NL3: Hardening with two variables under load control. T2D2 Fail

Disla · December 26, 2024, 8:26pm

Reference solution

Ccx is unable to solve this recommended Benchmark with the proposed T2D2 element.
Problem is solvable with regular beam B31 with very good agreement.

Error for T2D2 is very strange .
*ERROR in umpc_mean_rot no mean rotation MPC can be generated for the MPC containing node 18

Looks like truss element is unable to rotate more than 90 degrees. (It doesn’t have rotational degrees of freedom and front and rear faces do not follow the rotation?¿?. See picture).

Manitor also warns about linear MPCs and nonlinear MPCs depend on each other common node: 9 in direction 3 but there is not such node 9.

Attached inp.

All other Nonlinear benchmarks are solvable except for NL4 and NL7 which requires Riks algorithm.

*NODE
1,-4,0,0
2,-2.5,0,0
3,0,0.025,0
4,0,4.5,0
5,-2.5,0,1
6,0,0.025,1
*ELEMENT,TYPE=T3D2
1,5,6
*ELEMENT,TYPE=SPRINGA
2,4,3
3,2,1
*ELSET,ELSET=K2
1
*ELSET,ELSET=K1
2
*ELSET,ELSET=K3
3
*MATERIAL,NAME=MATERIAL
*ELASTIC,TYPE=ISOTROPIC
5000000000,0
*DENSITY
7850
*SOLID SECTION,ELSET=K2,MATERIAL=MATERIAL
0.01
*SPRING,ELSET=K1

1.500000000000E+003
*SPRING,ELSET=K3

2.000000000000E+003
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
2,2,,0
2,3,,0
3,1,,0
3,3,,0
4,1,,0
4,2,,0
4,3,,0
*AMPLITUDE,NAME=Ax_2_1
0,0
1,6600
*EQUATION
2
5,2,1,2,2,-1
*EQUATION
2
2,1,1,5,1,-1
*EQUATION
2
3,2,1,6,2,-1
*EQUATION
2
6,1,1,3,1,-1
*EQUATION
2
6,3,1,3,3,-1
*EQUATION
2
5,3,1,2,3,-1
*STEP,NLGEOM=YES,INC=5000,AMPLITUDE=STEP
*STATIC,SOLVER=PARDISO
0.01,1,0,0.01
*CLOAD,AMPLITUDE=Ax_2_1
2,1,1
*NODE FILE,GLOBAL=YES
U,RF
*EL FILE
S,NOE,E,ENER
*CONTACT FILE
CDIS,CSTR
*CONTROLS,PARAMETERS=FIELD
1.e30,1.e30,0.01,,0.02,1.e-5,1.e-3,1.e-8
*END STEP

fgr · December 26, 2024, 9:21pm

@Disla
output in the jobname.12d

 ELEMENT            1 with label "T3D2   R" and with nodes:
          5          6
  is expanded into a "C3D8I BR" element with topology:
          7         16         17          8         10         19         18          9          0          0
          0

Disla · December 26, 2024, 11:39pm

Hi Fgr and thanks.
I see. Truss is also expanded but nodes are not represented by default. I have modify my inp. Now I can see the truss brakes once passing the vertical position exploding. This do not happen with the beam element.

*ERROR in umpc_mean_rot no mean rotation MPC can be generated for the MPC containing node 10

EDITED: I have check if any buckling effect could be involved in the failure but buckling load is still very far from the loading conditions.

*NODE
1,0,0,0
2,1.5,0,0
3,4,0.025,0
4,4,4.5,0
5,1.5,0,1
6,4,0.025,1
7,0,0,0
*ELEMENT,TYPE=T3D2
1,5,6
*ELEMENT,TYPE=SPRINGA
2,4,3
3,2,1
*ELSET,ELSET=K2
1
*ELSET,ELSET=K1
2
*ELSET,ELSET=K3
3
*MATERIAL,NAME=MATERIAL
*ELASTIC,TYPE=ISOTROPIC
5000000000,0
*DENSITY
7850
*SOLID SECTION,ELSET=K2,MATERIAL=MATERIAL
0.01
*SPRING,ELSET=K1

1.500000000000E+003
*SPRING,ELSET=K3

2.000000000000E+003
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
2,3,,0
3,3,,0
4,1,,0
4,2,,0
4,3,,0
5,2,,0
5,3,,0
6,1,,0
6,3,,0
*AMPLITUDE,NAME=Ax_2_1
0,0
1,6600
*EQUATION
2
2,2,1,5,2,-1
*EQUATION
2
2,1,1,5,1,-1
*EQUATION
2
3,2,1,6,2,-1
*EQUATION
2
3,1,1,6,1,-1
*STEP,NLGEOM=YES,INC=110,AMPLITUDE=STEP
*STATIC,SOLVER=PARDISO
0.01,1,0,0.01
*CLOAD,AMPLITUDE=Ax_2_1
2,1,1
*NODE FILE,GLOBAL=YES,OUTPUT=3D
U,RF
*EL FILE
S,NOE
*CONTROLS,PARAMETERS=FIELD
1.e30,1.e30,0.01,,0.02,1.e-5,1.e-3,1.e-8
*END STEP

Durbul · December 27, 2024, 9:47pm

According to the manual, the T3D2 element has some additional constraints:

“This element is similar to the B31 beam element except that it cannot sustain
bending. This is obtained by inserting hinges in each node of the element.”

Depending on how those are introduced, this might explain the instability.

Disla · December 27, 2024, 11:42pm

Hi Durbul,

Thanks for joining the discussion.
I think Trusses have their longitudinal DOF automatically constrained. I can not act on the other two as they do not exist.

This is the same model but solved with B31. No issue and good agreement with expected references.Even without any rotational constrain. So problem is most probably on truss “DOF6”

*NODE
1,0,0,0
2,1.5,0,0
3,4,0.025,0
4,4,4.5,0
5,1.5,0,1
6,4,0.025,1
7,0,0,0
*ELEMENT,TYPE=B31
1,5,6
*ELEMENT,TYPE=SPRINGA
2,4,3
3,2,1
*ELSET,ELSET=K2
1
*ELSET,ELSET=K1
2
*ELSET,ELSET=K3
3
*MATERIAL,NAME=MATERIAL
*ELASTIC,TYPE=ISOTROPIC
5000000000,0
*DENSITY
7850
*BEAM SECTION,ELSET=K2,MATERIAL=MATERIAL,SECTION=RECT
0.1,0.1
-0.009999500038,0.999950003749,0
*SPRING,ELSET=K1

1.500000000000E+003
*SPRING,ELSET=K3

2.000000000000E+003
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
2,3,,0
3,3,,0
4,1,,0
4,2,,0
4,3,,0
5,2,,0
5,3,,0
6,1,,0
6,3,,0
*AMPLITUDE,NAME=Ax_2_1
0,0
1,6600
*EQUATION
2
2,2,1,5,2,-1
*EQUATION
2
2,1,1,5,1,-1
*EQUATION
2
3,2,1,6,2,-1
*EQUATION
2
3,1,1,6,1,-1
*STEP,NLGEOM=YES,INC=110,AMPLITUDE=STEP
*STATIC,SOLVER=PARDISO
0.01,1,0,0.01
*CLOAD,AMPLITUDE=Ax_2_1
2,1,1
*NODE FILE,GLOBAL=YES,OUTPUT=3D
U,RF
*EL FILE,OUTPUT=2D,SECTION FORCES
S,NOE
*CONTROLS,PARAMETERS=FIELD
1.e30,1.e30,0.01,,0.02,1.e-5,1.e-3,1.e-8
*END STEP

fgr · December 28, 2024, 9:40am

Where to start and where to end.
Except for the internal mpc then B31 and T3D2 should in basic be identically so by switching these few lines in the data set it should be possible to compare the outcome.

***ELEMENT,TYPE=B31
*ELEMENT,TYPE=T3D2

*SOLID SECTION,ELSET=K2,MATERIAL=MATERIAL
0.01
***BEAM SECTION,MATERIAL=MATERIAL,ELSET=K2,SECTION=RECT
**0.10,0.10

Looking in the outcome for jobname.12d files, both elements give this output:

ELEMENT            1 with label "T3D2   R" and with nodes:
          5          6
  is expanded into a "C3D8I BR" element with topology:
          8         17         18          9         11         20         19         10          0          0
          

ELEMENT            1 with label "B31    R" and with nodes:
          5          6
  is expanded into a "C3D8I BR" element with topology:
          8         16         17          9         11         19         18         10          0          0

The first to notice for T3D2 is that expanded node numbers are increased by 1 compared to B31. Personal I don’t really understand why since both elements in fact could be identical.

Next looking in outcome for the jobname.frd files, and then draw the element topology gives the result that for the B31 element the internal local axis is defined from node 5 to 6 but for the T3D2 element the internal local axis seems to be reversed and is going from node 6 to node 5 which from my perspective obviously seems strange.
This conclusion is based on that normal for the 1’st face in the topology should give same direction as 1’st node to 2’nd node in the element data card

I have been tracing a little in the source of ccx and decided that my life with the truss element will end here. From my personal use of the truss element, it would only be for compatibility with Abaqus and for that reason I don’t need it. But this shouldn’t keep other to dick deeper into the problem .

xyont · December 28, 2024, 11:34am

indeed, i experienced similar problem of spurious mode with truss element in CalculiX, it has been discussed in many threads also. Rotational restraint may be required in specific case, but in real case of truss e.g steel joist, the top and bottom chord is continuous and modeling approach as beam element. Since then, instability of truss element is avoided due to additional rotational restraint connected to beams.

p.s ideal truss element does not exist in reality, anyone can ignore these elements, no mater FE code being used. SAP also removing in the later versions.

Disla · December 28, 2024, 2:49pm

B31 is rotationally unrestrained and problem converges.

xyont · January 1, 2025, 3:11am

truss member in CalculiX could be better and suitable to modeling as beam element with separated or duplicated nodes at joint. Their connected with four equations constraint, three for equal displacement and one for equal rotational/torsional to eliminate instability. problem. This approach can be general solution and took advancement of nonlinearity i.e point or distributed loads along member, vibration, large deformation, contact and plasticity.

Durbul · January 11, 2025, 9:36am

Just a quick follow up: same issue (and same error) trying to do this with displacement control.

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NL3: Hardening with two variables under load control. T2D2 Fail

Reference solution

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