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Mult-layered compound pressure vessel design

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I am trying to calculate the stress and deformation of an assembly made of two cylinders with a water filled annulus. The assembly is frozen and the water expands, causing the inner cylinder to shrink, and the outer to expand.

 

To solve the problem, I am trying to write simultaneous equations: The contact pressure and diameter at the interface is unkown, but is equal at each ice-cylinder interface.

 

This approach should work, but I am struggling and would be grateful if anyone has any advice or good references or Mathcad calculations for compound, multi-layer, pressure vessel design.

 

Many thanks,

 

Sam


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