Dome Deflection Formula for Calculating Deflection from Point Load

[Tadders]

I am looking for a formula to give me the deflection of a dome if all dome perameters are known from a point load at the center of the dome towards the dome on the convex side. I do not have the Roark book so I need the actual formula, not just a reference.

 

[nvn]

Tadders: Can you provide numeric values for the following parameters, to narrow your question? Your question is currently slightly too generic to be easily answered.

nu = Poisson's ratio.
r = spherical dome mean radius.
t = spherical dome shell thickness.
phi = spherical dome subtended half angle, phi ≤ 90 deg, where phi = 90 deg is a hemispherical dome.
Also, type of edge support, if known (optional).

 

[Tadders]

nvn,
Here is the data:
Material 1070 steel
nu = 0.29
r = 22.08 inches
t = 4.5mm thick
phi = 21.24 degrees
edge support = free to rotate, there will be some lateral restraint for my application but for calc purposes say no restraint, and complete vertical restraint (vertical meaning in the direction of the central axis i.e. if the dome was a roof on a building, the edge could not move vertically).

 

[Tadders]

nvn,
PS to prior post. I am only interested in a point load deflection where the point load is at the center of the dome on the convex side towards the dome.
Thanks.

 

[nvn]

Tadders: I assumed your point load is evenly distributed over a small circular area having a diameter of 4.5 mm. Therefore, the deflection at the center of the load is y = -10.942*P/E, where y = deflection (mm), P = total applied load (N), and E = tensile modulus of elasticity (MPa).

This answer is applicable only if r = 560.83 mm, t = 4.5 mm, nu = 0.29, and the diameter of the circular area of the applied load is 4.5 mm.