Calculating Membrane Deflection of Clamped Rectangle

[pavel123]

Hi,

I have a rectangular membrane (material: laminated aluminum like food packaging). The membrane is clamped around perimeter. From one side I have uniform (gas) pressure.
The membrane is constrained from another side with rigid plate and, hence, do not deflect. But I can measure force that membrane pushes on the rigid plate and convert the force into pressure that I assume to be equal to pressure from another side of the membrane.
I need to convert this pressure into deflection of the membrane like if the membrane do not have the rigid plate from one side. At least in one point on the membrane surface (centre).
The deflection is not small - it is several (many) thicknesses of the membrane.

What equation should I use?

 

[CWatters]

Google something like "Deformation of a Membrane Under Pressure" ?

 

[Chestermiller]

You need to know the stress-strain behavior of the membrane at large deformations, and you need to do a differential force balance on a representative "window" of membrane. Then, you need to combine the two to calculate the deflections and stresses in your membrane under field conditions. Just characterizing the stress-strain behavior of the membrane is a big job, particularly if it is viscoelastic. All this is not a simple task. I suggest hiring a consultant who has experience with this type of thing.

Chet