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Non Uniform Torsion - QUAD4 vs QUAD9 1

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zannas

zannas

Structural
Sep 26, 2011
7
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).
x5tnvd.jpg

281rbc1.jpg

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:
3468fwk.jpg

QUAD9:
jqm4h1.jpg

In particular this is due to the fact that in the model with QUAD9 TauZX "disappear".
QUAD4:
257ddeu.jpg

QUAD9:
2eoi0ap.jpg

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.
 
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QUAD9 ? ... you mean, i think, QUAD8.

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.
 
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no no QUAD8! QUAD9! I need the same nr of nodes!
I'm testing the Non Uniform Torsion that is valid only for opened thin sections.

Enclosed tube isn't a thin opened section.
 
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SWComposites - Strand7 has Quad9 elements, and that's what the output looks like. I thought they were common.


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
 
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Theoretical stresses are the same of QUAD4.
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)
14cqjrc.jpg


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.
 
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ok, QUAD9 ... i guess that's a QUAD8 with a central node. but still both models have the same number of nodes, therefore the QUAD4 element density is 4x that of the QUAD9. and i would expect the QUAD4 mesh would give better answers.

again, do your own test case of a known problem to see how the elements compare.
 
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how are you loading this ? (to get non-uniform torsion)

or does the thread header refer to non-uniform torsional stresses ??
 
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1 element through the thickness? Minimum is 3.
Click to expand...

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:

Layers – For material non-linear analysis, the plate can be divided into a maximum of 20 layers, which in bending may yield independently of each other. The number of layers used can affect the progression of yielding through the thickness. The onset of yielding is not very sensitive to this setting because Strand7 automatically adds a very thin layer on the element’s surface to assist in detecting the onset of yielding. Generally, if more layers are used, a better representation of the yielding is achieved, at the expense of slightly increased solution times. If a plate element is primarily acting as a membrane, this setting has little effect.
Click to expand...

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
 
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Doug,
You're right. For some dumb reason I was thinking he was using solid elements (as in cubes). Ignore my previous post.
 
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[cite]how are you loading this ? (to get non-uniform torsion)

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 ;)

 
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"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)" ...

how is this a varible torque ? it sounds constant

 
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it sounds like you're applying a torque at the free end of the beam ?

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.
 
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Hi Zannas,

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?
 
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