Appropriate boundary conditions: over- versus under-constraining 1

[nmk321]

I am reading an interesting book entitled <i>Building better products with finite element analysis.</i> In the chapter about boundary conditions, the authors discuss what would be appropriate boundary conditions applied to a simple chair seat where the legs meet the seat, such that the model is not over- nor under-constrained, when simulating a uniform static load applied to the surface of the seat (i.e., a person sitting on the seat). Each chair leg connection patch on the seat is represented by a number, from 1-4, as depicted below.
_____________
| |
| (1) (2) |
|//////////////////|
|//////SEAT//////|
|//////////////////|
| (3) (4) |
|_____________|


The authors state that the following boundary conditions at the specified locations would be ideal, as the possibility of rigid body translation and rotation is eliminated, while the bending of the seat is still allowed by in-plane translation:
Location 1: Constraining all three translational DOFs.
Location 2: Constraining x and y translations.
Location 3: Constraining z and y translations.
Location 4: Constraining y translations.

I am new to finite element analysis, and am trying to justify to myself these boundary conditions. I can't quite figure this out yet, as I don't yet have a firm grasp on the principles of boundary conditions. I don't understand why all three translational DOFs at leg 1 have to be constrained. Why wouldn't just a y translational constraint suffice instead? Any insights into this problem I would greatly appreciate.

Thank you,
Nathan

 

[rb1957]

IMHO, the model would be over-constrained. you need y at all 4 legs ('cause it's sitting on the (level) floor). you x and z at one leg (to locate the chair on the floor). you need x (or z) at one of the other legs (to stop the chair rotating about the fixed leg) ... your post has two ways to react rotation about the fixed leg, therefore it is redundant.

 

[GBor]

The described boundary conditions allow the model to do this:

___________________
| | |
| (1) (2) | |
|/////////////| |
|////SEAT/////| |
|/////////////| |
| (3) (4) | |
|_____________| |
| |
| |
--------------------

The authors have made some assumptions (generally based on some engineering judgement) about how the chair will deflect and have restricted the chair to move in accordance with those assumptions. I don't think we can say it is over or under constrained based on their assumptions. I view their boundary conditions to be reasonable IF I assume that their chair is sitting in the corner so that one leg would push in to the corner (translation constrained in all three directions), one leg slides along one wall (two directional constraints), another leg slides along the other wall (also two directional constraints), and the fourth leg is allow to slide out in to the middle of the room. Is this correct?

Well, generally, I think of all four legs being allowed to slide equally outward, but you have to limit some inplane "sliding". This is often done with symmetry (modeling 1/2 or 1/4 of the model). Using symmetry, you typically assume that the center node displaces vertically.

JohnHors has a very good paper on using minimum boundary conditions in an FEA model. If he reads this over the next day or two, perhaps he can point us to the link again.

 

[johnhors]

The link that GBor is refering to is this:-

http://www.etm-project.com/Roshaz_Art_1a.htm

I have also attached the original pdf document which has clearer images.


There is also useful discussion in this thread:-

Minimal support - 2D Axisymmetric Model
thread727-215433

http://www.eng-tips.com/viewthread.cfm?qid=215433&page=3

 

[corus]

If the seat is in the XY Plane and the legs are in the Z direction then I'd use quarter symmetry to give me restraints in the X and Y directions (and reduce the model size). You then only need a Z restraint at the leg, that is if you decided not to model the leg. It would have to be a point restraint though as imposing Z restraints over the circular region of the leg would impose a local rotational restraint there, which would not strictly be correct. The point restraint of course would give you 'infinite' stresses at the leg which may interfere with the general stress distribution in the seat. Personally I'd be just as worried that the leg would be break as would the seat, so I'd model the leg too. The base of the leg could be allowed to slide (frictionless) and restrained at one point, and ignore the 'point' stress you'd get there, or restrained in all 3 directions.

corus

 

[GBor]

___________________
| | |
| (1) (2) | |
|//////////////////| |
|//////SEAT//////| |
|//////////////////| |
| (3) (4) | |
|_____________| |
| |
| |
|________________|

My original picture didn't come out quite right...I meant something closer to this.

 

[rb1957]

not much better ... the HTML converts the fixed pitch text into something else ... but i think we unsderstand what a chair looks like

 

[GBor]

Does a chair in Canada look the same as a chair in the US? What about Japan? Or Siberia? I think next time I will go with an embedded graphic...

 

[nmk321]

I thank you all for your valuable input.

Nathan