Buckling

About the development of the FEM module/workbench.

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Laurie Hartley
Posts: 522
Joined: Mon Feb 27, 2017 5:33 am
Location: Australia

Buckling

Post by Laurie Hartley »

Some weeks ago @thschrader kindly provided me with a buckling file to experiment with. At various times since then I have been trying to understand the mathematical correlations between the constraint force, the "buckling factor" , and the critical load.

I adjusted the FreeCAD file by decreasing the line length from 2000 to 1360, and increasing the constraint force to 44kn then saved the file which is attached.
I input the same information into an online "buckling calculator to establish the critical load:-
https://www.omnicalculator.com/physics/buckling
I took the radius of gyration from the design tables
Image attached. This returned a critical load of 342kN

I don't know if my logic is flawed but I then plugged that load into the FreeCAD file in the hope that it would come up with a critical load of 1. it came close (I think- 0.1069654E+01).

I have attached the ccx.dat output for both loads in code below: 342kn then 44kn as well as an image of the output from the online calculator.

I know that a buckling factor >1 means the member won't buckle how to make full use of this buckling factor to establish for example a safe working load? I would be grateful for such an explanation.

342Kn ccx.dat:-

Code: Select all

total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT and time  0.0000000E+00

       -3.142333E-10 -1.356909E-09  3.420000E+05

 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT001 and time  0.0000000E+00

        1.460439E-09 -1.588411E-09 -3.420000E+05

     B U C K L I N G   F A C T O R   O U T P U T

 MODE NO       BUCKLING
                FACTOR

      1   0.1069654E+01
      2   0.1069654E+01

                    E I G E N V A L U E    N U M B E R     1


 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT and time  0.0000000E+00

        8.213051E-01  2.349412E+01 -8.630971E-10

 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT001 and time  0.0000000E+00

       -8.349449E-01 -2.388429E+01  1.132904E-09

                    E I G E N V A L U E    N U M B E R     2


 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT and time  0.0000000E+00

        2.349412E+01 -8.213051E-01  8.168058E-10

 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT001 and time  0.0000000E+00

       -2.388429E+01  8.349449E-01 -1.002564E-09
44Kn ccx.dat

Code: Select all

total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT and time  0.0000000E+00

       -5.487710E-11 -1.898481E-10  4.400000E+04

 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT001 and time  0.0000000E+00

        2.072651E-10  9.596235E-11 -4.400000E+04

     B U C K L I N G   F A C T O R   O U T P U T

 MODE NO       BUCKLING
                FACTOR

      1   0.1802055E+01
      2   0.1802055E+01

                    E I G E N V A L U E    N U M B E R     1


 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT and time  0.0000000E+00

        1.067076E+01 -1.746170E+00 -2.360421E-09

 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT001 and time  0.0000000E+00

        1.070892E+01 -1.752415E+00  3.294811E-09

                    E I G E N V A L U E    N U M B E R     2


 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT and time  0.0000000E+00

        1.746170E+00  1.067076E+01  6.471672E-09

 total force (fx,fy,fz) for set CONSTRAINTDISPLACEMENT001 and time  0.0000000E+00

        1.752415E+00  1.070892E+01 -8.669460E-09
Attachments
Omnicalculater_Buckling_Critical Load_65x4x1360SHS.png
Omnicalculater_Buckling_Critical Load_65x4x1360SHS.png (67.09 KiB) Viewed 2199 times
Buckling_65x4SHSx1360_450mpa_342kN.FCStd
(37.6 KiB) Downloaded 74 times
Buckling_65x4SHSx1360_450mpa_44kN.FCStd
(38.53 KiB) Downloaded 75 times
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NewJoker
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Re: Buckling

Post by NewJoker »

Laurie Hartley wrote: Sat Dec 31, 2022 2:43 am I know that a buckling factor >1 means the member won't buckle how to make full use of this buckling factor to establish for example a safe working load? I would be grateful for such an explanation.
A typical approach is to apply unit force and then the critical load factor represents the actual buckling load.
Laurie Hartley
Posts: 522
Joined: Mon Feb 27, 2017 5:33 am
Location: Australia

Re: Buckling

Post by Laurie Hartley »

NewJoker wrote: Sat Dec 31, 2022 9:00 am
A typical approach is to apply unit force and then the critical load factor represents the actual buckling load.
Thank you for your response NewJoker. I have just realised that with the amount of help I have had, I should have known the answer to my own question :oops:

https://forum.freecadweb.org/viewtopic. ... 52#p531152
Laurie Hartley
Posts: 522
Joined: Mon Feb 27, 2017 5:33 am
Location: Australia

Re: Buckling

Post by Laurie Hartley »

Laurie Hartley wrote: Sat Dec 31, 2022 10:51 am
NewJoker wrote: Sat Dec 31, 2022 9:00 am
A typical approach is to apply unit force and then the critical load factor represents the actual buckling load.
Thank you for your response NewJoker. I have just realised that with the amount of help I have had, I should have known the answer to my own question :oops:

https://forum.freecadweb.org/viewtopic. ... 52#p531152
Well I thought I knew the answer to my question but maybe I don't. I looked at that buckling factor of 0.1802055E+01 and came to the conclusion (rightly or wrongly) that if I multiplied the force of 44kN by 8.02055 = 352.9 kN that would be the critical buckling load or approximately 3% more than the that of the online calculator.

The question is - is this correct or mere coincidence???

If my conclusion is correct why the difference? Maybe the online calculator is wrong? I decided I needed to know more about the technical side of buckling so I did some digging on the internet and discovered that there a number of formulas for calculating buckling. I read this article which is mostly above my pay grade but I got the general gist of things.
https://www.mdpi.com/1660-4601/18/22/12253

As a result I decided to see if I could produce a spreadsheet using the formulas and notation I found online . I managed it with a bit of help from "Ask Libre Office" with the units. A copy is attached. Rename it by deleting the .txt extension and it should open.

It was also suggested I would be better off using SMath for those types of calculations and was able to produce what appears to be a sheet that works. A copy of that is also attached - if you have SMath (its free :D ) it should open if you rename it by deleting the .txt extension.

It turns out that both documents produce the same results as the online calculator :shock: 8-)

If this post has brought a smile to your face you may burst out into raucous laughter when I tell you I am reading George Poyla's book "How to Solve Anything". My kids bought it for me for Christmas :lol:

He says it is not enough to know the answer is correct - you have to know why it is correct. I am getting there but there are a few things have got me stumped - radius of gyration. :!:

So back to my question - if I have interpreted the FreeCAD output correctly, does FreeCAD use a different formula from the Johnson-Euler formula?

I wish I was 55 years younger - I think I would have liked to be an engineer.
Attachments
Chord Buckling - Load Case 4.sm.txt
(60.84 KiB) Downloaded 56 times
Buckling Check Spreadsheet.xls.txt
(66 KiB) Downloaded 57 times
thschrader
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Joined: Sat May 20, 2017 12:06 pm
Location: Germany

Re: Buckling

Post by thschrader »

Laurie Hartley wrote: Tue Feb 07, 2023 6:29 am ...
It was also suggested I would be better off using SMath for those types of calculations and was able to produce what appears to be a sheet that works. A copy of that is also attached - if you have SMath (its free :D ) it should open if you rename it by deleting the .txt extension.

It turns out that both documents produce the same results as the online calculator :shock: 8-)

...
I get the same buckling-factor of 7,8 as you do with Smath.
Seems you are on the right track :)
See pdf. My commercial software calculates a maximum utilization of 0,128=12,8%.
==> 1/0.128=7,8 buckling-factor.

I cant reproduce the result with FC-FEM, when using 1D/2D elements.
Especially for the 2D-case I get odd results (play with max element size)
buckling_SHS65x4_2D.FCStd
(11.72 KiB) Downloaded 55 times
buckling_SHS65x4_1D.FCStd
(26.27 KiB) Downloaded 55 times
SHS65x4-buckling.pdf
(45.54 KiB) Downloaded 73 times
thschrader
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Posts: 3129
Joined: Sat May 20, 2017 12:06 pm
Location: Germany

Re: Buckling

Post by thschrader »

Did some test with the SHS 65x4 profile using Euler-case 1, which is easier to model.

With 1D-beam elements and using a tube with equivalent Iy, I get the same first buckling
factor as the theory says, with different meshes.

With 2D-shell elements I allways get these strange local buckling forms below the first
beam buckling mode. The local buckling depends heavy on the mesh size.
For a simple geometry like this the local buckling is not possible, in my opinion.
But what will you do when you have a complex geometry, lets say a big frame with stiffeners.
Is the local buckling real or not?

zip contains smath, FC-FEM and commercial calculation:
Smath_FreeCAD_pdf.zip
(243.99 KiB) Downloaded 58 times
stability_fun001.JPG
stability_fun001.JPG (89.73 KiB) Viewed 1483 times
stability_fun002.JPG
stability_fun002.JPG (148.05 KiB) Viewed 1483 times

Code: Select all

OS: Windows 10 Version 2009
Word size of FreeCAD: 64-bit
Version: 0.20.2.29177 +426 (Git)
Build type: Release
Branch: (HEAD detached from 0.20.2)
Hash: 930dd9a76203a3260b1e6256c70c1c3cad8c5cb8
Python 3.8.10, Qt 5.15.2, Coin 4.0.1, Vtk 8.2.0, OCC 7.6.3
Locale: German/Germany (de_DE)
Installed mods: 
  * BIM 2021.12.0
  * CfdOF 1.21.3
  * Curves 0.5.8
  * Defeaturing 1.2.0
  * DesignSPHysics 0.6.3(24-09-2022)
  * dodo
  * fasteners 0.4.4
  * Manipulator 1.4.9
  * Plot 2022.4.17
  * Reinforcement
  * WorkFeature
Laurie Hartley
Posts: 522
Joined: Mon Feb 27, 2017 5:33 am
Location: Australia

Re: Buckling

Post by Laurie Hartley »

Thanks for looking into this Thomas. I am away from my computer so I am not able to open your file until tomorrow. I was able to open my spreadsheet on my iPad and when I inserted your variables into it the resulting “Euler” critical load produced was 162kN.

I am looking forward to opening the files you posted.
thschrader
Veteran
Posts: 3129
Joined: Sat May 20, 2017 12:06 pm
Location: Germany

Re: Buckling

Post by thschrader »

thschrader wrote: Wed Feb 08, 2023 10:03 am ...
But what will you do when you have a complex geometry, lets say a big frame with stiffeners.
Is the local buckling real or not?
Here is an example to show what I mean.
Taken from
https://rules.dnv.com/docs/pdf/DNVPM/co ... P-C208.pdf
See page 46.

They use a displacement of 1 cm as loading, which is equivalent to a force of P=76420 N
at the tip of the frame. The ABAQUS/CCX eigenvalues of 6,24 vs 6,21 are pretty much the same.
But CCX computes an additional lower eigenvalue of 1,48. The eigenform is mechanical not possible,
the upper flanges are under tension. Why do they buckle? Do I miss something?
Very strange...

File for testing:
DNV_B2_bucklingFrame.FCStd
(19.59 KiB) Downloaded 62 times
frame001.JPG
frame001.JPG (79.87 KiB) Viewed 1427 times
frame002.JPG
frame002.JPG (101.07 KiB) Viewed 1427 times
Laurie Hartley
Posts: 522
Joined: Mon Feb 27, 2017 5:33 am
Location: Australia

Re: Buckling

Post by Laurie Hartley »

thschrader wrote: Wed Feb 08, 2023 4:39 pm the upper flanges are under tension. Why do they buckle? Do I miss something?
Very strange...
When I looked at those images my first impression was it is impossible. Maybe it has something to do with rotation of the flanges once the bottom half of the flanges stat to fail under the load?
Laurie Hartley
Posts: 522
Joined: Mon Feb 27, 2017 5:33 am
Location: Australia

Re: Buckling

Post by Laurie Hartley »

Laurie Hartley wrote: Wed Feb 08, 2023 9:43 pm
thschrader wrote: Wed Feb 08, 2023 4:39 pm the upper flanges are under tension. Why do they buckle? Do I miss something?
Very strange...
When I looked at those images my first impression was it is impossible. Maybe it has something to do with rotation of the flanges once the bottom half of the flanges stat to fail under the load?
Perhaps it is a question of understanding the model. If it was a "goal posts" frame the buckling would make sense.
Attachments
DNV sketch.png
DNV sketch.png (66.45 KiB) Viewed 1354 times
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