Pressure between a membrane and a solid body

[wiyosaya]

I would like to understand this a bit better, so I am looking for a reference to refer to and not necessarily an explanation in a reply.

I have a non-porous membrane of a compressible material wrapped around a solid body. I then draw out the air between the membrane and the solid body. I want to understand the transmission of the pressure from the outer surface of the membrane to the surface of the solid body particularly how the thickness of the membrane affects the transmission of pressure from the outer surface of the membrane to the surface of the solid body.

Is there a reference work that will help me understand this? I have searched using various search engines, but so far, I have been unable to find a reference that helps me understand the physics involved. Perhaps I am using the wrong keywords.

Thank you.

 

[Nidum]

If it is truly a membrane and there are no other loads acting then applied stress on the outside and reaction stress on the inside will be almost exactly the same .

If the membrane is replaced by solid tubes of increasing thickness then the tubes become progressively more self supporting and progressively there will be less reaction stress on the inside .

Quite simple calculations will give you actual answers for specific problem configurations .

Beware though that whilst analysing this type of problem is not difficult getting accurate answers requires knowing for certain what the class of fit of the tube on the bar is .

 

[Chestermiller]

Is the surface of the solid body curved? Is there friction between the solid body and the membrane, or is the membrane capable of easily sliding on the surface, even under normal load? Do you have any idea what the mechanical properties of the membrane are, in terms of stress-strain behavior?

 

[Nidum]

If the body has a non simple surface geometry and particularly if there are any concave areas then the analysis becomes much more difficult since the membrane may span the concave areas rather than bedding down completely when the air is pumped out . External pressure then causes that region of membrane to be in tension and that tension may affect adjacent areas of the membrane . Friction forces then become relevant because they can be large and hold sections of membrane in place and so localise tension effects or they can be small and let sections of the membrane slip and so cause tension effects to spread over larger areas .

If you could answer @Chestermillers questions and ideally sketch one of the body shapes of interest then we could give more definite answers .

Some specific reference material might exist somewhere but with these types of odd problem it is usually easier - and often more instructive - to analyse them from first principles .