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## #1 2018-12-06 20:55:06

draf1992
Member
From: Warsaw
Registered: 2018-04-17
Posts: 11

### [SOLVED] Hinge with rotational spring between two beam elements

Hello everyone,

I would like to learn how to model a hinge with a rotational spring. I know how to model a single hinge.
To get the hinge I used LIANSON_DDL.

LIAISON_DDL =_F ( NOEUD     =  ('V2', 'V3'),
DDL       =  ('DX', 'DX'),
COEF_MULT = (1., -1.),
COEF_IMPO =  0.,           )

LIAISON_DDL =_F ( NOEUD     =  ('V2', 'V3'),
DDL       =  ('DY, 'DY'),
COEF_MULT = (1., -1.),
COEF_IMPO =  0.,           )

LIAISON_DDL =_F ( NOEUD     =  ('V2', 'V3'),
DDL       =  ('DZ, 'DZ'),
COEF_MULT = (1., -1.),
COEF_IMPO =  0.,           )

Case 1 and 2 are in attached file. In the first case without rotational spring I received a Singular Matrix. In the second case without rotational spring I received correct results consistent with analytical calculations. I would like to avoid using discrete element SEG2. I tried with a discreet element of POI1. I added the zero 0D element to the V2 and V3 nodes. I'm not sure if this is a good solution.

Boundary conditions in the hinge wrote:

U=Y, QL=QP-F, ML=-k*(Up-Yp), MP=k*(Yp-Up).
U - displacement of the left beam
Y - displacement of the right beam

Up - derivative of displacement of the left beam
Yp - derivative of displacement of the right beam

k - spring stiffness

Ql - shear force in the left beam
QP - shear force in the left beam

M -  bending moment

How to add these additional conditions except that the displacements are to be equal for node V2 and V3. For any tips thanks in advance

Best
Rafał

Last edited by draf1992 (2018-12-14 22:28:00)

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## #2 2018-12-10 13:32:37

jlf
Member
Registered: 2007-11-22
Posts: 211

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Hello,

You could try a DIS_TR (a K_TR_D_L on a SEG2 with a null size or not) with the same LIAISON_DDL for UX, UY, UZ.
You have 6 values to give for the K_TR_D_L :
- 3 values for displacement, with the LIAISON_DDL the values doesn't matter.
- 3 values for rotation, k

Watch out for the orientation of the SEG2, especially if its size is zero!

JLF

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## #3 2018-12-12 03:00:52

draf1992
Member
From: Warsaw
Registered: 2018-04-17
Posts: 11

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Hi jlf,

Thank you for your response. This method works for case 1 and case 2. I received correct results consistent with analytical calculations. Both beams were along the X axis and the Y and Z axes in the local system corresponded to the Y and Z axes in the global one. What does the SEG2 orientation look like when the size is zero?  My system constructed of beams will be very complex. Therefore, I would like to avoid adding an additional element like DIS_TR and problem with his orientation.  Is there another way to achieve the same result?  I do not know how to impose bending moment as a function of the derivative of displacement of another node. Then it may be possible to write the function ML = -k * (Up-Yp) and use LIANSON_DDL instead of the additional element.

Best
Rafał

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## #4 2018-12-12 18:04:05

jlf
Member
Registered: 2007-11-22
Posts: 211

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Hello,

If you want to release DDL, the only way is to model a SEG2 between the 2 nodes.
There no way to write relation between Force and Deplacement (duals variables) in commands file, in fact it's a behavior.

The solutions I propose to you, simple or not :

*** Case where the hinge have the same 'k' is in the 3 directions, no torsion in the beams:
- you create a SEG2 between the 2 nodes (length and direction don't matter)
- the sames values for rotation  KRX, KRY, KRZ

*** Case where the hinge have KRY=KRZ and a different for KRX
- when you create your beams you made 2 nodes with very slightly different. The X direction for the spring is the V2V3 vector. In this case, if the length is not null you don't need to use ORIENTATION keyword when KRY=KRZ.
- the same values for KRY, KRZ and another for KRX.

JL

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## #5 2018-12-12 21:51:49

draf1992
Member
From: Warsaw
Registered: 2018-04-17
Posts: 11

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Hello jlf,

Thank you for your response and tips. Is it possible to add new boundary conditions in the form

u(2)-u(3) = 0
Q(2)-Q(3) = 0
MY(2)-k (DRY(2)-DRY(3)) = 0
MY(3)-k (DRY(3)-DRY(2)) = 0

The node number is in brackets. I obtained the first of these conditions thanks to LIANSON_DDL.

Best
Rafał

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## #6 2018-12-14 10:39:53

jlf
Member
Registered: 2007-11-22
Posts: 211

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Hello,

No you can't.
In LIAISON_DDL you can only have relations between Degree of Freedom (DDL=DoF). MY,MZ are not a DoF

Cf U4.44.01 : AFFE_CHAR_MECA documentation in §5.1 of the DoF

JL

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## #7 2018-12-14 22:26:28

draf1992
Member
From: Warsaw
Registered: 2018-04-17
Posts: 11

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Hello jlf,

Thank you for the explanation.

Best
Rafał

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## #8 2018-12-17 15:34:02

Lore
Member
Registered: 2016-04-01
Posts: 6

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Hi JL,
is it possible to have some kind of reference of the zero-length SEG2 elements?

I was not able to define them, and as they are very useful, I'm very interest in their implementation in models.

Thank you

Lorenzo

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## #9 2018-12-17 16:33:39

jlf
Member
Registered: 2007-11-22
Posts: 211

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Hello,

You can find a lot of examples in the test cases of code_aster  :
In command file you search the words : 'ORIENTATION' with 'K_TR_D_L' | 'K_T_D_L' | 'K_TR_L' | 'K_T_L'.
If in AFFE_CARA_ELEM/ORIENTATION you have GROUP_MA with CARA= 'ANGL_NAUT', it's found.

The [V6.02.135] 'ssnl135' is a study on a structure with lot of springs with null size.

JLF

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## #10 2018-12-17 17:23:07

Lore
Member
Registered: 2016-04-01
Posts: 6

### Re: [SOLVED] Hinge with rotational spring between two beam elements

Thank you very much JLF!!

Lorenzo

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