- #1
roy_lennon
- 9
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Hello. I'm trying to simulate a plate deflection using finite element analysis software ALGOR. Previously I made analytical calculations and I got the maximum deflection like this: (My plate is simply supported on all edges, so I used Navier's Method. Got the theory from Szilard's Theories and applications of plate analysis)
w(x,y) = (16p/[[tex]\pi[/tex]^6]D) [tex]\sum[/tex][tex]\sum[/tex]
(sinm[tex]\pi[/tex]/a)(sin n[tex]\pi[/tex]/b)/[mn[(m/a)^2+(n/b)^2]]
where
p = gC = (9.81m/s^2)(11 kg/m^2) = 107.91
D = Eh^3/12(1-v^2) = (72 GPa)(0.005 m)^3 / 12(1-0.17^2) = 772.32
a = 0.11 m
b = 0.09 m
both sumations go from m,n = 1 to infinity, only for odd numbers.
My plate dimensions are: 110 mm x 90 mm x 5 mm
Young Moudulus: 72 GPa
Poisson's ratio = 0.17
Density = 2.2 g/cc
with this method I get a maximum deflection of 54.82 nm. I also tired Levy's Method and got the same value.
Now, I go to ALGOR import the plate from SolidWorks, write in all the material parameters. set the boundary conditions to all four edges fixed, turn in the gravity in -z and then run the simulation and I got maximum displacement in the center of the plate of 30 nm.
I have made the simulation many times, and I'm sure I've all the right values and still I don't know why this value is different from the one I got using analytical models.
I would be REALLY greatful for any help you can give me.
Thanks!
rgm
w(x,y) = (16p/[[tex]\pi[/tex]^6]D) [tex]\sum[/tex][tex]\sum[/tex]
(sinm[tex]\pi[/tex]/a)(sin n[tex]\pi[/tex]/b)/[mn[(m/a)^2+(n/b)^2]]
where
p = gC = (9.81m/s^2)(11 kg/m^2) = 107.91
D = Eh^3/12(1-v^2) = (72 GPa)(0.005 m)^3 / 12(1-0.17^2) = 772.32
a = 0.11 m
b = 0.09 m
both sumations go from m,n = 1 to infinity, only for odd numbers.
My plate dimensions are: 110 mm x 90 mm x 5 mm
Young Moudulus: 72 GPa
Poisson's ratio = 0.17
Density = 2.2 g/cc
with this method I get a maximum deflection of 54.82 nm. I also tired Levy's Method and got the same value.
Now, I go to ALGOR import the plate from SolidWorks, write in all the material parameters. set the boundary conditions to all four edges fixed, turn in the gravity in -z and then run the simulation and I got maximum displacement in the center of the plate of 30 nm.
I have made the simulation many times, and I'm sure I've all the right values and still I don't know why this value is different from the one I got using analytical models.
I would be REALLY greatful for any help you can give me.
Thanks!
rgm