho wrote:

On second thought, I am wrong about the shear stiffness's dependence on
the beam axis location.  There is no dependence.

I just ran one more case and I think that I am onto something.  The case
that I ran is the same case that you wrote about, but with the bottom
material chopped off and a  This is the solution that increasing \alpha
to infinity must converge to.  My VABS output from this case is
attached.  You can see that the two shear stiffnesses (as well as all of
the other terms) are in excellent correlation with the my previous 
values as \alpha goes to infinity.  So I think that presuming that
chopping the square into a rectangle and expecting that the stiffness
will be half is not correct.  I believe the case is closed, right?

Jimmy




Jimmy C Ho wrote:
> Wenbin,
> I've never participated in an online forum and don't plan on starting
> this practice, so I'll just write what I have to say in this reply.
>
> First of all, I was able to reproduce all of your VABS results using
> VABS 3.4.  However, I only reproduced the results if I do not divide
> \nu by \alpha.  Just as you wrote, one is supposed to divide by \alpha.
>
> My results with \nu divided by \alpha is attached.  You can see that
> my numbers for S22 and S33 are different from yours although it still
> exhibits that strange behavior that you had mentioned.
>
> Here is what I am wondering and I think that it may very well be the
> explanation.  Is the shear stiffness dependent on the location of the
> beam axis?  If it is dependent on the location and I believe that it
> is, then there is no reason to expect S33 to be half of what you would
> have with \alpha = 1 when \alpha increases to infinity.  On the other
> hand, we do have symmetry about the x3 axis, therefore, we should
> expect S22 to be half of what you have with \alpha = 1 as \alpha
> increases (and it does seem to converge to that value).
>
> Jimmy
>
>
>
>
> Wenbin Yu wrote:
>> All,
>>
>> While I have all most of the brain power here about VABS, I am
>> directing your attention to a very strange problem of VABS results
>> brought up by a user. Please direct your web browser to
>> http://groups.google.com/group/hifi-comp/browse_thread/thread/5b8be380008bace0?hl=en
>> <blockedhttp://groups.google.com/group/hifi-comp/browse_thread/thread/5b8be380008bace0?hl=en>
>> .
>>
>> If you are not a member of the group, please join it in case you want
>> to participate in the discussion.
>>
>>
>> Wenbin
>

[Wenbin Yu]

Forgot the attachment.

Jose,

Thanks a lot for the more detailed comparison. I posted a thread on this issue on the discussion group yesterday, hoping somebody will come up with a sensible explanation.

Wenbin
At 12:58 AM 12/2/2010, you wrote:

Wenbin,

I thought you might find this useful. Please find in attachment some results I've obtained concerning the value of the shear stiffness for inhomogeneous cross sections.

Regards
José
________________________________________
From: Wenbin Yu [wenb...@usu.edu]
Sent: 01 December 2010 18:57
To: José Pedro Albergaria Amaral Blasques; Perry Johnson
Cc: hifi...@googlegroups.com
Subject: A possible workout for the Linux version

Perry and Jose,

The following is suggested by a user of my another code VAMUCH. It has similar set up as VABS. He originally has the problem "cannot load shared libaries". He did the following and it works. You can need to replace VAMUCH with VABS in his commands, hoping it works for you too.

This is my process to deal with the LINUX VAMUCH2.0 version, you can propose it for other user maybe :

1. Copy folder VAMUCH2.0ReleaseLinux11-11-2010

2. Rename the following files

        mv Recovery.dll librecovery.so

        mv Constitutive.dll libconstitutive.so

3. Compile Fortran module

        gfortran -Wall -c GlobalDataFun.f90 CPUtime.f90 IO.f90

4. Compile Fortran main program with links

        gfortran -Wall -o VAMUCH2.0.exe Main.f90 *.o -L. -lrecovery -lconstitutive -lm

5. Execute

        LD_LIBRARY_PATH=$PWD ./VAMUCH2.0.exe 3DTet10.vam


 Wenbin