How to calculate deflection of sheet of metal with hole in it.

I need to calculate the deflection of a sheet of metal with load distributed over a limited rectangular region in the middle of the sheet. To make it more complicated there is a hole in the middle of the sheet of metal.

The specific situation is that I have a one inch square aluminum tube with 1/16 inch wall thickness. There will be 3/8 inch round holes drilled in the middle of each of the four walls (each at the same position along an axis running through the middle of the square tube; in other words all four holes are the same distance from the end of the square tube) and there will be rectangular "feet" (21/64 inches by 1.75 inches) inside the tube pressing outwards on all four walls directly over the drilled holes. The feet are centered over the holes and aligned parallel to the length of the tube.

I need to be able to calculate how much the walls will flex/deflect outwards for a given outward force applied by the rectangular "feet."

For me to be able to calculate this exactly would be great. If there is a way to get an approximate idea of the deflection that would also help.

Thanks in advance.