# Explain the Föppl–von Kármán equations

I am a newbe to elasticity.
Could someone please explain to me briefly how the Föppl–von Kármán equations work?
What are we trying to solve for?
Is there some kind of intuition to the way they look?
Are the two terms being subtracted have any significance?
$$\frac{Eh^3}{12(1 - \nu^2)} (\nabla^2)^2 \zeta - h \frac{\partial}{\partial x_\beta} \left(\sigma _{\alpha \beta}\frac{\partial \zeta}{\partial x_\alpha}\right)=P ^2 \\ \frac{\partial \sigma_{\alpha\beta}}{\partial x_\beta} =0$$ Each letter is explained on Wikipedia.

-
So far I figured out the first thing I am trying to solve for is \zeta which is how much the sheet rises or slopes on the y axis, due to the stress on the x axis. But that is not all since there are two equations. –  GuySoft May 18 '13 at 15:50