CA equivalent for RBE2 and RBE3

JMB365 · 2011-03-25 17:08:00

Hello,

Could anybody recommend the type of elements in CodeAster that are equivalent to RBE2 and RBE3 of NASTRAN?

Note: I read that RBE2 adds infinite stiffness to attached nodes which means both nodes to exactly the same displacement whereas RBE3 is an interpolation element and distributes the loads and the mass depending on the length. Any help and clarification is appreciated. Thank you.

Regards,
JMB

jeanpierreaubry · 2011-03-25 17:54:34

hello

as far as i remember this is the right definition for RBE2 in NASTRAN and SAMCEF,
i am no so sure about RBE3
to me the sibling is LIAISON_DDL
i used it very little,
in fact it is very cumbersome to write down,
mind you it is no easier with the other two monsters unless you use one something like PATRAN
and you have to make some tests to be sure the results is what you wanted!

for all my practical purposes, simulating joints with relaxed or not dof i use DISCRET , K_TR_D_N (or L)
this as to be meshed, but it gives the forces in the element

jean pierre aubry

JMB365 · 2011-03-25 18:10:36

Hello jeanpierreaubry,

Thank you for your reply.

jeanpierreaubry wrote:

as far as i remember this is the right definition for RBE2 in NASTRAN and SAMCEF,
i am no so sure about RBE3
to me the sibling is LIAISON_DDL

LIAISON_DDL is the sibling to RBE2 or RBE3? I think you meant LIAISON_DDL is the sibling to RBE2 in your previous paragraph.

for all my practical purposes, simulating joints with relaxed or not dof I use DISCRET , K_TR_D_N (or L)
this (h)as to be meshed, but it gives the forces in the element

K_TR_D_N (or L) is what I have used in the past but wondered if there is an equivalent to RBE3. RBE3 appears to be different and I have not located the actual document that describes it quite yet.

Regards, JMB

PS: Anybody else please feel free to comment too...

BL · 2011-03-25 20:46:33

While I have no experience with Nastran, one of my previous coworkers claimed LIASON_SOLIDE was what Nastran called RBE2.

CLF · 2011-03-26 00:18:21

Hi JMB

I concur with jean pierre aubry, that the sibling indeed is LIAISON_DDL. Similar stuff may be going on in other LIAISON functions, but they do not do the the job in the same way.

The RBE2 contraint is not very complicated, but laborious and error prone to write down - which is one reason why the RBE2:s came into existence.

Looking at a simple example using 2points (A & B), that are separated by distance L and at an angle Phi from the X axis, with 3DOFs (X;Y;RZ) the RBE2 constraints looks like this when points A and B use the same cartesian coordinate system:
Ax = Bx + L*cos(Phi) - Brz*L*sin(Phi)
Ay = By + L*sin(Phi) + Brz*L*cos(Phi)
Arz = Brz
where Ax implies point A and dof X and so on.

The Master dof is A. If you want to constrain more slave points than B, you add these to the RHS and simply continue to build on the equation, e.g.
Ax = Bx + Lb*cos(Phiab) - Brz*Lb*sin(Phiab) + Cx + Lc*cos(Phiac) - Crz*Lc*sin(Phiac)
Brz = Crz

To sum up, the convenience in using RBE2s lies in it doing the geometry calculations for you and in it catering also for any coordinate transformation that may be involved between the nodes. I believe RBE2s would make a very useful addition to CA who has other constraints that are very convenient to use. .

{ The nasty thing with RBE2s is that if you connect solid elements (XYZ dofs each) to a single beam node (6dofs), the slaves must be on the solids. You want to use rotation in the RBE2. However, as the solids only carry translational dofs, the rotational dofs become constrained, i.e. the rotation dofs on the solids get blocked (Brz==0 in the example above), which in turn can lock the model. The workaround then is to add thin shell elements on the solid to get all 6dofs. }

The functionality is already in CA, but the convenience and 'robustness' clearly are missing. As jean pierre aubry states, one does hesitate to do the job manually as the risk of doing something wrong is high indeed.

Workarounds:

If nodes are separated a non negligible distance, I would not use an idealized spring element (type F = K*X) as a replacement to RBE2s - as such elements do not carry any information on the L variable. Spring elements with some form of length constraint in them may do the job (similar to CBUSH).

The old fashioned way, i.e in the near antique pre RBE2 time, was to use ordinary beam elements. Beam elements tend to increase the numerical span of the stiffness matrix and may make the model hard to run - which is the other reason why the RBE2 type constraints came to use.

I haven't looked into the matter, but - there are nice LIASON functions where you simply let the beam element end somewhere in the solid element volume and let the connection become constrained by some convenient commands. The gentlemen developing CA know what they are doing, so there is a more than fair chance such constraints are handled in a very nice manner.

What I am driving at is that a 'near RBE2' way of modeling may be a combo of a beam element and a convenient-to-use CA constraint on the slave side. This may have been what BL was driving at? Please report back on your finding if you choose to investigate.

The RBE3 is simpler on the face but the more cumersome to foresee actual outputs. It transfers a weighted force and moment load from the slave nodes onto the master node. The weighting factors are computed from the nodal geometry information. I haven't used it much as I wasn't comfortable with it.

Last but not least, RBE2s is a problem for Nastran/CA conversion as the RBE2s cannot be transferred without major effort into CA. I believe this problem does have industrial relevance due to Nastran being such a common code.

I guess the way to go the whole way on RBEs is for someone to write up a Python script?

Hope this helps
Claes

Last edited by CLF (2011-03-26 00:40:18)

todd_alan_martin · 2011-03-26 02:46:23

Hi JMB

The closest thing CA has to RBE2 is LIAISON_SOLID, but it constrains all DOFs on the dependent nodes.

One of the nice things about RBE2 elements is the ability to pick and choose which translation/rotation DOFs to constrain on the dependent nodes and which coordinate system (cartesian,cylilndrical,spherical) to use for imposing those constraints. So, for example, a part can be constrained to slide on the surface of a pin by restraining the radial component of the dependent nodes using a cylindrical coordinate system defined on the axis of the pin. This is a problem in CA, since CA does not have a coordinate system object.

The RBE2 is actually just a series of multi-point constraints, defined in global cartesian space, between the dependent nodes and the independent node. So it can be fully replicated in CA for specific DOFs using LIAISON_DDL. As others have commented, this is tedious and error prone, if you must do it by hand.

RBE3 elements transfer load, but not stiffness from the independent to the dependent nodes. This can be achieved in CA using LIAISON_ELEM from a beam to a solid, or a beam to a shell.

Todd.

Last edited by todd_alan_martin (2011-03-26 02:47:35)

jeanpierreaubry · 2011-03-26 08:24:31

hello

the two previous gentlemen produced wise informations
patricularly concerning solid modelling (which have never done on an industrial scale)
if it may help i join the documentation about RBE in SAMCEF
(i probably have the same for NASTRAN within some paper stack somewhere, i did not used NASTRAN for years now)
if somebody wants it i will look for it

jean pierre aubry

Last edited by jeanpierreaubry (2011-03-26 08:31:17)

Attachments:
samcef_rbe.pdf, Size: 216.98 KiB, Downloads: 5,277

rthhert · 2011-03-27 09:24:50

JMB

Noone has answered your rbe3 question so .......

Rbe3 has one dependent node and multiple independent nodes
The displacement of the dependent node is dependent on the weighted average of a subset of the degrees of freedom displacements of the independent nodes. The constraint equations are written with the kinematics of a rigid link.

It is commonly thought of as distributing mass or force (and this is often the effect) but I think it can be dangerous to view it in thiforce, if you think of it as what it is you will be safer.

You need to be careful with defining relationship between dependent and independent nodes, it doesn't make much sense (though is admissible and is often done) to make rotations of the dependent node dependent on rotations of the independent nodes.

Tom

JMB365 · 2011-03-27 14:28:28

Hello!

To all who have so graciously replied and provided such in-depth explanations - thank you very much! I am yet to embark on this project, which is several weeks away, but the insight into RBE2/3 was most useful.

-> rthhert (Tom), I did not quite understand what you meant by:

but I think it can be dangerous to view it in thiforce, if you think of it as what it is you will be safer.

would you kindly explain?

-> todd_alan_martin (Todd) you wrote...

RBE3 elements transfer load, but not stiffness from the independent to the dependent nodes. This can be achieved in CA using LIAISON_ELEM from a beam to a solid, or a beam to a shell.

Do you know if LIAISON_ELEM is capable of distributing loads based on length as RBE3 is purported to do? Here I am assuming that the RBE3's relationship is inversely proportional, i.e. the greater the length the lesser the mass and force that is transferred.

Thank you all!

Regards, JMB

CLF · 2011-03-27 15:16:46

Hi JMB

I can forward some more information to you if you send me a mail, .

Sincerely
Claes

jeanpierreaubry · 2011-03-27 16:35:28

hello

what do you mean by

JMB365 wrote:

Do you know if LIAISON_ELEM is capable of distributing loads based on length as RBE3 is purported to do?

do you want to put a distributed load on the element making the LIAISON_ELEM?
if yes i personnaly thing this is just crazy!

and here i do not understand

JMB365 wrote:

Here I am assuming that the RBE3's relationship is inversely proportional, i.e. the greater the length the lesser the mass and force that is transferred

maybe you could describe your problem in a few words or a sketch!

are you sure that RBE* are the solution to your problem?
they are as their name imply Rigid Body Element,
they will transmit displacements and hence forces from one side of a model to the other side with some multipying factor (that maybe 0) on the DOF
it seems to me that the exact sibling to RBE* is LIAISON_DDL (i put my hands on the NASTRAN doc)

again you should not think this way,
what is the best replacement for "this NASTRAN" command unless you know exactly what i does
but think of you physical problem and find out in Code_Aster what suits (usually ther will be several answers)

jean pierre aubry

Last edited by jeanpierreaubry (2011-03-27 16:37:40)

JMB365 · 2011-03-27 16:54:11

jeanpierreaubry wrote:

maybe you could describe your problem in a few words or a sketch!

Assume that a point force is applied to a node, and that this point node is connected by RBE3s to a 3D surface of a 3D solid. The intent is to have a diminishing effect of the point force as one gets further way from it on the surface. I hope that is adequate clear enough an explanation. Additionally the diagram would be:

       ^ Force (could be pushing downward too!)
       |
       o
      /|\
     / | \ RBE3s (multiple, but just 3 shown here...)
    /  |  \
===o===o===o=== 3D surface
XXXXXXXXXXXXXXX 
XXXXXXXXXXXXXXX  Underlying solid
XXXXXXXXXXXXXXX

are you sure that RBE* are the solution to your problem?

Yes - because the customer requires it to done that way and I am not in a position to say no! What I am trying is to get an understanding of is the key difference between RBE2 and RBE3 and a suitable replacement for it in CA. Presently I am still learning...

Regards, JMB

Last edited by JMB365 (2011-03-27 16:56:24)

jeanpierreaubry · 2011-03-27 17:01:56

JMB365 wrote:

Yes - because the customer requires it to done that way and I am not in a position to say no! What I am trying is to get an understanding of is the key difference between RBE2 and RBE3 and a suitable replacement for it in CA. JMB

of course that is a good reason
here is the extract of MSC NASTRAN Quick Reference Guide
i am afraid the quality is low, as i do have only a paper thik book

jeanpierreaubry · 2011-03-27 17:07:30

part1

Attachments:
part1.tar.gz, Size: 1.68 MiB, Downloads: 927

jeanpierreaubry · 2011-03-27 17:08:44

part2

Last edited by jeanpierreaubry (2011-03-27 17:12:49)

Attachments:
part2.tar.gz, Size: 1.26 MiB, Downloads: 821

jeanpierreaubry · 2011-03-27 17:14:07

part3

Attachments:
part3.tar.gz, Size: 1.19 MiB, Downloads: 838

jeanpierreaubry · 2011-03-27 17:15:18

part4

Attachments:
part4.tar.gz, Size: 1.4 MiB, Downloads: 796

jeanpierreaubry · 2011-03-27 17:16:27

and the end

Attachments:
rbe010.jpg, Size: 399.92 KiB, Downloads: 559

todd_alan_martin · 2011-03-27 22:39:13

Hi JMB365

Regarding LIAISON_ELEM. It is my understanding that, if the force is vertical, the load is uniformly distributed to the nodes. If it is horizontal the forces are distributed such that the bending moment and shear force is applied with the vertical reactions varying linearly along the nodes (maximum at the extremities) and the horizontal reactions uniformly distributed. So the reactions are weighted like those in a bolted/riveted joint.

The best way to find out would be to build a simple model and test it by observing the nodal reactions using CALC_NO
OPTION=('FORC_NODA','REAC_NODA',)

Todd.

Last edited by todd_alan_martin (2011-03-27 22:45:15)

onnomobile · 2011-03-28 16:02:11

Hello,

I find this topic very interesting and I have done some research as well, without finding a miracle solution.

RBE2 is actually just an automatic combination of equations linking one node to many others (MPC : multipoint constraint). It can be completely replaced by LIAISON_DDL as long as they are applied one by one ... as explained previously.

The more interesting "element" is RBE3, which has been called "remote displacement in ANSYS" and even "remote constraint" where one can apply a force from a distance. The advantage is that you can make links to surfaces that stay deformable (don't turn rigid). I use it to simulate a shaft bearing under bending load for example.

I haven't found any formulation of these elements and I'm not cleaver enough to reinvent them. What I understood though, is that they are interpolation elements (as you said) which means there is an interpolation factor which defines how much reaction force is applied from the master node on each slave node. I secretly imagine a series of elements with variable directional stiffnesses that are tuned in order to achieve the resulting equilibrium... :-) Nevertheless they are not individual elements, but are dependent of each-other.

The researcher will say it looks nice but that it's dangerous because you don't fully understand what's going on behind, but the engineer is so happy to have a fast and useful tool ... (I'm an engineer)

Hope this was of any help. Have fun !

jeanpierreaubry · 2011-03-28 16:57:37

hello

i am here again

if you read careffully the documentation about LIAISON_DDL, U4.44.01,
you will find out that the key words COEF_MULT and COEF_IMPO allow some amplification factor to the displacement from one DDL to the other
by the way they are just mandatory!
difficult to explain, better read yourself
you should carefuuly read the doc and make benchmarks to find out what is happening

i admit that the doc maybe hard to understand
and that the writing of this command is extremely cumbersome
but it is no easier in NASTRAN

i once made a NASTRAN model with several hundreds RBE2, it was a nightmare, and only linear statics!

i rather use K_TR_D_L it is much easier to understand what you are doing

jean pierre aubry

keeswouters · 2011-03-28 18:52:02

Hoi,

I just throw in my use of LIAISON_DDL:
http://www.caelinux.org/wiki/index.php/ … c/cylinder
http://www.caelinux.org/wiki/index.php/ … pythonlist

you can make the internal relations as complex as you want. As long as you understand.

kind regards - kees

CLF · 2011-03-31 19:23:08

Hi

I guess something similar to what Kees has been doing is the way to go for the RBE2/RBE3 addict.

Sincerely
Claes

Last edited by CLF (2011-03-31 19:24:01)

pdupuis75 · 2011-04-01 18:19:17

elements RBE2,RBE3 have geometric stiffness in left and right rotation
they converge to the same results, but geometric stiffness of RBE2,RBE3
are non symetric. RBE2,RBE3 work as linear relations in linear solver
Pdupuis75

pierre_j · 2012-03-23 13:22:35

Hi,

As should be indicated soon in a news, RBE3 have been made available in Code_Aster 11.1.13..
This functionality has been evaluated on an industrial test case, but any additionnal feedbacks will be welcomed.

Have a good day.
Bests,

Pierre

#1 2011-03-25 17:08:00

CA equivalent for RBE2 and RBE3

#2 2011-03-25 17:54:34

Re: CA equivalent for RBE2 and RBE3

#3 2011-03-25 18:10:36

Re: CA equivalent for RBE2 and RBE3

#4 2011-03-25 20:46:33

Re: CA equivalent for RBE2 and RBE3

#5 2011-03-26 00:18:21

Re: CA equivalent for RBE2 and RBE3

#6 2011-03-26 02:46:23

Re: CA equivalent for RBE2 and RBE3

#7 2011-03-26 08:24:31

Re: CA equivalent for RBE2 and RBE3

#8 2011-03-27 09:24:50

Re: CA equivalent for RBE2 and RBE3

#9 2011-03-27 14:28:28

Re: CA equivalent for RBE2 and RBE3

#10 2011-03-27 15:16:46

Re: CA equivalent for RBE2 and RBE3

#11 2011-03-27 16:35:28

Re: CA equivalent for RBE2 and RBE3

#12 2011-03-27 16:54:11

Re: CA equivalent for RBE2 and RBE3

#13 2011-03-27 17:01:56

Re: CA equivalent for RBE2 and RBE3

#14 2011-03-27 17:07:30

Re: CA equivalent for RBE2 and RBE3

#15 2011-03-27 17:08:44

Re: CA equivalent for RBE2 and RBE3

#16 2011-03-27 17:14:07

Re: CA equivalent for RBE2 and RBE3

#17 2011-03-27 17:15:18

Re: CA equivalent for RBE2 and RBE3

#18 2011-03-27 17:16:27

Re: CA equivalent for RBE2 and RBE3

#19 2011-03-27 22:39:13

Re: CA equivalent for RBE2 and RBE3

#20 2011-03-28 16:02:11

Re: CA equivalent for RBE2 and RBE3

#21 2011-03-28 16:57:37

Re: CA equivalent for RBE2 and RBE3

#22 2011-03-28 18:52:02

Re: CA equivalent for RBE2 and RBE3

#23 2011-03-31 19:23:08

Re: CA equivalent for RBE2 and RBE3

#24 2011-04-01 18:19:17

Re: CA equivalent for RBE2 and RBE3

#25 2012-03-23 13:22:35

Re: CA equivalent for RBE2 and RBE3

Board footer