Roark Young Formulas Stress and Strain for curved plates.

[innovative acrylics]

I need to know if there is a formula for calculating the stress and deflection of a curved plate in 4 configurations. See diagrams below. All configurations will be subjected to non-uniform hydrostatic loading. Assume uniform radius throughout the plate.

Edges on 3 side designs are fixed no rotation.
Edges on 4 side designs are simple support with translational rotation.

To date we have been using FEA modeling but need a simple hand calculation to confirm.

 

[innovative acrylics]

convex 3 side support panel

 

[innovative acrylics]

concave 3 side support panel

 

[innovative acrylics]

4 side convex panel

 

[innovative acrylics]

concave 4 side support panel

 

[rb1957]

Roark's reference is work done by Moody with the Corp of Engineers, maybe there's something there. You can find the original paper (which has a lot more data in it) online, google "moody rectangular plates" (seriously).

but why would these panels be much different to flat panels ? unless (of course) you're providing inplane reactions (ie tension along the edges) ... but then they'd be like curved panels (hoop stress).

another day in paradise, or is paradise one day closer ?

 

[MFJewell]

Maybe this?

 

[IRstuff]

Why can't you treat it as a normal cylindrical shell with uniform loading?

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[rb1957]

depends if the edge restraints will react tension.

another day in paradise, or is paradise one day closer ?

 

[innovative acrylics]

Lets first start by saying that these plates will be used in hydro applications.
Depending on the plate type the edge constraint detail is different.
3 side support structures are fixed in all axis along the jambs and sill.
4 side support structures are simply supported at the edges.
We could absolutely use normal cylindrical shell formulas for 3 side support structures that took into consideration a unconstrained top edge.
4 side support structures could possibly use the "roark formula reference 21" however no consideration is given to the base or header constraints.

 

[innovative acrylics]

could someone please reference the "normal roark young cylindrical shell formulas"

 

[rb1957]

check his reference, moody with the corp of engineers ... google "moody rectangular plate"

another day in paradise, or is paradise one day closer ?

 

[MFJewell]

could someone please reference the "normal roark young cylindrical shell formulas"

Is this what you are looking for?