Graduate How much thickness for sphere to withstand atmospheric pressure?

[phys_hep_81]

TL;DR

Hollow sphere withstanding the atmospheric pressure

Imagine a hollow sphere made of a material with high elasticity constant(e.g. steel). How much thickness should it have to prevent it from crushing when the air inside is pumped out?
Is it valid to use Lame solution to quantify the answer? What about Finite Element Analysis?

 

[Chestermiller]

This would be a stability problem involving buckling.

 

[Lnewqban]

Manufacturing such sphere would be a difficult task.
The material would have internal stresses and would be unevenly deformed; therefore, even shell thickness and welds and perfect sphere shape would be difficult to achieve.
If built, the calculations should allow a generous safety margin.

Please, see:
https://www.sciencedirect.com/science/article/pii/S0020768318302592#:~:text=The classical buckling pressure of,shell thickness and its radius.