I've attempted to read up some on a problem I have, but am essentially unable to go forward. Maybe someone here can give me a direction.
I'm attempting to solve a Kirchhoff Plate problem. A circular plate is simply supported near the edge, but also has a single support at the center.
To a pseudo-first-order, the plate is flat on both sides, but in reality is axisymmetric; not necessarily the same on both sides. The thickness is on the order of 1/40 the diameter, so the shear mentioned by Selke is probably not a problem, I think. The solution given by Kirstein and Woolley seems close, even if it doesn't include shear, provided I can take the limit as n->infinity. However, it only has ring of supports.
The material is, I think, quite isotropic and the downward pressure is uniform (air pressure) across the surface.
I could deal with a solution in either one of two forms. Ideally, I would like to express the solution as a function of the height, relative to the edge support, of the center support. However, I could also deal with a solution where the upward pressure of the center support is expressed as a fraction of pi*q*c^2 (where q is the original downward pressure per unit area and c is the plate semi-diameter).
However, I will also need more precise form of confirmation, I think in some sort of FEA tool that I can use to construct a model. Any suggestions in this direction (hopefully close to freeware) would be appreciated.