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9:27 AM
10
A: Test a wooden board's vibration mode

user21The only reason I am attempting to answer this is to perhaps get a Reversal badge. There you go... We will go slowly and this answer is the basis for what comes next. Let's start with two dimensions. You'll see why. We create a rectangular region: Needs["NDSolve`FEM`"] mesh = ToElementMesh[Ful...

 
user21
user21
@m_goldberg, thanks for the edit.
 
Öskå
Öskå
Oh god, that's brilliant. "Step by step" you said, it seems like you are ready for the next step ;)
 
user21
user21
@Öskå, lol! Maybe, do not take me too seriously :-) - I am just a fem-slob ;-) And now there is this Navier-Stokes question...
 
Öskå
Öskå
You should have known that question would come when working on FEM :D But I assume that 450seconds is quite bad, wouldn't take much time on Abaqus/Ansys-like software.
 
user21
user21
@Öskå, the problem with Eigensystem as it is used here is that this calls a direct solver for the generalized eigenvalue problem. I need to find a better solution for that. You do not by any change have access to Abaqus/Ansys or the like and could try?
 
Öskå
Öskå
9:27 AM
I do have access to Abaqus, did you take exactly the same length as on the picture?
And lets remove the comments there :P
 
user21
user21
OK, I could try to export the mesh and you could load that exact same mesh. What can Abaqus import?
 
Öskå
Öskå
I usually import .inp files, I'm not sure what else can be used
 
user21
user21
Hm, why do all of those tool have their own file format.... I do not have a file format specification for inp files. Do not spend too much time on this. The dimensions I used are from the drawing, except that the hight is not 0.3 but 5. The mesh uses about 3500 linear tetrahedra.
Please, this is really only if do not have anything else to do right now.
 
Öskå
Öskå
And you are apparently missing the two 6mm holes. It's free day in all Christian country ;o) I just have a few cooking-related things to do
 
user21
user21
I did not even get that those are holes.... I thought it was some kind of thickness...
Don't tell anyone - it might ruin my reputation :-)
 
Öskå
Öskå
9:40 AM
I believe they are holes :D
I'm afraid that anyone can read this ;)
 
user21
user21
ohhhhh, there it goes....
 
Öskå
Öskå
Would you have by any chance the possibility to export your geometry in a STL format?
So we have exactly the same (without holes :D)
 
user21
user21
For reference, with gc = NDSolveFEM`ElementMeshToGraphicsComplex[bmesh]` you can convert the boundary mesh to a graphics complex.
here is the complex: GraphicsComplex[{{0., 0., 0.}, {40., 0., 0.}, {40., 76., 0.}, {0.,
76., 0.}, {0., 0., 5.}, {40., 0., 5.}, {40., 76., 5.}, {0., 76.,
5.}, {17.5, 4., 5.}, {22.5, 4., 5.}, {22.5, 35.5, 5.}, {38., 35.5,
5.}, {38., 40.5, 5.}, {22.5, 40.5, 5.}, {22.5, 72., 5.}, {17.5,
72., 5.}, {17.5, 40.5, 5.}, {2., 40.5, 5.}, {2., 35.5, 5.}, {17.5,
35.5, 5.}, {17.5, 4., 10.}, {22.5, 4., 10.}, {22.5, 35.5,
10.}, {38., 35.5, 10.}, {38., 40.5, 10.}, {22.5, 40.5, 10.}, {22.5,
72., 10.}, {17.5, 72., 10.}, {17.5, 40.5, 10.}, {2., 40.5,
Where should I put the stl file?
 
Öskå
Öskå
I can do it
Since I now have the GraphicsComplex
 
user21
user21
You'd use Export["~/boundary.stl", Graphics3D[gc]]
 
Öskå
Öskå
9:49 AM
Well, that was the plan :P
There you go :P
 
user21
user21
Did not know about sketchfab. If you could compute the eigenmodes of this and have a look how long the eigensolver take and possibly how much memory it uses. As a PDE model I used a stress formulation - not sure how you'd specify that in Abaqus.
 
Öskå
Öskå
I do need to refresh my memory regarding Abaqus, so I will tell you that very soon :P
 
user21
user21
No worries. please do not spend too much time on this; cooking is a very attractive alternative :-)
 
Öskå
Öskå
I will do it today, I just don't know when exactly it will be done :P
 
user21
user21
sounds great!
 
Öskå
Öskå
10:01 AM
But now I need to switch on Windows, that's the hardest part.
 
user21
user21
Yes, you got my sympathies. So if nothing else with Mathematica you are able to do FEM on Linux/Mac and do not have use that other system... ;-)
 
Öskå
Öskå
That's it.., everything can be done with Linux, including Mathematica, but the rest is tougher :(
"Mike has invited you to join Room for Mike and Öskå. See your invitations." Gosh, I'm so wanted today.
 
user21
user21
I am going to have lunch as well now...
 
Öskå
Öskå
Have a good one, I will keep you posted :)
 
halirutan
halirutan
10:36 AM
@Öskå You still around?
 
Öskå
Öskå
10:53 AM
@halirutan I am :)
 
halirutan
halirutan
@Öskå I wrote you in the main chat.
 
 
2 hours later…
Öskå
Öskå
12:44 PM
@user21 I think you too 5cm instead of 5mm for the middle beams?
and same goes for the depth, it's more like 5cm than 5mm?
 
user21
user21
Yes, 5 cm, right.
 
Öskå
Öskå
so some measurement are wrong.. :)
and it takes 450secnds.. :D
Here is my mesh: i.imgur.com/iLWjVev.png
 
user21
user21
1:06 PM
But the mesh looks the same size. It takes, 450 seconds? Really? I got it down to 45 seconds with a FEAST solver and a tolerance. What type of CPU do you have?
 
Öskå
Öskå
I meant it takes 450 seconds for you, I'vent run it yet :)
And yeah, I made it the same size :P
 
user21
user21
Got it
 
Öskå
Öskå
What value did you take for the material?
Y and ν, Y stands for?
I assume ν is the poisson's ratio
I guess this should be enough
"Abaqus kernel exited with an error."
 
user21
user21
1:28 PM
Y is Young's modulus and I set it to 100 and ν is set to 1/3
 
Öskå
Öskå
mh, Y like Young ofc, I don't know why we do write "E" here :P
It's supposed to be 10GPa for spruce according to W|A
 
user21
user21
Y = E it's the same. I'll rerun with 10GPa.
 
Öskå
Öskå
And Abaqus needs the density (which seems quite legitimate).
 
user21
user21
I have to think about the model more carefully, take 1 - that should work.
 
Öskå
Öskå
I took 0.43 as stated by W|A, but I can take 1 if it fits your model
 
user21
user21
1:39 PM
I don't think it matters much it will shift were the eigenvalues are but not the qualitative behaviour.
 
Öskå
Öskå
2:19 PM
Results are here
Images are here
Mesh:
Number of nodes: 14069
Number of elements: 8435
Element types: C3D10
Density = 1;
Y = 10000000000 = 10e9
nu = 0.33
 
user21
user21
OK, looks similar. Great and...... the time? How long did it take to solve?
 
Öskå
Öskå
Oh
JOB TIME SUMMARY
USER TIME (SEC) = 16.700
SYSTEM TIME (SEC) = 0.90000
TOTAL CPU TIME (SEC) = 17.600
WALLCLOCK TIME (SEC) = 19
But I have the crappiest laptop ever:
W7-32B (=> only 3GB of RAM) & Intel core i3 at 2.13GHz
And finally:

THE LANCZOS EIGENSOLVER IS USED FOR THIS ANALYSIS Abaqus WILL COMPUTE UNCOUPLED STRUCTURAL AND ACOUSTIC MODES.
Here is the folder with each images.
 
user21
user21
Since mosrt of the time is spend in the eigensolver we could say it's roughly about a factor 5 faster in Abaqus. Thanks so much for doing this. This is much more valuable information for me than any upvotes and stuff.... Again thanks a lot for you time!
 
Öskå
Öskå
My pleasure! You can ask anything you want, since I have no job (yet?) I have all the free time needed if you need to compare Mathematica/FEM Software
 
user21
user21
Apply at wolfram
 
Öskå
Öskå
2:35 PM
I only have a Master degree in Mechanical/Structural analysis (and I am 24yo). Although I graduated in 2013 so it has now been almost a year since I graduated.. :/
I doubt Wolfram would take me :P I kinda (or should I say hate?) c/c++. Or maybe our teacher just sucked :P
But I'm not good enough to apply there I'm afraid
Mechanical/Structural engineering*
But I was a bit rusty, so I was more than happy to do that and I'm glad it helped. Could you update the mma.se post with the new spruces properties? So I can see the fancy images and frequencies :)
 
 
2 hours later…
user21
user21
4:18 PM
I hope something that you like soon. The images do not change that much, since the Y is kind of just a scale factor. I am off to the week end now. Thanks again.
 
Öskå
Öskå
But what about the frequencies? Are they approximately equal to what Abaqus finds?
And thank you, I would totally fancy working at Wolfram though :) Have a great weekend!
 
user21
user21
No, those are different. Those are probably because the model I used differs from what is in Abaqus. Concerning working at Wolfram, give it a shot. In worst case it does not work out, which is no worse that your current situation. Concerning C - quite a bit of the FEM code in Mathematica is written in Mathematica it self and you see the timing issue here is in the (C) eigensolver. So one can write efficient code without using C.... Have a nice weekend.
 
Öskå
Öskå
4:34 PM
Well, coding in Mathematica would be indeed interesting.
And like I said, don't hesitate to ask if you feel like checking what you get with Mathematica compared to Abaqus. I'm more into mechanical analysis but I did Fluids as well, I'm not really into the heat equation though :p
 

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