U1 Element Direction Issue

SBlade · February 17, 2025, 2:13am

Dear ALL,
I have the following code which was originally excerpted from userbeam.inp and slightly modified to suit my needs, I have difficulty of understanding the orientation and direction assignment in Claculix code, for orthogonal systems it converges with other commercial softwares but if the elements are oblique then it starts to deviate.

I’ve seen that comparison exmaples but this is for very basic element and doesn’t totally corresponds to what I really need.

My shape is actually like that:

I think that orientation is what is malfunctiniong here, the 3rd line under the BEAMSECTION keyword, your guidance will be appreciated.


**   Structure: cantilever beam.
**   Test objective: user beam element U1
*NODE, NSET=Nall
1, -4.,0.,0.
2, -5.,0.,3.
3, -1,0,6
4, 4,0,3
5, 3,0,0

*ELEMENT, TYPE=U1
     1, 1,2
     2, 2,3
     3, 3,4
     4, 4,5

*USER ELEMENT,TYPE=U1,NODES=2,INTEGRATION POINTS=2,MAXDOF=6

*ELSET, ELSET=E1
1
*ELSET, ELSET=E2
2
*ELSET, ELSET=E3
3
*ELSET, ELSET=E4
4

*BOUNDARY
1,1,6
5,1,6

*MATERIAL,NAME=EL
*ELASTIC
210000,.3

*BEAM SECTION,ELSET=E1,MATERIAL=EL,SECTION=GENERAL
0.0625,3.2552083333e-4,0.,3.2552083333e-4,0.8333
1,0,0

*BEAM SECTION,ELSET=E2,MATERIAL=EL,SECTION=GENERAL
0.0625,3.2552083333e-4,0.,3.2552083333e-4,0.8333
0,1,0

*BEAM SECTION,ELSET=E3,MATERIAL=EL,SECTION=GENERAL
0.0625,3.2552083333e-4,0.,3.2552083333e-4,0.8333
0,1,0

*BEAM SECTION,ELSET=E4,MATERIAL=EL,SECTION=GENERAL
0.0625,3.2552083333e-4,0.,3.2552083333e-4,0.8333
1,0,0

*STEP
*STATIC
*CLOAD
3,3,1000

*NODE PRINT,NSET=Nall
U

**EL PRINT,ELSET=Eall
**S

*END STEP

xyont · February 17, 2025, 4:25am

beam element orientation at input just below section properties related to element local axes not global.

below an example of modified version from test case in distribution,

SBlade · February 17, 2025, 11:37am

thanks for the response I’m reading the section 6.3.3 of user manual but it still mentions the global coordinates, most probably I don’t get it, It would quite good to have that example, do you mind to share that modified example with us ?

Calc_em · February 17, 2025, 11:43am

Because local directions are defined relative to global directions. So you specify the global X, Y and Z coordinates of a unit vector that will form the local 1 direction.

SBlade · February 17, 2025, 12:14pm

Because local directions are defined relative to global directions. So you specify the global X, Y and Z coordinates of a unit vector that will form the local 1 direction.

Thank you but, In any case any working example( more complicated than simple ones which includes U1 element) will be the best guide.

xyont · February 17, 2025, 4:11pm

it seems previous orientation not properly aligned since all beam section properties are the same, i do simple modified to visualize with rectangular section.

and modified version of swing.inp from test case.

Disla · February 17, 2025, 5:28pm

Do you meanlike this?. ¿Is that deviation wrong or unexpected?

Try to refine:

SBlade · February 17, 2025, 5:38pm

Exact solution is more like yours, look below almost identical

SBlade · February 17, 2025, 5:41pm

I mean if you look the displacement I got from runing the script that I previously shared deviation only occurs on rotational component of 6 DOF node 5th component see below

SBlade · February 17, 2025, 5:45pm

@Disla If you run my code with correct direction/up vectors what displacement do you get ?

xyont · February 17, 2025, 6:04pm

user element of beam (U1) and shell (US3) in CalculiX is improved version from standard structural analysis package in the market such as SAP2000. I can confirm to be more accurate for shell user element, but not yet for beam.

it can be clearer if the problem sketch from other FE results provided, specifically in beam shape and section size, element local axes rotation also.

regarding to beam deformation along member length is only visualization, as i know result of single element processed further by slope-deflection analysis to eliminated meshing or element division and computationally effective.

SBlade · February 17, 2025, 6:46pm

Thanks for clarification, it is good to hear that shell element is more robust, it seems that I was exepecting Calculix to be in total convergence with standart applications.

Aside from that, I shuffled through the code that I wrote in the past and noticed that I used (PREMIZNIECKI Eq. 5.116 / Fig 5.4) local stiffness matrix which was totally finding the same results with SAP2000.

I know it is very hard to respond immediatley to that but is that implementation(PREMIZNIECKI Eq. 5.116 / Fig 5.4) resemble the way that Calculix handles the Timoshenko beam or does it differ ?

Thanks in advance,

xyont · February 17, 2025, 7:13pm

is the book mentioned from sixty era? probably differs with CalculiX user beam element implementation (link)

Disla · February 17, 2025, 10:21pm

Hi,

The frame has a maximum height of 6 units and your vertical displacement is 38.69 units.
I know it’s only aesthetic but I have reduced the load to 10N.

My numbers and reference are different. I am using as the strong axis the same and only one they all have in common. (0,1,0) It shouldn’t matter as they all have the same section,… but.
I’m using a Timoshenko shear coefficient for a rectangle cross-section of K= 3/2=1.5.

*NODE, NSET=Nall
1, -4.,0.,0.
2, -5.,0.,3.
3, -1,0,6
4, 4,0,3
5, 3,0,0
*NSET,NSET=Node_1
1
*NSET,NSET=Node_5
5
*NSET,NSET=Nodes_all
1
2
3
4
5
*ELEMENT, TYPE=U1,ELSET=Eall
1,1,2
2,2,3
3,3,4
4,4,5
*USER ELEMENT,TYPE=U1,NODES=2,INTEGRATION POINTS=2,MAXDOF=6
*ELSET, ELSET=E1
1
*ELSET, ELSET=E2
2
*ELSET, ELSET=E3
3
*ELSET, ELSET=E4
4
*TRANSFORM,NSET=Node_1,TYPE=R
-1,0,3,0,1,0
*TRANSFORM,NSET=Node_5,TYPE=R
-1,0,-3,0,1,0
*BOUNDARY
1,1,6
5,1,6
*MATERIAL,NAME=EL
*ELASTIC
210000.,0.3
*BEAM SECTION,ELSET=E1,MATERIAL=EL,SECTION=GENERAL
0.0625,3.25520833333333E-4,0.0,3.25520833333333E-4,0.833333
0,1,0
*BEAM SECTION,ELSET=E2,MATERIAL=EL,SECTION=GENERAL
0.0625,3.25520833333333E-4,0.0,3.25520833333333E-4,0.833333
0,1,0
*BEAM SECTION,ELSET=E3,MATERIAL=EL,SECTION=GENERAL
0.0625,3.25520833333333E-4,0.0,3.25520833333333E-4,0.833333
0,1,0
*BEAM SECTION,ELSET=E4,MATERIAL=EL,SECTION=GENERAL
0.0625,3.25520833333333E-4,0.0,3.25520833333333E-4,0.833333
0,1,0
*STEP
*STATIC
*CLOAD
3,3,10
*NODE PRINT,NSET=Nodes_all,GLOBAL=YES
U
*EL PRINT,ELSET=Eall,GLOBAL=YES
S
*END STEP

SBlade · February 18, 2025, 4:06am

yes I think so I can not find it even among my own books, google retrives nothing, pretty weird

Thanks for the link btw

SBlade · February 18, 2025, 4:31am

I can confirm that with your settings in 2nd case I get the same results as yours in Calculix,
1st example’s 5th DOF rotation is more than expected, IMHO I’d expect %3~4 percentage deviation normal but %12,48 is realy huge.

Disla · February 18, 2025, 8:06am

Which is your deviation criteria?. Mine for first node_first term is computed as:(0.20469-0.2117)/0.2117*100=+/-3.3% (¿0.7%?)

Regarding the expected values, I think results are very good for just 1 element. Your reference seems to have at leat 6 sections per member. That’s not fair.

Disla · February 18, 2025, 11:51am

Reading in detail the original paper used for implementing U1 elements, seems there could be some error in the value and meaning of the Timoshenko shear coefficient shown in the manual.

Mr. Yunhua, Luo paper shows the element stiﬀness matrix terms where K always go toghether with G and A (kGA). That means K is not the Timoshenko shear coefficient 3/2 but it’s inverse.

By other hand Sblade value for the rectangular beam (K=0.83333) is the inverse of the Form Factor which is something different.

Now it is not clear to me what value is the user expected to enter for the User element K?

This pdf could maybe bring some light. Just Goole it.

SHEAR FACTORS FOR BEAM ANALYSIS By Tom Irvine

EDITED: Seems it’s just a different naming convention. Wikipedia uses the Timoshenko shear coefficient name for the K value accompanying GA. So U1 example above should contain a K value of 2/3 instead of 3/2 (Modified) or it’s more accurate version (5/6 used by Mr.Kraska on his Github example file)

3. Gere and Timoshenko, Mechanics of Materials, Brooks/Cole Engineering Division,
Monterey, California, 1984.

xyont · February 18, 2025, 5:34pm

i deleted previous post since it’s clear related to inverse value in table by equation formed, one use ‘k’ as division and many other as multiplier. Lookup table need to use form factors as noticed more accurate even naming match with another but roughly approach.

btw, nice table is that general in use? i miss two columns but did not know where is gone.

Disla · February 18, 2025, 8:03pm

By “one” I guess you mean Mr.Timoshenko?

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U1 Element Direction Issue

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