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thick rect. flat plate, circular hole, annular line load, deflection?

thick rect. flat plate, circular hole, annular line load, deflection?

thick rect. flat plate, circular hole, annular line load, deflection?

(OP)
I am trying to determine the maximum deflection for a thick, rectangular, flat plate with a central opening and annular line load about the opening.  The support is fixed along the two short edges.

I have made literature search for an already developed equation that fits this case, and haven't found anything that is close. I can always go to a program such as RISA-3D, but I would prefer an equation to use with Mathcad, if possible.  

Does anyone in our group have a good method for this problem.

Best regards,
          Downeast tech

DowneastTech
Mechanical Engineer
Magnus R & D, Cypress, TX

RE: thick rect. flat plate, circular hole, annular line load, deflection?

Could you give us some of the basic dimensions?

Steve Braune
Tank Industry Consultants
www.tankindustry.com

RE: thick rect. flat plate, circular hole, annular line load, deflection?

(OP)
At this stage, I am doing preliminary work to develop a "generic" procedure.  I wa told that I will be assigned the analysis of a piece of equipment where this particular problem is the central issue. So, no I don't have dimensions as yet.

Thanks for the reply,

             DowneastTech

DowneastTech
Mechanical Engineer
Magnus R & D, Cypress, TX

RE: thick rect. flat plate, circular hole, annular line load, deflection?

I doubt you'll find a canned answer for that specific geometry.  

Are the plate dimensions fixed relative to each other?  IE, always square or 2:1 ratio or something?

Or, is the hole diameter always fixed relative to one or both plate dimensions?

If either answer is yes, you should be able to non-dimensionalize the problem similar to the flat plate formulas in "Formulas for Stress and Strain", so that you only need one function of R/L or L1/L2 to find deflections.  And, in that case, you can run a half dozen different geometries on FEA software to find that function across the range of interest.

RE: thick rect. flat plate, circular hole, annular line load, deflection?

(OP)
Thank you for your input JStephan.  Your approach may be workable because the L1/L2 ratio should not vary, at least I expect very little variation. The Opening will remain about the same size too.  The loads will the variable with greatest range.

 

DowneastTech
Mechanical Engineer
Magnus R & D, Cypress, TX

RE: thick rect. flat plate, circular hole, annular line load, deflection?

You don't mention how thick the plate is, but check if your solution includes shear deflection, which becomes important in very thick plates.

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