Shear force increase near hole in out-of-plane loaded slab

[maskarp]

Hello everyone,

I have a few questions regarding holes and shear forces in FE analyses of slabs that I was hoping you could help me answer.
To better illustrate the problem, I put together a small FE example (please see the attached picture).

FE EXAMPLE:
- a rectangular slab is simply supported at all edges
- the slab is loaded out of plane by a uniform surface load
- the slab is modelled using shell elements (i.e. 6 DOFs/node)
- results show the shear force variation along a section of the slab

QUESTIONS:
A) Why does the shear force increase in the region of the hole? Is this only a result of some singularity problem in the FE analysis, or is the increase to be expected in reality?
B) Why is the increase in shear force greater in the region of a small hole than a large?
C) Why would you / would you not design a concrete slab for these peak values in shear force?

Suggestions on where I could read more about this phenomenon (preferably online resources) are also much appreciated.

 

[keyen]

I wonder if that's a result of stress concentration. Can you post a result of the von Mises stress in the same manner? Does anyone have any opinions on the matter?

maskarp: what software did you use for that analysis?

 

[keyen]

After running a couple studies myself, I think this stress peak is the result of a singularity. Any opinions on how to handle this sort of thing? Is removing the small hole the answer?

 

[Denial]

I do not think this is caused by any sort of singularity.

I have reproduced similar anomalous shear results using the Strand7 program.[ ] My guess (note guess) is that it is because nearly all shell element formulations are targeting bending moments rather than transverse shears.[ ] Remember that plate bending moments are a linear combination of the three second derivatives of transverse displacement with respect to position (d²/dx² & d²/dy² & d²/dx.dy), whereas the transverse shears are a linear combination of the four third derivatives.[ ] Thus the shears will tend to be an order of magnitude less accurate that the bending moments.[ ] This problem will be exacerbated as your element shapes deviate from the ideal shape of a pure square, which in your meshes happens as you get closer to the hole, and which happens more severely with your smaller hole model.

If I am right that the problem is intrinsic to the element formulation, then the problem should diminish as you use a finer and finer mesh.[ ] On the other hand, if the problem is caused by a singularity then it will get worse with a finer mesh.[ ] I cannot perform this experiment on my model because I am restricted to the Demo Version of Strand7, which is limited to problems containing less than 100 shell elements.

You might need to use what looks to be a ludicrously fine mesh before the problem goes away.[ ] You can lessen the resulting problem sizes by taking advantage of the double symmetry, and modelling only a quarter of the slab (but this would require you to have your line of interest along a line of element boundaries rather than across the middle of a line of elements).

If anyone does this experiment, please report back to the forum.