# Expansion of a thin elastic disk under uniform pressure on both sides

What is the radial expansion $$\delta$$ of a thin elastic disk homogeneous in all directions of thickness t under a constant uniform tension T pressing on both sides, like in the picture? e.g. The tension could be due to a uniform pressure. I suppose that it can be computed from the strain $$\epsilon = \frac{2 T}{t E}(1-\nu)$$ obtaining $$\delta = \epsilon r$$. Is this correct?

Any good suggestion for a reference book? I need to compute the same for a truncated sphere (a sphere with a hole and one with the hole covered by a flat end).

• By tension do you mean compression? Does the disc have the same characteristics in all dimensions? Jan 31, 2022 at 17:45
• Hi Solar Mike, yes homogeneous uniform compression on both sides, perpendicular to the surfaces. Same characteristics of the disk in any direction. Feb 1, 2022 at 10:45
• Then you should edit paragraph 1. Feb 1, 2022 at 10:55

The arrows show compresion. But it dosent matter much. only signs change.

If we consider the disk as a section of a bar its axial deformation is,

$$\delta= \frac{PL}{AE}$$

$$\epsilon= \delta/L$$

• P = stress

• A = area of the disk.

• $$\nu=$$ poison's ratio

and its orthagonal chenge is $$r_{final}=r\_{initial}*\nu*\epsilon$$

if the stress on the disk is tension the diameter will decrease, if it is compression it will increase.

• Thanks kamran! After some thinking, it makes sense. Feb 1, 2022 at 11:37
• @adras81, if it answers your question please check it as accepted so others can use it. thank you. Feb 1, 2022 at 15:39