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Roark's Flat Plate Equations vs. FEA... what's the deal?
6

Roark's Flat Plate Equations vs. FEA... what's the deal?

Roark's Flat Plate Equations vs. FEA... what's the deal?

(OP)
I started a new topic since this one was closed:

http://www.eng-tips.com/viewthread.cfm?qid=171673&page=4


I'm looking at a flat plate that will be subjected to a pressure load.  The finite element model results were ~15% off of my hand calcs so I'm back to a simple case and I still can't figure it out.

Basic problem I'm looking at in Roark's:

10" x 12" x 0.125" thick steel plate
6.7 psi pressure load
All edges fixed

Roark's results:
stress along edge = 16440 psi
stress at center = 5943 psi
deflection = 0.016 in

MSC Nastran results:
14100 psi (14% off of Roark's)
6933 psi (16% off of Roark's)
0.021" (24% off of Roark's)

Nastran model was run with various mesh sizing, CQUAD4 elements, and all nodes along edges fixed in 123456 directions.

I don't think I'm violating any of the assumptions presented for these tables so why is there such a big difference in results?

I'm not a structural analyst by trade so sorry if I'm overlooking something simple.

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

4
I belive you are looking at von Mises stress.  The values from Roark are normal stresses in either the x or y directions (in the shorter direction of the rectangle).  

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

(OP)
yes... that works... and I feel a little stupid now. I knew it would be something simple.  :)

Thanks for the reply.  

 

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

How about giving namklof a star since his/her response was helpful:

Just click on "Thank namklof for this valuable post!" under the post that was helpful.  Another screen will pop up to confirm.

It's a nice way of saying 'Thank you'.

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

That doesn't explain the difference in deflection though does it?

It's unusual to see an FEM softer than real world.
 

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

I get different values for the hand calculation.  I make the Roarke values:

ymax         -2.22E-02
Sig side    -16440.192
Sig cent    7692.672

Results from my FEA program (Strand7) were:
in the same order as above

4 node 12x10 grid    
-2.35E-02    105.5%
-16370            99.6%
7788            101.2%

8 node 12x10    
-2.30E-02    103.5%
-16190            98.5%
7686            99.9%

8 node 24x20    
-2.301E-02    103.5%
-1.637E+04    99.6%
7.558E+03    98.2%

9 node 24x20    
-2.301E-02    103.5%
-1.637E+04    99.6%
7.558E+03    98.2%
 

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

The Strand7 Verification Manual gives the following results for central deflection in a similar problem (square plate, clamped sides), using a 4x4 mesh of 1/4 of the plate with symmetrical boundary conditions:

Tri3:  -5.3%
Quad4  +4.7%
Tri6   -12%
Quad8  +0.48%
Quad9  +0.48%

So it seems the quad elements are a little softer than the analytical solution in this case.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

Linear FEM should be softer than real world because it ignores the membrane stiffness.

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

Greg - yes, but so does the analytical solution.  I don't recall the derivation of the equations for recangular plates, but I'd imagine they contain some fairly significant approximations.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

As I recall, the analytical solution by Roark also neglects transverse shear deformations which are included in the elements discussed.  If that is true, one could expect a well refined mesh to give slightly larger displacements, as noted by IDS.

RE: Roark's Flat Plate Equations vs. FEA... what's the deal?

(OP)
Thanks IDS, Greg, & Namklof.

IDS, yes, there is a problem with my Roark's calculations posted above.  Not sure what I did, but what you posted is the correct deflection & center stress.

Did a little reading and have a rested mind so things are much clearer now.

Thanks again for the help.

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