Non Uniform Torsion - QUAD4 vs QUAD9
Non Uniform Torsion - QUAD4 vs QUAD9
(OP)
I took the now famous double-T section, and I modeled once with QUAD4 and once with QUAD9.
Obviously I maintain constant the number of nodes.
In practice: 1 QUAD9 = 4 QUAD4
I maintain the same material and same boundary conditions (loads and constraints).


I found that the von Mises stress along the edge of the wing in the beam modeled with QUAD9 do not tend to the theoretical solution given by Non Uniform Torsion (Sectorial Areas)
QUAD4:

QUAD9:

In particular this is due to the fact that in the model with QUAD9 TauZX "disappear".
QUAD4:

QUAD9:

I know that the only thing that changes between the 2 modeling to provide the result are the shape functions (biquadratic for QUAD 9 and bilinear for QUAD4). This means that the solution found with the QUAD9 should be closer to that reality.
The fact is:
-where are the missing TauZX? Who takes them?
-why the solution with QUAD4 is closest to the theoretical one given by Non Uniform Torsion? (I was expecting the opposite)
I'm pretty sure that the answer lies in the shape functions and its derivatives, but I am not yet clear what exactly.
Obviously I maintain constant the number of nodes.
In practice: 1 QUAD9 = 4 QUAD4
I maintain the same material and same boundary conditions (loads and constraints).


I found that the von Mises stress along the edge of the wing in the beam modeled with QUAD9 do not tend to the theoretical solution given by Non Uniform Torsion (Sectorial Areas)
QUAD4:

QUAD9:

In particular this is due to the fact that in the model with QUAD9 TauZX "disappear".
QUAD4:

QUAD9:

I know that the only thing that changes between the 2 modeling to provide the result are the shape functions (biquadratic for QUAD 9 and bilinear for QUAD4). This means that the solution found with the QUAD9 should be closer to that reality.
The fact is:
-where are the missing TauZX? Who takes them?
-why the solution with QUAD4 is closest to the theoretical one given by Non Uniform Torsion? (I was expecting the opposite)
I'm pretty sure that the answer lies in the shape functions and its derivatives, but I am not yet clear what exactly.





RE: Non Uniform Torsion - QUAD4 vs QUAD9
if i understand you right you're comparing a mesh with QUAD8s with a meash with 4 QUAD4s ... i'd expect the QUAD4 mesh would give you better answers, cause it's calculating 4x the number of elements.
i would also do a patch test with a QUAD4, 4x QUAD4, and QUAD8 elements to see which mesh produces the better results. use a very simple geometry so you know the right answer (i'd use an enclosed tube).
also not sure looking an vM stresses, which combines the three stress components together, gives you the clearest picture.
RE: Non Uniform Torsion - QUAD4 vs QUAD9
I'm testing the Non Uniform Torsion that is valid only for opened thin sections.
Enclosed tube isn't a thin opened section.
RE: Non Uniform Torsion - QUAD4 vs QUAD9
RE: Non Uniform Torsion - QUAD4 vs QUAD9
RE: Non Uniform Torsion - QUAD4 vs QUAD9
zannas - It's not obvious to me what is the exact difference between the results that you are concerned about, and what the lines are. Are they top, middle and bottom face stresses? Couls you post a graph with the theoretical stresses you expected to see?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Non Uniform Torsion - QUAD4 vs QUAD9
Here there are a comparison with VM's stresses along the edge of the wing (1) and along the center of the wings (2)
Then you can find a theoretical stresses, it's sigma(1)-TNU and sigma(2)-TNU
Numerical results are from model with QUAD4.
For QUAD9: watch the previous images that are taken along (1), you can see that VM's stress from z=180cm to z=400cm are less than 40MPa!! It's because there aren't enough TauZX
(it's in italian..but it easy to translate and undestand)
I use Strand and throught the thinkness there is always 1 element.
Theoretical hypothesis are:
-opened section
-thin thikness
-Poisson Coefficient = 0 (but in both models I use 0,25)
-No deformation in plane of section.
There should not be much differences for VM's stresses between the top (italian=superiore) and the bottom(italian=inferiore) of the elements.
RE: Non Uniform Torsion - QUAD4 vs QUAD9
again, do your own test case of a known problem to see how the elements compare.
RE: Non Uniform Torsion - QUAD4 vs QUAD9
RE: Non Uniform Torsion - QUAD4 vs QUAD9
or does the thread header refer to non-uniform torsional stresses ??
RE: Non Uniform Torsion - QUAD4 vs QUAD9
Why would you want more than 1 element in this application? I assumed the analysis was linear, but even if it was non linear the Strand7 plate-shell element is divided into layers (default 10) for use with non-linear analysis. Here is what the help says:
Maybe the difference between the FEA results and the theoretical is that the 9 noded element is modelling shear deformation better, resulting in reduced shear stresses.
Is it possible to post the model so I can have a play with it? If you also post the results file anyone interested can have a look with the free Strand7 viewer, even if they don't have a copy of the full program.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Non Uniform Torsion - QUAD4 vs QUAD9
You're right. For some dumb reason I was thinking he was using solid elements (as in cubes). Ignore my previous post.
RE: Non Uniform Torsion - QUAD4 vs QUAD9
or does the thread header refer to non-uniform torsional stresses ?? [/cite]
To simulate the presence of a twisting moment I entered at the end of the beam 2 shear stress applicated in the wings:
tauZX=M/(h*thik)
Then thank to IDS, I think u've found the answer to my question:
"...the 9 noded element is modelling shear deformation better, resulting in reduced shear stresses."
When I come back home I upload the models ;)
http://ingsolution.net
RE: Non Uniform Torsion - QUAD4 vs QUAD9
tauZX=M/(h*thik)" ...
how is this a varible torque ? it sounds constant
RE: Non Uniform Torsion - QUAD4 vs QUAD9
Torsion angle unitary is different for each z
http://ingsolution.net
RE: Non Uniform Torsion - QUAD4 vs QUAD9
if you're only loading the flanges, i'd expect to see a "shear lag" effect as the torque (applied to the flanges) is reacted as first only by the flanges and further along the beam by the entire section.
try some test models to investigate the behaviour of your elements.
RE: Non Uniform Torsion - QUAD4 vs QUAD9
Theory and Results
Have a nice day!
http://ingsolution.net
RE: Non Uniform Torsion - QUAD4 vs QUAD9
Very interesting post. Could you clarify one thing? In your first post, the graphs have error bars on them. How are these errors computed? Do you get the error estimates from your analysis software?
RE: Non Uniform Torsion - QUAD4 vs QUAD9
They should be the results from adjacent elements
http://ingsolution.net