Today's Mechanical Engineering Question

Today's Mechanical Engineering Question

I found this page that tells me that the deformation of a member is equal to the force times the length divided by the Young's modulus, and again divided by the cross section of the member. The application is I am trying to figure out how much deformation a sheet of metal (probably aluminum) of a particular thickness will suffer when a particular weight is placed on it, said weight being evenly distributed across the entire surface. When the surface if parallel to gravity would seem like the most severe strain, so I can use this as my worst case.

I suspect that the equation looks something like:

F = pressure in newtons (kg * 9.8)
L = width of the sheet in meters
X = thickness of the sheet in meters
Y = Young's modulus for the material in newtons/square meter

D = FL/Y/X

If the force were exerted over only a small part of the sheet, the equation would be more complicated (and I suspect the deformation would be more severe).

Any hints would be appreciated. I'm trying to get the minimum thickness of aluminum sheet for the mirror cell to reduce cost, weight, and the difficulty of cutting the parts.

UPDATE: A reader points me to this explanation of determining deflection intended for those building model railways. It's still a linear situation where I am looking at a circular situation, but I suspect that treating the diameter of the circle the same as a rectangular beam is probably pretty close.