Deflection of aluminium plate

1. Mar 24, 2016

lavecchiasignora

Dear Engineers,

I have a rectangular plate (3 x 2 m) made of aluminium (12 mm thickness). I also have a evenly distributed load of 2500 kg spread over the entire plate. How can I calculate the maxiumum deflection at a certain point on the plate? The plate is fixed in all directions on the edges.

Thank you.

2. Mar 24, 2016

SteamKing

Staff Emeritus
How are the edges of this plate supported? Simple supports, fixed supports, what?

3. Mar 24, 2016

lavecchiasignora

Hi, The plate is fixed in all directions on the edges, i.e. fixed. :)

4. Mar 24, 2016

NumericalFEA

One way is to use an analytical solution; you would probably find some useful formulae in the works of Stephen Timoshenko, who published several books on the topic. Another approach would be to use a finite element program, for example like the one described below (the link also contains an example very similar to yours, including stress distribution contours, etc.):

5. Mar 24, 2016

lavecchiasignora

Thanks for your reply. I forgot to write that I shall verify my numerical FE model with an analytical calculation. I have done an numerical but need to verify it now.

6. Mar 24, 2016

Nidum

7. Mar 25, 2016

lavecchiasignora

Those equations are very very complicated. Im just trying to find an simple analytical formula for calculating deflection and stress.. should it be so hard?

8. Mar 25, 2016

NumericalFEA

There is no simple formula for that problem.

9. Mar 25, 2016

SteamKing

Staff Emeritus
Have you tried looking in a structural handbook like Roark's Formulas for Stress and Strain?

You can find a copy online if you search for it. This book is chock full of simple formulas which can be evaluated by a calculator or spreadsheet.

10. Mar 25, 2016

lavecchiasignora

Thank you! Do you know if these formulas can be applied on aluminium?

11. Mar 25, 2016

SteamKing

Staff Emeritus
I don't see why not. Most structural metals are isotropic. The formulas in Roark use Young's modulus and Poisson's ratio to calculate deflection.

12. Mar 30, 2016

lavecchiasignora

Hi again, I have used Roarks equation for deflection of a plate with uniform distributed load and all clamped edges. The answer I get is larger than the palte thickness so these Roark equations do only apply for small deflection theory and not large defcletion theory... Now I need equations for large deflection theory.. any idea how to do it?

13. Mar 30, 2016

NumericalFEA

You have a geometrically non-linear problem, i.e. the membrane forces cannot be ignored, since they contribute (significantly) to the deflections and to the overall stress fields. The way to go is to use a commercial-quality FEA system.

14. Mar 31, 2016

lavecchiasignora

Thank you for your reply... I have already done a FE analysis of the plate, now I need to verify it by hand calculations.. I was thinking that I could use "Large deflection of plates" in Timochenko and calculate (p*b^4) / (D*h) but I get a value of 1600 and the graph only shows values up to 250...

15. Mar 31, 2016

NumericalFEA

Analytical solutions for large displacements mean that the relations between strains and deflections are non-linear. From the mechanical point of view, when the edges of the plate are jammed, non-linearity naturally leads to the fact that membrane (tensile) forces appear, which significantly reduces the deflection. I think you should check if the Timoshenko's solution takes into account the membrane forces in this case. If it does, another reason for the discrepancy may be that Timoshenko and the FEA developers have used different plate theories, for example Kirchhoff-Love and Mindlin theories.

16. Mar 31, 2016

Nidum

You haven't told us what actual deflections your FE analysis and other calculations give but let's say they are of same order as plate thickness .

Deflection of order of 12mm for a plate 3000 mm by 2000 mm by 12 mm thick with more than two tons load on it does not seem unreasonable .

12 mm deflection is only 0.4 % of 3000 mm . Small deflection theory probably gives results of adequate accuracy .

Last edited: Mar 31, 2016
17. Mar 31, 2016

Nidum

Quick calculations using two different methods give deflections of 12 and 13 mm .

If this was a real job I would check the stress levels as well to ensure that they were within safe limits .