Balance at the rotation of a table (static analysis)

About the development of the FEM module/workbench.

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Balance at the rotation of a table (static analysis)

Post by domad » Tue Aug 11, 2020 12:03 pm

OS: Windows 8 (6.2)
Word size of OS: 64-bit
Word size of FreeCAD: 64-bit
Version: 0.19.22209 (Git)
Build type: Release
Branch: master
Hash: 9c3f9b72a82249d5fcf1f543dd69a78740251b26
Python version: 3.6.8
Qt version: 5.12.1
Coin version: 4.0.0a
OCC version: 7.3.0
Locale: Italian/Italy (it_IT)

Greetings to the whole community!
I have already posted this calculation model FEM - CalculiX on the Italian forum to give an answer to the question of “biros".
Unfortunately, to date no one has experimented with another solver if the calculation model is valid and if the calculation results are reliable.
I propose my experimentation again in the FEM forum:
The question of "biros":
- is it possible to determine with FEM, with good approximation, the maximum load applicable to the top of the“ table ”system consisting of a support surface supported by two parallelepiped-shaped supports placed orthogonally detached from each other, avoiding overturning?

Workbenches and / or macros added:
- CenterOfMass.Fcmacro

Material assumed for the "table" system:
- Generic wood - 700 Kg / m³

CalculiX Limitations / Conditions:
- Unique solid "table" system;
- unique material (top and supports).
(It must be said that load and / or geometry patterns / forcing could be set to simulate the different materials making up the system).

Simplifying, the system can be traced back to a mere lever of the first kind, then set, through the "Spreadsheet" workbench, a simple analytical calculation which allowed me to obtain a value ("measurement meter") to be compared to that obtained from CalculiX.
For any experimentation and visualization of the results, from the link below, you can download the file: "simul_equil_ribalt_tavolo.FCStd" whose structure is as follows:
- CARICO: hypothetical surface-thrust (object supported);
- tavolo: geometry of the product;
- Analysis: FEM solver settings and results;
- PAVIMENTO: hypothetical table support surface;
- polig_equilb_ribalt: polygon / roll-over stability area;
- Cent_mas_tav_completo: center of mass table system;
- appoggio0: geometry of support "0";
- appoggio1: geometry of support "1";
- Cent_mas_appog0: center of mass of support “0” (counterweight);
- Cent_mas_appog1: center of mass of support “1” (counterweight);
- bracci-carichi: load arms and relative distances from the hypothetical axis of rotation (for the calculation of static moments);
- asse_rotazione: hypothetical axis of rotation of the "table" system;
- Cent_mas_semi_tav1S: center of mass of the hypothetical semi-table side to the detriment of overturning stability;
- Cent_mas_semi_tav2S: center of mass of the hypothetical semi-table side in favor of overturning stability (counterweight);
- max-rotazione-tavolo: maximum rotation of the center of mass of the “table” system as a whole, with respect to the overturning stability polygon;
- dimensioni_generali: general dimensions and overall dimensions of the "table" system;
- Verif_analit_rotaz_calc_semplif: simplified analytical verification max load overturning stability obtained with the Spreadsheet workbench by importing the calculation data directly from the properties of the objects;
- compl_semitavolo1S: semi-table geometry to the detriment of overturning stability;
- compl_semitavolo2S: semi-table geometry in favor of overturning stability;

- the settings of the constraints (displacements / rotations) are to be considered valid only for the overturning check;
- exclusively static simulation.

Simulation results:
The maximum (theoretical) applicable load that does not cause overturning, without prejudice to the constraints and forces indicated above, calculated with the FEM- “CalculiX” bench is 457.0635 N (46.59 Kg).
In fact, by increasing the value of the force (ConstraintForce) by 1 N we will have displacements "Z" with values in meters, therefore overturning with rotation in the same direction as the load resting on the plane; decreasing it, again by 1 N, there will be displacements "Z" with values in meters but with the opposite direction of rotation to that of the load placed on the plane, therefore in favor of stability.

The result of the simplified analytical calculation, equal to 375.678855 N (38.2955 Kg), was obtained by summing the moments determined by the various masses with respect to the hypothesized rotation axis.
N.B. some unit of measure values automatically set in the various cells are incorrect, therefore, refer to the one indicated in brackets in the column header.

To view the animation of the simulation: -> Analysis -> double click on "CCX_Results", in the "Actions" panel set "DisplacementZ", put the check mark on "Show" and bring the value "Max stroke to 100" ”, Then operate the selector lever placed immediately above“ Factor ”.

Furthermore, in this panel the minimum and maximum values of the "Displacement Z" obtained with the aforementioned load can be appreciated.

In conclusion, it would be desirable to share the results of a simulation obtained through the use of other solvers, with the aim of evaluating, in this case, both the validity of the calculation scheme and the reliability of the CalculiX solver.

The link:
Good day and good job everyone!
fem_simulaz_sollecit_100-20-v-front.jpg (102.25 KiB) Viewed 1168 times
fem_simulaz_sollecit_100-20.jpg (105.03 KiB) Viewed 1168 times
dimensioni_generali.jpg (50.18 KiB) Viewed 1168 times
condiz_sollecitaz.jpg (39.94 KiB) Viewed 1168 times
Last edited by domad on Thu Aug 13, 2020 11:42 am, edited 1 time in total.
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Post by Kunda1 » Thu Aug 13, 2020 10:52 am

Thank you for sharing. Great presentation.
One thing: please replace the ALLCAPS title with capitalcase or just a capital letter at beginning of sentence. Thank you.
Want to contribute back to FC? Checkout:
#lowhangingfruit | Use the Source, Luke. | How to Help FreeCAD | How to report FC bugs and features
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Re: Balance at the rotation of a table (static analysis)

Post by domad » Thu Aug 13, 2020 11:51 am

.... thank you! sorry for allcap, i have corrected.
I am waiting for some FEM expert to confirm the results / calculation model using another solver.
Good continuation of the day!
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Re: Balance at the rotation of a table (static analysis)

Post by thschrader » Thu Aug 13, 2020 4:45 pm

Interesting problem.
For me using sketcher and formulating equilibrium seems the fastest and most reliable way.
Does it makes sense to solve a rigid-body problem with FEM, which uses a totally different approach (mesh-deformation)?
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Re: Balance at the rotation of a table (static analysis)

Post by HoWil » Fri Aug 14, 2020 6:43 am

Please have a look at e.g. MBDyn in FreeCAD ... 20#p394526.
I think this is more suitable than FEM (calculix, Elmer, ...) even if I never used it myself.
FEM gives you information about the e.g. deformation of the bodies, but you are interested in the dynamic behavior, right?
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Re: Balance at the rotation of a table (static analysis)

Post by raback » Fri Aug 14, 2020 7:55 am

Currently there is no special method in Elmer to find the force at balance. One could increase the force until the contact is lost (reaction force becomes negative) but that is inefficient.

Is there some idea what how the equilibrium force would be found? I could think that for linear system we could try to find c such that for the resulting matrix equation Ax=b+c*f the reaction force vanishes at desired location. This kind of simple algo is infact in use in Elmer for temperature control where heating is tuned such that temperature at control point becomes the desired one.

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Re: Balance at the rotation of a table (static analysis)

Post by domad » Fri Aug 14, 2020 9:44 am

Good morning to the whole community

Thanks to “HoWil” and “raback” for their contribution.

Hello! Thschrader
Sorry for the late reply, but i only found the time now.
Given that i do not want to argue but on the contrary invite you not to give hasty answers.
Reading what you wrote i have doubts that you are an insider. (designer, structural engineer, engineer, architect, etc.)
Above all, do not give obvious and somewhat trivial answers (you have unknowingly offended "kunda1").
- this forum is specific for FEM questions (!)
- before posting (banality) you should read and understand the issues well, especially download ( and deeply analyze the attached files.

Your trivial solution is already included in the attached file without the need to use the calculator but the “spreadsheet”, therefore, i suggest you download the file and analyze it there you can get ideas on how to use the FreeCad tools.

To answer your statement if it makes sense to use FEM for this issue:
"... a stone can do the work of a hammer very well even if it is not a hammer!"

Since you did not understand the meaning of the matter i will explain it to you briefly:
1) can the problem be solved with FEM? (not required if it makes sense !!!)
2) the model and the results proposed by me (domad) are confirmed using other solvers other than CalculiX? (not required if it makes sense !!!)

Finding solutions to borderline cases makes FreeCad great !!!!
In conclusion, therefore, if you are a technician and you know the FEM try to give a concrete answer. (not off topic).

Good mid-August to all

Good day and good work to the whole community!
Posts: 1903
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Re: Balance at the rotation of a table (static analysis)

Post by thschrader » Sat Aug 15, 2020 10:32 am

Hi domad,
thanks for your detailed advices to me.
Please have a look at your numbers from your first post:
46,59 kg FEM-calculated versus 38,29 kg analytical/graphic gives an error of 22%.
Your model reacts super-sensitive to the input: varying the input load by 1 N (0,2 % !)
breaks your analysis, you get meters of deflection.
In this case the stone does not replace the hammer… ;)

BTW 1:
I checked your model before my first post, remeshing with netgen not possible, gmsh
gives an error. But this can be my fault.

BTW 2:
Keep im mind that there are forum readers which have no experience with FEM. Their
conclusion is, that the FEM-wb does not work. Which is not true.

BTW 3:
I read and translated biros post in the Italian forum. When I understand biros right, he was looking
For a fast and reliable method to calculate the equilibrium. I can see no banality in it, to check that
and make my post.

BTW 4.
Must I be an engineer to get the entrance-ticket for the FEM-subforum?

BTW 4:
And yes, your presentation is good, I agree to kunda1.

And now: weekend :)
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Re: Balance at the rotation of a table (static analysis)

Post by domad » Sat Aug 15, 2020 5:50 pm

Hello and well found thschrader!
In the meantime, thanks for your reply.

Given that i do not want to enter and feed a useless controversy especially in technical matters and in particular when the interlocutor does not want to understand the meaning of the matter.

With my words i simply wanted to make you understand that there is no need to repeat what has already been calculated with the same method, in this case with the sum of the moments (you have found the same value as mine), but simply to reason with a polite way and respectful.

Since you still write with little technical shrewdness and taking a cue from what you say: ".... your model reacts in a super sensitive way to the entrance .... since it causes deviations in meters ... etc.", i ask you:
- considering only the force of gravity and not external factors (friction, contact of supports, surface adhesion, air temperature and density, atmospheric pressure, etc.) if the system is in perfect equilibrium with 38, 29 kg do not believe that the increase of 0.01 kg (one hundredth of a N) can cause in the same way what you define "super sensitive inputs ... they break your analysis and cause meters of deviation ”and that i simply call overturning?
As you can see, the stone-hammer comparison is always valid.
So to definitively close this useless and not very productive controversy:
1) thanks (!), The judgment on the presentation is already sufficient and flattering that of Kunda1;
2) careless statements and judgments can cause a bad reputation of the writer certainly not form misconceptions about FEM functioning;
3) proposing limit problems (in any field) does nothing but pose exciting and formative challenges as well as opportunities for growth (in all senses), in this case of FreeCad and FEM and of the whole developer community;
4) on the contrary, by giving unwary answers (falling within the obvious), interest in the instrument is lost (as it is considered, probably erroneously, not able to overcome them);
5) whoever goes to experiment with FEM still has a minimum of technical basis (my case) to try to solve the problems anyway;
6) certainly you don't need a ticket to enter the forum or be an engineer, what everyone needs is definitely the spirit and mentality of a man of science (curiosity, intuition and experimentation, this is what i meant).

In conclusion i repeat, i do not want to know what i have already told you that i know, but:

7) can the problem be solved with FEM? (it is not enough to say no as it has been shown that it is possible, in fact the simulation has the effect of overturning in one direction +M and in the other -M)
8) the model and the results proposed by me (domad) find confirmation using other solvers other than CalculiX?

I salute you wanting to apologize if i have offended you in some way but it certainly was not my intention.

Pending concrete responses to points 7 and 8

Happy weekend to the whole community
Posts: 1903
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Re: Balance at the rotation of a table (static analysis)

Post by thschrader » Mon Aug 17, 2020 2:34 pm

My 2 cent...
Asuming that I dont know the analytical result, I would set a test load (lets say 1000 N) and trigger
this up/down until a point, when there remains a tiny compression sigma_zz in zone A.
At 330 N loading (33kg) I get sigma_zz=-0,106 MPa.
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