FBD to match FEA

[mmar2087]

Hello.
I have a case, that probably is easy to explain, but that I'm stuck on for the moment.

In picture below there are 3 plates connected to each other by guide pins.
The left and right side of the 2 outer plates are fixed.

Blue and red areas are cavities where a pressure is applied.
In this example the forces on the blue cavities are F=10000N and on the red cavities F=4000N

As I see it the result forces acting on the left plate fixture should be Z= +10000N.
The forces acting on the right plate fixture should be Z=-10000+4000-4000 = -10000N.

Trying to verify this with FEA gives result force 10000N. All good so far.
But what happens if the cavities are off centre?

With my simplified FBD, the resulting forces should be the same.
Even if the red area would be increased, as long as its force is below 10000, it shouldn't add to the result force.

Doing a FEA on this example gives a result force of 10500N (25% addition from the 4000N force)
Moving the red cavity down even further, completely off centre (edge to edge) gave a result force of 12000N (50% addition from the 4000N force)

What am I missing?
Thank you in advance for your time.

 

[GrouchyStressedTensePoor]

How does the FEA program measure force? If we think of the applied forces as stresses and stress fields then it makes sense that the stress distribution will not be even over the edges but will instead be higher at the top and lower at the bottom. This would be analagous to having a higher force locally at the top and a lower force locally at the bottom, which would average out to your 10kN. The FEA might then be reporting this maximum force.

Another way to think about it is that the offset forces create a couple that results in an internal moment. The support of the plates along their edges is indeterminate and they will resist roation at the support, they cannot be thought of as pins. The resistance to rotation can be approximated as a couple of unequal reaction forces.

GSTP

Graduate Mechanical Design Engineer
UK

 

[3DDave]

You are comparing a pure series condition to a partial parallel condition.

 

[Compositepro]

Where the cavity areas overlap only the higher pressure cavity contributes to force. The lower pressure cavity would collapse except that it is made of steel. Where they do not overlap the lower pressure cavity adds to the total force. Imagine that the cavities were instead rubber bladders between two plates.

 

[pylfrm]

What am I missing?

Your post does not appear to contain any free body diagrams. Create one for each relevant component of your assembly. If you've done that and haven't found the answer, post the FBDs here. That would probably go a long way toward clarifying your question.


pylfrm

 

[mmar2087]

Hi.
The problem is solved.
It was a boundry condition problem due to over constraining.
Using reaction forces and minimum constraint gives expected result.

Thank you for your advices.