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Re: SAP, RISA 3D, STAAD - Master/Slave Relationships

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Answering Bruce Bates:
 << Designed to model rigid body inclusion within the deformable system...
 << This enables us to model diaphragms (floors in building skeletons) in a
 << following simple way (assuming Z as vertical direction, consider that
 << 1,2,3,4 are the nodes by which 4 columns are hinged to the in-plane
 << perfectly stiff floor) it is enough to put:
 <<  2 3 4  LINK  1 UZ  RX RY 
  > What if my entry were (either intentionally or erroneously) :
  > RIGID 2 3 4 LINK 1  UZ RX RY RZ
  > or this:
  > RIGID 2 3 4 LINK 1  UX UZ RX RY 
  > Would you perform the transformation anyway, would you flag this as an
  > error, or would you do something else? 
 All combinations of relaxed DOFs are accepted, but of course some are
 recommended for users as particularly suitable for modeling diaphragm.
 Algorithm used is general, we accept selective DoF Rigid Link for any
 arbitrary sequence of relaxed DOFs.
 << I have to admit that programming this selective DOF rigid link option
 << was one of the most complicated parts of the whole development. 
> That depends on what you do with situations such as I've described
> above. If you require the rotational transformation, it's pretty
> straightforward. If you try to handle any user request, it starts to get
> interesting.

 As I said above, any sequences of relaxed DOFs are accepted, which _is_
 interesting (and quite not trivial).
<<  "COMPATIBLE NODES" to handle very common situation when different nodes
<< share user-specified DOFs. Example - pinned connection of crossing X
<< The corresponding nodes should however occupy the same position in the
<< space. Attachment of the same DoFs to the group of nodes occupying
<< DIFFERENT positions in the space, but without "rigid link" type
<< transformation is not physically based, and as such, would never lead to
<< correct results...[clip] 
> Consider this example: I'm analyzing a simple 2D frame (XY plane, 2
> column lines) for lateral (X dir) modes lock out Z translations and X and
> rotations, giving me a 3 dof model. Now I slave the X translations to
> reduce the size of the matrix. I'm now using slaving of physically
> separated nodes without transformations to get the results I want. 
<< The only known physically based and sensible application of such an
<< option is imposition of periodic boundary condition in the case of FEM
<< analysis of the representative cell of the periodic composite, but I do
<< think that this was the reason of the appearance of this option in early
<< codes.
>  Huh? 
> The original intention of the master/slave relationship was to eliminate
> dof's in models where simplifying assumptions can be made. The extension
> master/slave to diaphragm modeling requires that dof be slaved in groups
> that the rotational transformations can be performed, i.e. X translation
> can not be slaved without also slaving Y translation and Z rotation. This
> requirement does now make master/slave applicable to diaphragms, but
> lost the ability to slave dof's in a wholly independent way. I can see
> ROBOT addresses this by offering the RIGID LINK option AND the COMPATIBLE
> NODES option, giving the ability to do it either way. What ROBOT
> as "compatible nodes" is termed the master/slave relationship in RISA-3D.
> What ROBOT calls the "rigid link" option is termed the rigid diaphragm
> option in RISA-3D.
> Bruce Bates
>  RISA Technologies

I agree that for some particular situations the "Slave-master"
relationship, as you describe it, is sufficient.

The problem is that _in general_ this option is not physical. Our
understanding of a constraint in statics is such that any constraint should
correspond to the presence of certain body (which may be idealized as
perfectly rigid and not be a subject of our interest) which acts on our
deformable system constraining its displacement and inducing reaction

Slaving selected translational DOFs in distant nodes corresponds physically
to introduce a perfectly rigid rod between them. The problem is that it
makes sense only when the direction of the rod corresponds exactly to the
direction of slaved D.O.F . e.g. when they have the same Y & Z coordinates
and slaved UX displacements.
In your example, as long as the selected nodes have the same Y and Z
coordinates, slaving UX displacements is perfectly OK. However, when the
connecting rod goes out of plane Z=0, or is no more horizontal, such
slaving has no physical sense. That is why we resigned from building the
option which is not properly physically based.

With the selective DOF Rigid Links we put:
	P1 LINK P2  Rx Ry Rz
and now the imaginary rod P1-P2 bounds the displacements of the nodes P1,
P2 without setting any constraints to their rotations.

Aleksander Urbanski
author of the computational module of ROBOT