The reference on analytical solutions of plates (any shape) as follows,

 A. W. Leissa, Vibration of Plates (Scientific and Technical
Information Division, Office of Technology Utilization, NASA, 1969)

Same author has also a book "Vibration of Shells" by NASA.

Regards,

Gokhan Percin

On Thu, 30 Jul 1998, WJ Karl wrote:

>  Dear colleages,
>
>  I am looking for an analytical solution to calculate the deflection
>  and the stress/strain behaviour of a clamped circular/square or
>  rectangular membrane. It seems there is no complete analytical
>  model for this published (especially in the rectangular case) and
>  everybody uses FEM instead.
>
>  I am looking for a plug-in solution able to do the following (yes,
>  I am optimistic ..) :
>
>  + any geometry/aspect ratio (rectangular case) can be calculated
>  + deflections bigger than membrane thickness are valid
>  + deflection and strain/stress values as function of position
>
>  Any hint appreciated. Please ... don't just mention Timoshenko.
>
>  Thanks,
>
>  Werner.
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