Accuracy in FEA

[100868]

Without having any knowledge of the FEA "inner workings" I've tried to model a rectangular beam with solid elements
( Thetra4 ) in Cosmos. The beam is fixed at one end and loaded at the other. To my surprize the deflection appeared to be proportional to the number of elements.Why would a finer mesh show increased deflection ? And how does one know when to stop ?

 

[GregLocock]

Why would a finer mesh show increased deflection ?

Because a given FE element type can only deflect in certain ways, and is generally (always?) too stiff in the other ways.

And how does one know when to stop ?

Plot end deflection against mesh density. Decide what limit it is approaching. Check that this is the same as the analytical solution.

If it isn't, do some more experiments. Think about the limitations of (1) simple beam theory (2) The FE approach.

Good questions both, and we're often asked to pay for analyses where these questions haven't been asked properly. The unhappy analyst gets sent away to do the job again. In the real world ask your customer if he has any criteria on mesh size. We have manuals on this sort of thing - roughly speaking a car's body would be meshed at 10 mm to get deflections right, 3 mm to do a dynamic or stress analysis, and 1 mm for non linear results.







Cheers

Greg Locock

 

[100868]

Thanks !
I was trying to model a beam 0.1 by 0.1 by 1m . What surprized me was the fact that the deflection was almost proportional with the number of elements generated and that in 5 or 6 successive tests starting with 40 elements and ending with 12000 there was no indication of convergence. None. This is strange. Makes a newcomer wonder if this FEA really works...Also the closest result was 4 times the theoretical one.

 

[GregLocock]

I think you have some more problems, not just mesh density. For what it's worth even this cynic acknowledges that FE does work, but an insight into the likely behaviour of your structure is essential to a successful project.

In your case I think that beam elements were the wrong choice to do this experiment on - would you really expect a beam that is .08 mm long, by 100 mm by 100 mm, to obey classical beam theory? Noooo. I wouldn't mind betting your best result was with between 4 and 10 elements. With such a stubby cantilever I'd expect shear to be somewhat significant, so even the beam theory might be a few percent out.

Anyway, keep experimenting, and read some books. Other threads have recommendations.
Cheers

Greg Locock

 

[100868]

Thanks Greg !

My beam was 1 meter long and you are right the best result came from 10 elements. I'm a complete idiot when it comes to these things. If you could recomend a good book please do.
After reading the DOC in Cosmos I was under the impression that increasing the numer of elements was the way to go. And by the way, I used 3D thetra10 elements.

Thanks again,

Alex

 

[austim]

If you are using 3D solid elements, then you may find that improving your element shapes will get you close.

I suggest that you try keeping all of your elements pure cubes. ie, start with 10 elements (100mm cubes), then go to 80 elements, (50mm cubes), then to 640 (25mm cubes), then to 10,000 (10mm cubes).

By then I would expect reasonable convergence (but since I have never used 3D solid elements, I could well be very wrong indeed).