Relative strength of a dome Is there a rough way to determine how the height of a dome affects the load that dome could support? For instance, assuming the bases of two domes are 24" in diameter, and one dome is 2" high while the other is 4" high. Is there a way to understand how much stronger the 2nd one is compared to the first one?
 A: The study you are looking at is falls under loaded annular disks and flat round plates with references here and here as well as the venerable Roark formulas for Stress book. Structural engineers design domes all the time and here is a reference to their calculations. They seem to like Conoidal Domes.
However adding the complication of a curved plate, or dome shaped, is doable analytically, yet very complex to carry out. Even for the flat plates the formulas are quite involved.
So at this stage you are left to do a more thorough web search for thin dome stress values, and I am left with some notes from engineering experience:


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*If the dome is flat, then any vertical load is going to tend to pull-in the supports causing tensile stresses near the edges of the dome, as well as near the center where the load is applied.

*When curvature is added, additional compressive stresses are added near the supports canceling out the tensile stresses making the structure stronger. 

*When the curvature is too much (dome is too high) you are going to start to push out the material at the supports making it weaker.


So there is an optimal dome shape, but calculating it for any real life case is going to be challenging. If you are serious about it, you can either conducts tests of different designs, or hire an engineering consultant to do a Finite Element Analysis design study to find the optimal design. Check your local university, as they seems to have an abundance of grad students with nothing to do in general.

BTW: Have you considered a conical shape which is going to be stronger than a curved shape when a single load is applied?
