Plate Bending FEM Convergence Study Vs Theoretical Mc/I
Plate Bending FEM Convergence Study Vs Theoretical Mc/I
(OP)
Dear Friends, I am in the process of double checking a simply supported 10" x 4" plate, supported at the 1.0" from the short edges. The edges are only constrained along TZ. A weak spring is used right in the middle to avoid any fatal errors. Then I used three different mesh sizes to look at the convergence of the normal stress. I have attached the model.
The plate is 0.25" thick and the applied load is 1000lb along -Z.
When we do a simple bending stress calc, Sigma = Mc/I, we get 48ksi.
In the model however (looking at the shell normal-X bottom output vector), it is close but higher than theory for the fine mesh, and the coarser mesh is closer to theory.
So I was wondering what you guys think about this. The goal is to use mesh convergence and hopefully get closer to the theoretical Mc/I at the middle of this plate.
The plate is 0.25" thick and the applied load is 1000lb along -Z.
When we do a simple bending stress calc, Sigma = Mc/I, we get 48ksi.
In the model however (looking at the shell normal-X bottom output vector), it is close but higher than theory for the fine mesh, and the coarser mesh is closer to theory.
So I was wondering what you guys think about this. The goal is to use mesh convergence and hopefully get closer to the theoretical Mc/I at the middle of this plate.
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RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
Again, just a wild guess based on your description.
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
There are three mesh size based groups in the model, the contour plot levels adjust automatically when you look at each active group, assuming you have done this in FEMAP.
I am not sure if I follow what you said but may be I am misreading it. The support conditions are the same for all three mesh sizes and they are based on geometry.
All associated nodes in each mesh size are constrained (the constraints and loads expand to the nodes from geometry) in the three different cases, no problem.
See the attached picture.
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RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
b = 4.0"
h = 0.25"
c = h/2 = 0.125"
I = bh^3/12 = 4*0.25^3/12 in^4
Mmax = PL/4 = 1000*8/4 = 2000 in-lb (simply supported beam, ROARKS)
Bending Stress = Mmax*c/I = 2000*0.125*12 / (4*0.25^3) = 48,000 psi
This should be the value that the FEM normal stress along X needs to match. Basically the top and bottom fiber normal stress Sigma X which.
Its not like the results are way off, but I am looking for a meaningful convergence of the FEM results with mesh size refinement, which I am not seeing in the FEM unless I am missing something.
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RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
The load is applied on the full width as well 250 lb/in, as a running load.
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RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
www.stressebook.com
Stressing Stresslessly!
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
Corus/s10 have a pretty good idea too, but I'd expect a point load singularity to give a pretty high stress, not just a few percent error.
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
Good points though. I did notice an hourglass type of contour, it makes sense now based on the cupping you mentioned.
In the version I have it is Section 8.11, Beams of Relatively Great Width. Thanks for pointing it out. Its more complicated than I thought.
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RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
What you are missing is that in plate theory (you are using plate theory in your model) you need to account for lateral constraint due to Poisson's ratio. The effective section moment of inertia has to be divided by 1-ν2=0.91 (for ν=0.3) with respect to the one for a beam with the same section.
So your stress is closer to 53,000 psi than to 48,000. Does this give a better picture of the convergence with finer meshes?
prex
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RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
Timoshenko gives a reduction of 0.988 for max stress in a uniformly loaded plate with your proportions (b/a=2), as compared to a very narrow plate that has the same stress as a beam. Didn't find any treatment for a center load like yours.
So I can't explain your result, would need more data and results.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
There is the transverse bending stress induced due to the anticlastic curvature effect = poisson's ratio * longitudinal bending stress Mc/I
If rho is the radius of curvature after bending:
We have 1/rho = M/KEI
Where:
rho = radius of curvature
M = Max moment PL/4
K is the factor in the table in ROARKS based on poissons ratio Vs b^2/(rho*h)
I have 0.33 for Poisson's ratio
But how to calculate radius of curvature rho?
Once I have that, I could get the combined max moment and use it in Mc/I to calculate the maximum stress, that is the plan at least.
In the FEM, I could clearly see the anticlastic curvaure effect in the deformed shape. See attached.
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RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
http://members.ozemail.com.au/~comecau/quad_shell....
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
www.stressebook.com
Stressing Stresslessly!
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
The analysis was done in Strand7 with a Poissons Ratio of 0.25, but I would expect results to be close to identical from any other package (using the same PR).
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Plate Bending FEM Convergence Study Vs Theoretical Mc/I
So in real life, there should be a higher stress at the edges than at the center due to the anticlastic curvature effect, but the Roark's table is for the average stress.
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