Rectangular Plate, large deflections
Rectangular Plate, large deflections
(OP)
I am looking into stresses and deflections of relatively thin (span/thickness approx 300) rectangular plates (clamped against rotation and somewhat rigid in the plane of the plate along the perimeter of the plate). I read that when the deflection is in the order of the plate thickness (or above), that some finite element assumptions no longer apply. I want to consider support of uniform load carried by not only plate bending, but also membrane tension. The membrane tension I would be like to consider is the same as what supports a trampoline canvas (and it is not plate bending). Is there an algoithm that will handle this, or a short routine, possibly mathcad? I do have SAP 2000 and know that with non linear large deflection elements that this can be solved, but would rather input my variables (two widths, plate thickness and properties, and uniform pressure).





RE: Rectangular Plate, large deflections
You are right when you say that the normal assumptions wont apply. Can you try modeling it by using a general Finite Element Package? Just a thought.
amar
RE: Rectangular Plate, large deflections
If there is a local university library, I would check there. The specific form governing plates is the bi-harmonic equation. From what I understand, specific solutions to that equation have been the subject of doctoral dissertations. I think there would be a pretty good chance that your solution is out there.
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Joseph K. Mooney
Director, Airframe Structures - FAA DER
Delta Engineering Corporation
RE: Rectangular Plate, large deflections
RE: Rectangular Plate, large deflections
RE: Rectangular Plate, large deflections
Sorry, a sheet for large deflections of bent rectangular plates is not yet available there.
prex
http://www.xcalcs.com
Online tools for structural design
RE: Rectangular Plate, large deflections
Roarks Formulas for Stress and strain has a table for most edge conditions that can be programmed in to a spread sheet.
I have the 5th edition and the table is on page 408. The only problem with the table is that it only gives the max. membrane and bending stresses and its location which may not be at the edge but most likely is at the center of the span.
RE: Rectangular Plate, large deflections
http://www2.nttc.edu/leads/
Contained in this site are NASA tech briefs.
Look up GSC-13561 and GSC-13367
These are documents with derived formulas for Deflection and Stress in Preloaded Rectangular (and Square) Membrane.
I just finished a problem where I used this information to determine the necessary preload on a thin stretched mylar film. The equations are based on the strain energy theory which is the same as the Timoshenko formulas. To simplify the derivation, Timoshenko formulas assume a Poisson ration of .3. The NASA formulas make no material assumptions.
RE: Rectangular Plate, large deflections
Shaggy18VW: I tried to get the two tech briefs you mention but cannot find them on the NASA website. Could you please give me a little more direction?
RE: Rectangular Plate, large deflections
"Fixed" means the edge can't move or rotate in any direction. In this case "not fixed" means the edge can rotate.
"Held, not fixed" also has to mean that the plate is supported vertically at the edges.
RE: Rectangular Plate, large deflections
Held not fixed gives the largest deflection out of the table on ROARK 5 p 408. Held and riveted is next. Held and fixed is substantially the least deflection.
If Held, not fixed is rotation but no translation (vertically or horizonatlly). What is held and riveted?
RE: Rectangular Plate, large deflections
David R. Dearth, P.E.
Applied Analysis & Technology
RE: Rectangular Plate, large deflections
Unfortunately your condition is not provided by Roark (it would be called 'not held, not fixed').
Check from time to time the site below: large deflections of rectangular plates are due to come soon.
prex
http://www.xcalcs.com
Online tools for structural design
RE: Rectangular Plate, large deflections
However this doesn't change much in the conclusions.
prex
http://www.xcalcs.com
Online tools for structural design
RE: Rectangular Plate, large deflections
In regards to the Nasa Tech briefs, go to the site listed in the above message. You will need to become a member (free, just fill out the form). Once in, you can download technical articles that appeared in print as NASA Tech Briefs. The above mentioned numbers can be input into the "case number" field. There is a selection as to which format you would like. The one you'll want is: "View electronically a NASA Technical Support Package (TSP) with more detailed information related to this technology if one is available."