Analytical solution for deflection of plate

Hi all,

I am a third yr undergraduate student of Aerospace Engineering department, IIT Kharagpur.

I have a very fundamental question in strucutral mechanics.

Is
there any analytical solution available for deflection of plate under
distributed load ? The governing equation (for classical plate theory) is well known as shown in the figure. The boundary conditions can be taken as classical boundary conditions. That can be any combination of a) hinged b) clamped and c) free boundary conditions.

If the solution is available, please suggest me the appropiate reference. If the solution is not available, please tell me whether any research is going on that direction.

 
Thanks....