3-2-1 Constraints approach in FEA analysis.

[sharpedge]

Does a 3-2-1 constraint approach really makes much difference in a Non-Linear analysis. Also, from mathematical point of view, what other benefit does it provide in linear static analysis apart from the widely aclaimed balance of global forces and does it mtter which plane the contraints actually lies?


Also, for lug analysis, what benefit does the use of spring force has over direct surface foces/traction.

Regards.

 

[GBor]

JohnHors...sounds like a question for you!

You may want to visit

http://www.roshaz.com.

I think there is a paper there that goes in to some depth of argument, but I believe it is only addressing static analysis.

The gist, though, is prudent everywhere: a fixity is an artificially rigid constraint where the software makes some assumption as to just how stiff it is. Using equivalent forces to balance your model limits the artificial nature of the load path, which is drawn to stiffer regions. Using springs allows you to set the stiffness, but is only as accurate as your judgement and calculation assumptions can be. If you are sitting on a chair and it isn't breaking underneath you, then the floor is pushing back with a force equivalent to your weight, but the legs may be allowed to deflect outward slightly. Fix them with hard constraints and they can't move.

 

[sharpedge]

Ok, good link..thought the roshaz software was pretty impressive... althought looks like its only a pre and post precessor with no independent solver.
The example in the movie clip with the 3-2-1 constraint abit misleading. Higher stresses occuring at the node positions where the body was restrained from rigid body tranlational motion in the X,Y,Z and Y,Z planes.
From global balance of forces.. the argument seems logical but with higher stress occuring at node positions where these restrain are applied, I am yet to be convinced if that truly simulate realistically the true deformation of the body.
****Curious..is Roshaz relatively new? I do not appear to have heard of it apart from it being talked about in this forum. Looks like a really great FEA tool.

 

[GregLocock]

Obviously 321 doesn't restrain the model 'correctly', unless you design your test rig to duplicate it (that's what I do).

But it is better than fixing one node in 6 dof, or overconstraining the system as in GBor's example.

I usually try to represent the supporting structure as springs, given the choice. I see other people use inertial relief.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[GBor]

Roshaz has a static linear solver, and interfaces with several other solvers (ABAQUS, Calculix, etc.), but my goal wasn't to push the software...I just know the developer is a strong believer in 321 for linear analysis.

 

[sharpedge]

To Gbor,
Sorry I didn't intend to say you were advertizing the software..Just thought user interactivity was fully thought when the software was being created. I would be keen to try it out and see how it benchmarks some of the other known FE softwares.
Put it simple, the concept of 3-2-1 is to avoid rigid body motion of the structure but I am yet to see any evidence to show that it truly does achieve this rather I am still of the opinion that it does result in over constraint of the whole structure.

To Greglock, H
How would you determine the location of that one node you intend to fix in 6 dof. Any formulation you can point to that clearly shows this does prevent rigid body motion of the structure in linear static analysis?

ta.

 

[GregLocock]

"How would you determine the location of that one node you intend to fix in 6 dof. Any formulation you can point to that clearly shows this does prevent rigid body motion of the structure in linear static analysis?"

I think you need a mechanics textbook.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[rb1957]

"Higher stresses occuring at the node positions where the body was restrained from rigid body tranlational motion in the X,Y,Z and Y,Z planes."

that sounds like a problem to me ... your supports are either "real" where your structure reacts the applie loads or "imaginary" needed for the FE to solve (ie restraining rigid body motion) ... these should be zero 'cause you don't want them reacting load.

consider a simple 2D beam model. it'd have two "real" reactions at the ends (the pinned supports) ... these solve 2 rigid body motions so you need 4 "imaginary" supports to fix the beam in mathematical space.

 

[gurmeet2003]

Sharpedge,

I recently tried the 3-2-1 support in a Non-linear problem involving metal yielding. The 3-2-1 support model was unable to converge, because of excessive deformation at one node. This occured due to rotation of loads due to finite deformations, therefore load balance could not be maintained.

I think this concept is more useful in linear analysis. Even then load balance is inherently not better. If your model has some constraints, which most real models do, then the best approach is to try and apprroximate the degrees of freedom constrained in the model in the relevent sub-regions. I have seen some people claiming that load balance approach is inherently better. But that is not correct. The correct constraints are those which approach the real ones.

An underconstrained model can also lead to higher stresses in an area of interest.

Gurmeet

 

[GBor]

I didn't take any offense or even read that you questioned my motives. I do market Roshaz. It has been around for a few years, but back to your question.

All software packages have ways of handling boundary conditions. In some, you apply conditions to entire surfaces. In others, localized constraints away from areas of critical interest. In some, balancing forces as much as possible and letting single node boundary conditions "clean up" the round-off error in the calculations is chosen.

Load path follows stiffness. This is often why stresses are higher in corners of cut-outs...corners are geometrically stiff. Most softwares apply a very high stiffness to boundary conditions (1e9 whatever units, for instance). These virtually rigid hardpoints insure that your model doesn't "drift off in to space", but it may also alter your load path if applied incorrectly.

Take the chair example from my previous post. With even one leg fully fixed, try to push the chair across the floor. What happens? Well, instead of the chair sliding like it probably would in "real life", it is bound at that one leg and all the load goes in to bending that leg, so it has a high stress. Fix all four legs and the load is carried by all four. Apply springs approximating friction and your analysis results may be closer to accurate.

In this case, there is a rigid body mode...translation across the floor. Linear analysis probably wouldn't be the most accurate, and using a hard constraint instead of Greg's springs probably would show the best result either.

You have to have a variety of "weapons in your arsenal" and understand how to properly employ them. Each of these methods provide speed, accuracy, precision, all of the above, none of the above...

Garland E. Borowski, PE
Engineering Manager
Star Aviation

 

[jhardy1]

I'm a bit intrigued by the direction this discussion is taking - surely the best approach is to model constraints "correctly" for the particular application being modelled, rather than sticking rigidly to any particular method.

If your structure is "fixed" to ground (such as a building) then you would typically apply fixed or spring restraints at the structure's supports.

If your structure is "free-floating" (e.g. aircraft in flight, free vibration modes, etc), then "Inertia Relief" can be a useful technique, if your software supports it; otherwise, the 3-2-1 approach can generally be applied, but it is important to note that the restraints should be carefully positioned such as to not attract any spurious net force that can't actually go to the fictitious support nodes.

If you apply any more than the minimum 3-2-1 restraints, you may have over-constrained the model, and there is a real chance that you will not be able to get solution with "zero" reactions at all of the artificial constraints (especially if you are conducting a non-linear analysis). You need to ensure also that the locations of the artificial restraint nodes don't influence vibration modes shapes or buckling mode shapes of interest (e.g. if one of your restraints is halfway along a beam, you may not be able to recover the fundamental vibration mode of the beam). That is, your applied load sets should all be in self-equilibrium, so that no net load goes to any of the artificial restraints, and the restraint nodes are used only to provide the "numerical fixity" that the solver requires.

If your structure is such that it has redundant support conditions (true of MANY real-world applications!), then you may need to consider some sort of sensitivity analysis for different restraint sets, to make sure you have considered the envelope of possible scenarios. For example, consider the classic case of a four legged chair on uneven ground - it is tempting to assume that all four legs are vertically "fixed", but most of the time, only there legs are actually carrying load.

The main thing is to not over-constrain the model (which will lead to erroneous load paths), and to not under-constrain the model (which may result in failure to solve).

 

[johnhors]

Judging by some of the comments in this thread there appears to be a degree of confusion and misunderstanding of the 3-2-1 approach.

Firstly, this method is only applicable to solid 3D elements. The nodes of these elements have only translational degrees of freedom, no rotational degrees of freedom. Therefore a 3D solid model cannot be restrained at a single node. The minimum number of nodes necessary to fully support a model is three (not in a straight line!). The minimum number of degrees to fix in total, to correctly support the model is six, using a 3-2-1 approach.

To apply the 3-2-1 technique, three convenient nodes are selected, they should be well separated. The first node is restrained in all three axes. The second node is restrained in the two axes orthogonal (normal) to the vector from node one to node two. There should be no restriction to deformation along the line from node one to node two. Finally the third node is restrained in a direction normal to the plane formed by the three points. A simple thermal expansion load case can be applied to test the supports. The model should expand or contract under temperature loading and have zero stress throughout the model. The supports will not react any loads.

Of course for structural loading a near perfect balance must be applied if these supports are not going to react any loads.

The method cannot be used in conjunction with non-linear geometry analyses (the NLGEOM parameter in Abaqus), as this involves updating the model stiffness as it deforms under loading and it is obvious that what was a load balance on undeflected geometry will not balance with deflected geometry. However, it is still possible and valid to apply the technique to models that incorporate localised plasticity and/or non-linear contact within an assembly model.

To utilise this method the analyst must have a complete understanding of the forces applied to the part being modelled. Free-body diagrams labelling all loads, their directions and positions will provide this information. The 3-2-1 method will not accommodate any errors in load application, it is inherently self-checking. If the supports react zero or very nearly forces then the loading is fine, otherwise a mistake has been made. With models that are built to react loads at the supports, there is no simple similar check available. An analyst who never makes mistakes does not exist!

The basic theory underlying finite element analysis is that it is only valid in a continuum. Introduce a discontinuity and the basis of the method is invalidated and incorrect results will be output. Discontinuities occur at a change of material properties, change of element type, rigid body elements, partially connected elements, contact with other mesh regions and of course at supports. Or in more mathematical terms, anything that disturbs or cannot honour the element shape/displacement functions is a problem. Thus with the 3-2-1 technique, because the supports don’t react anything the continuity is not disturbed and the results are not invalidated. In contrast, supports that react load produce erroneous stress contours.

It goes without saying that only pressure loading should be applied to a model, discrete point loadings must be avoided. (Not to be confused with a pressure that is actually applied as a set of equivalent point loads). Pressure loading on an element face takes account of the element shape/displacement functions and is therefore not a problem.

The results produced by balanced loading with minimal 3-2-1 supports err on the side of caution. With no benefits gained by supports the part is made to work harder within itself. However if the model is of a part within an assembly or a test rig then the deformation of the part may become unreasonably and unrealistically large. In that case, improved results are best obtained by including the support structure into the model, but this need only be done if results from the first pass are not acceptable.

 

[GBor]

In this case, there is a rigid body mode...translation across the floor. Linear analysis probably wouldn't be the most accurate, and using a hard constraint instead of Greg's springs probably would show the best result either.

I meant to say "wouldn't"...