Learning Forum

[SteveSmith]

Hallo,

I am investigating the influence of different roots of the cantilever beam. Unfortunatly, i cann´t validate any of my results becaurse of singularities in the coners of the fixed support. Is there any workaround to get finite results despite the singularity?

[peteroznewman]

The way to study a cantilever beam is to have a large blend radius at the base of the beam where it intersects a larger plate or solid block volume. Put the Fixed Support on the side faces of the solid block so that those faces are separate from the face of the block where the beam base intersects the block with the large blend radii.
Also, don't apply the force to the edge of the tip of the beam, apply it to the whole end face.

[SteveSmith]

Did you mean some thing like this?

[peteroznewman]

Yes exactly. Now you have a shape where the peak stress converges on the true value.

[SteveSmith]

results from Ansys are still much higher than those from algebraric calculation: 262,9 kPa. (~13% more). With more area moment of inertia, we get more tension.

[peteroznewman]

Please show details of the algebraic calculation. I expect it does not include the effects of the blend radius.

[SteveSmith]

I guess that's true. I thought that the blend radius would be interpreted as an increase in the area moment of inertia. To get an estimate in the first approximation, I calculated the bending beam with Bernouli beam theory (Sigma=M/W) without rounding at the root. H=B=378mm; L=2268mm(up to blend edge); F=893N; Radius=189mm; L_max=3005mm
Using Bernouli beam theory, the maximum bending stress at the root should be smaller.

[peteroznewman]

That equation is the root stress on a uniform cantilever. If you ignore the stress concentration and probe the stress on the continuous edge opposite the start of the blend edge, in the orange color band, what is that stress and what answer do you get from the equation?

[SteveSmith]

Orange color band from your screenshot or near normal stresscon centration in my last screenshot?
"what is that stress and what answer do you get from the equation?"
Isn't it a kind of normal stress averaged over the area? And yes the normal tension on the center line is closer to the algebraic solution than that from concentration.

[peteroznewman]

The blend creates a stress concentration. Algebraic equation computes the normal stress on a beam that has no stress concentration.

[SteveSmith]

I tested it extensively and then extended my sample a little. Bernouli's bending beam theory provides bending stress of 2,437 * 10 ^ 5 Pa. Avarage accuracy 2,4 %, good!
It may sound a bit stupid but, may you advise me to use a method to determine the stress concentrations algebraically / analytically.

[peteroznewman]

It's a good question. There are figures of stress concentration factors for many common geometries. Here is one reference.
https://www.ux.uis.no/~hirpa/6KdB/ME/stressconc.pdf

[SteveSmith]

Thank you very much!

I have tried various things with bending stress concentration calculation. That's why a late reply.