Stress results in a cantilevered beam

[Tunalover]

As I often do, I solve a simple problem with hand calculations then solve the same problem using FEA just to see how well they compare. When I FEA analyzed a simple rectangular cross-section cantilevered beam (with 2:1 the highest aspect ratio) with a vertical point load in the middle of the free end, I found that the highest stress does not appear at the wall, and, regardless of mesh density the highest stress is always one element away from the wall. Why is this?


Tunalover

 

[GregLocock]

Because FEA is displacement based, and you have constrained the nodes at the wall to have zero displacement.

Cheers

Greg Locock


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[rb1957]

are you TET meshing ?

Greg's point is (I think) that you are constraining the nodes at the end of the beam so one face of an element cannot move.

Try this, constrain the restraint nodes only in the load direction (this should react 3 rigid body motions (if you've got a sea of nodes on the end of the beam). now pick nodes to constrain in the other directions ... what we call 3-2-1 constraint ... in your case 1 is the load direction (say X) at node X,Y,Z, then 2 is an X and Y constraint at a node X, Y, Z2; and 3 an X, Y, and Zat node X, Y2,Z ...

clear as mud ?

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

 

[Tunalover]

rb1957-
Yes I am constraining all the DOFs at the wall. But your method is hardly intuitive. Maybe if you can provide a sketch? That would be a big help.

Bruce Jackson



Tunalover

 

[rb1957]

if you're "nailing" (fully suppressing) every node on a surface, then you're over constraining the face (you're stopping, for example, poisson effects; yes?).

do some research on minimal constraint for models.

lets say X and Y are the inplane directions, and Z is out of plane.
then at every node suppress Z ('cause every node should be reacting out-of-plane load)
This constrains 3 rigid body motions (yes?, if not, research "rigid body motion")
so you have 3 more to constrain (X, Y, and RZ; yes?)
constrain 2 nodes with different Y co-ord in X (to constrain Y and RZ)
constrain 1 node in X
this is commonly referred to as 3-2-1 constraints (one node is constrained in 3 directions, another in 2, and the third in 1).

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

 

[GregLocock]

Perhaps in a very simple example. You have reinforced one cross ection of your material with an infinitely rigid plate. It won't let the neighbouring cross section move, and if it can't strain, it can't stress, in certain ways. So it rather depends on how you define your stresses. Perhaps a higher order element formulation might not show the same effect.

I'm handwaving, FEA theory bores me to tears, but 35 years of experience with FEAers has led to a certain familiarity with the concepts.



Cheers

Greg Locock


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[rickfischer51]

Its a Poisson effect at the wall because you are constraining degrees of freedom you dont consider in your hand calculations. Set Poisson's ratio to .000001 and the stress will drop.

Rick Fischer
Principal Engineer
Argonne National Laboratory