Circular plate - non-linear analysis

[vultur77]

Hello everybody,

I have a circular plate structure subjected to a uniform pressure load. The plate can be regarded as a membrane and it is clamped around the circumference (the first "circle" of nodes has all 6 DoFs constrained).
I ran a linear analysis and I got high displacements in comparison with the tickness of the plate. Now I am trying to run a non-linear analyis with Nastran but I am facing some convergency problems.
Is anybody out there who can point me the right direction?
Where can I find on Roarke a set of formulae which describe my case?

Thank you all in advance.

 

[rb1957]

i think the plate is working like a membrane but you've modelled it with plate elements, right? (to distribute the pressure).

i think you need to look into a large displacement analysis, something like Marc.

the old irish stresser tim O'shenko "plates and shells" will tell you more of this problem than you'll want to know. basically you're looking for a balance between plate bending and membrane tension to react the applied pressure.

 

[prex]

You might look in the first site below, under Plates -> Large defo -> Solid circular pl. -> Clamped (or Clamped&held) -> Unif.load (or go directly here).

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes and launchers for fun rides

http://www.levitans.com

: Air bearing pads

 

[vultur77]

Thanks for the insight rb1957.

Yes, I am using CQUAD4 elements to simulate the structure.
I am already taking into account large displacements and follower forces but, as I said, I cannot reach convergence in SOL 106.

I will take a further look at Timoshenko..didn't know he was irish though ;-)

 

[vultur77]

Thanks a lor prex!
I will take a look at the link you provided.

 

[rb1957]

i'd rerun SOL106 with less pressure and smaller steps till you get a converged run (there's no reason it shouldn't converge)

 

[vultur77]

Splitting the load in several subcases could be another approach.
Thank you for the hint rb1957.

 

[Denial]

If the plate can be truly "regarded as a membrane", then its bending stiffness can be completely ignored. (And, as a consequence of this, it will make no difference whether the edge is supported "clamped" or "pinned".)

A circular "membrane" plate acted upon by a uniform pressure acting transversely to its (displaced) surface will deflect into the shape of a spherical cap. The problem is now fairly trivial.

We have the following three known quantities: plate thickness t, plate radius r, and applied pressure loading p. Our unknowns are: radius of resulting sphere R, central deflection of plate d, and the membrane stress in the plate s.

The geometrical theorem about the intersecting chords of a circle give us
r^2 = d(2R-d)
which, for the relatively small d values you would expect in an engineering problem simplifies to
r^2 = 2dR

The plate has been uniformly stretched in all directions such that a line on its surface whose length was r now has a length of
R[arcsin(r/R)]

Imagining the resulting spherical cap extended to being a full hemisphere leads to the required equilibrium equation for the plate stress
s = pR/(2t)