Roark's Flat Plate Equations vs. FEA... what's the deal? 7

[score33]

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.

 

[namklof]

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).

 

[score33]

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

Thanks for the reply.

 

[GBor]

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'.

 

[GregLocock]

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

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IDS]

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/

 

[IDS]

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/

 

[GregLocock]

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

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IDS]

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/

 

[namklof]

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.

 

[score33]

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.