Shell element vs. frame element analysis 1

[MadeleineVincent]

Hi everybody,

I have a model of a tall, slender structure that I am investigating using both shell and 3D frame elements.

The shell elements are type MITC4, 4-node membrane elements. The frame elements are the basic line (1D) elements found in any introductory structural analysis / stiffness method book - they include axial, bending, and torsion, but no shear deformation.

Both analysis are linear-elastic (no geometric or material non-linearties), small-deformations using the direct-stiffness formulation.

As a test case, I loaded the structure with a unit load at the top node (or nodes, for the shell element model), once in a direction perpendicular to the long axis of the structure (X-axis), and once down the axis of the structure for pure axial loading (Z-axis). I neglected all self-weight for this test case.

[I also compared X and Y direction bending, which matched exactly as expected, since the structure is symmetric.]

I compared these results with those found by simple hand computations for a linear-elastic beam:

Axial deformation (Z-axis) = PL/AE Bending deformation (X-axis) = PL^3 / 3EI

For the frame element model, these results matched exactly. For the shell element model, the axial value was nearly identical (which I take as a good sign that the area is correct).

The bending deformation for the shell element model were somewhat smaller (~8%).

What I would like to know is, is this expected behavior? Should I expect the shell element model to be "stiffer" than the frame element in general?

I understand that the choice of Poisson's ratio in the shell element has an effect here as well. I'm using 0.30 for steel.

Thank your and regards,

Madeleine.

 

[ShellsPlatesMeshes]

Yes, the Poisson's ratio does count.
More about the MITC elements here (in particular, the numerical errors are discussed):

http://www.adina.com/newsgD03.shtml

 

[btrueblood]

Yes, beam/frame models will tend to be "stiffer" than more general models, due to the absence of shear terms. A somewhat better explanation is in

http://en.wikipedia.org/wiki/Timoshenko_beam_theory.

You could also do a numerical comparison using beam vs. shell elements of a simple beam, and compare to theory. (You should be able to find a copy of Mr. Tim O'Shenko's book "Mechanics of Materials" where the analysis is covered in much greater detail).

 

[JoshPlumSE]

TrueBlood -

He said the deformation was smaller for the the shell element model. I'd expect it to be greater for a couple of reasons:
1) Shear deformation
2) Plane sections may not remain plane.

My guess is that the plate elements need to be sub-meshed a bit. When a plate element model is undermeshed it will always be a bit too stiff.

 

[rb1957]

it all depends on the details ...

i'd expect the shells to be stiffer in bending 'cause you've got the full web working for you, if the linear elements model effective area (like 30t effective width of the webs).

but if the area of the linear elements is the same as the webs (ie fully effective) then I'd've expected the linear elements to be stiffer ('cause you've put all the area at the extreme fiber).

unless you placed the linear elements at the centroid of their effective area, then they should be really similar. mind you 8% usually counts as "really similar" in FEA.

another day in paradise, or is paradise one day closer ?