# Finite element analysis problem

1. Mar 14, 2005

### brewnog

Hello all,

I've been trying to model a plate under uniform tension using FEA techniques (in ANSYS). The plate has a circular hole in the centre, and has two axes of symmetry so I've created a mesh based upon the 'top right' quarter of the plate.

I'm pretty sure I've done everything right, the mesh looks good, my boundary conditions are sound, I think it's all good. I've constrained the base, and applied a static load to the 'top' edge. I'm solving for the local stresses (in X and Y directions) in the plate.

However, when I've run the simulation and obtained my values (which do appear to be in the right ball-park), my answers become further away from the exact solution the more I refine the mesh. I can't understand this!

In all fairness I'm really not up to speed with my FEA, any help would be a big bonus!

Cheers.

2. Mar 14, 2005

### Staff: Mentor

Is there any part of the stress distribution that agrees with the exact solution? Or, is the distribution shape OK, but the magnitude off?

Is the mesh size uniform, or is variable with large cells away from the hole, and smaller cells near and around the hole?

Are the stresses off, or the strains, or both?

Are the stresses limited to the yield stress?

3. Mar 14, 2005

### kashoo

esults very much depends on the type of element u chose for this particular analysis...plz take a look again on material library to see specific properties of the elements......like in 2D elemnts u will have to select plane stress with or without thickness ....
Selection of element then the theory of failure (according to which u see ur results) are important factors....
Most of the time DIstortion Energy Theory or MAximum Shear Stress Theory coincides with our results...

Design Needs Team Work (kashoo....Mechanical-Boy^^)

4. Mar 15, 2005

### PerennialII

Could emphasize first on the element type ... if there is some numerical instability or locking going on the results might be going "the wrong way" with mesh refinement. Then naturally if the analysis is elastic-plastic we've got another set of issues which may cause problems.

Would think the analysis itself be ok, you only need the symmetry bcs and applied loading, so there shouldn't be anything fundamentally wrong in it.

5. Mar 15, 2005

### brewnog

Thanks for the replies!

My stress distribution is of the right shape, it's just the magnitude of the values which get "worse" as I refine my mesh. The mesh isn't uniform; there are smaller elements around the hole, but the further away elements aren't all that much bigger. I'm doing a plain stress analysis, because the plate is relatively thin. Both stresses and strains are in the right ball-park but as I said, they diverge from the exact solution when I refine my mesh. The stresses are not limited to the yield stress, I think this plate is going to fail anyway.

My elements are elastic quads with 2DOF.

Thanks to all!

6. Mar 15, 2005

### PerennialII

If you're still interested ... I suppose a characteristic measure of element size could be element side / hole radius (or diameter) or element side / hole ligament .... what order is one of these in your model ? And while at it, what % from analytic is the deviation as a function of mesh refinement.... These could be used to assess whether the behavior is "normal". The elastic quads in ansys are really robust as far as I know so this is actually quite interesting.

7. Mar 15, 2005

### brewnog

Well, I've not got the model in front of me, but I would guess that the element sides are probably to the order of 50 times smaller than the hole diameter. This isn't gonna sound very technical, but when I doubled the number of elements in the mesh, the solution diverged by possibly 25% of its original value, when beforehand the solution was near enough (within a few percent) to the analytical value.

I'm pretty flummoxed, but I've got too much work on at the moment to be concentrating on this! Why do they wait until the last 6 weeks of my degree course to pile on four projects?!

8. Mar 16, 2005

### PerennialII

Yeah, the piling up is one of those wonders never ceasing to amaze ....

I wouldn't have though you could find this sort of a "concentration" problem in a L-E analysis (it really shouldn't have the ability to perform such in a sound implementation) .... 1/50 of hole diameter is pretty small though (scientifical, yeah!), but still ... weird.

9. Mar 16, 2005

### brewnog

Ah well, as long as there's nothing obvious that I've overlooked. I had a word with the guy in charge and he pointed me in the direction of some useful library references, if I get chance to have a look I might come back and enlighten you all! But it's been bumped down the priority list one more place!