A cantilever beam subjected to the uniform pressure load

[Yuchi Kang]

Hello everyone,
I am trying to calculate the max deflection u2 of a cantilever beam. The cross-section is circle whose radius (r) is 0.01m and length (l)is 1m.One end is fixed and one end is free. This beam is subjected to a pressure on its upper circumferential surface with 10000Pa. In order to verify this model, I calculate the deformation in this way:
p*2r*(l^4)/8/E/I
E is 210*10^9Pa, I=pi*(2r)^4/64
The hand calculation of deformation at the free end is 1.516mm. However, the numerical result is 1.627(for C3D8I) and 1.704 (for C3D8R).
What's the reason for this discrepancy?

Yuchi

 

[IceBreakerSours]

With regard to the numerical side of things, how many elements do you have through thickness?

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[Yuchi Kang]

Hi, IceBreakerSours.
Total element is 5200. The globe size is set as 0.005.

 

[IceBreakerSours]

Correct me if I am wrong: Are you saying you have 20 elements through thickness? If yes, then (keeping your question aside) that seems overly excessive.

More importantly, on the analytical side, you have a long and thin beam under stress. I have not done any hand calculations but I wonder if the theoretical assumptions are even valid.

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[Yuchi Kang]

Hi. Sorry for reply late. I think it's correct about the analytical side although Large deformation is considered. I think the main reason maybe associated with the element type(C3D8I). I will continue to work on this then post my new findings.