Different Stress Values between brick, beam and hand calculation?

Hi Murat,

 I'm not sure what boundary conditions you used for the brick element nodes at the wall.  However, I suspect that you pinned them all at the support.  If this is the case, then this may be the reason.  You need to make all of the nodes rollers and only pin the nodes that are at mid depth of the beam.  So if the beam axis is along the x direction and the y axis is parallel to the applied load then at the supports make them all have x axis constraint only, then at mid depth of the beam make the nodes have x,y,z restraint.

 This happens I believe because the beam elements and hand calculations are basic mechanics of materials equations, whereas the 3d fem solution is a continuum solution with more local information provided in the model at the restraint nodes.  Hence, local stresses are developing at the support which the simpler beam and hand calculations cannot represent.  The simple equations do not consider restraint of the beam cross-section from deforming whereas pinning all the nodes does restrain the local cross-section.

As an additional check of your results you should check the top and bottom stresses of your cantilever at mid-length of the beam by hand, beam elements, and 8-node brick elements(these should match due to St Venant's principle even if at the support your restraint of the nodes is not quite right).  If these do not match with your current support configuration, then there is some other additional problem.  However, even if these do or do not match you should make sure your supports are as I mentioned previously above.

Clearly, this then becomes a modeling issue.  The question is, which way should you constrain the nodes at the support to model the real life condition?  If you are just wanting to see the hand, beam, and brick calculations match then my discussion above should lead to a match in results(with grid refinement).  However, if you really want to model a cantilevered pipe that is say welded continously at the support then perhaps you would want all the nodes pinned to model the true condition and get the maximum bending stresses that result at the support.

 I hope this helps,

Louie

Hi Murat,

 It is certainly good that the bending stresses match for the three methods at mid-length of the cantilever pipe. This indicates that the difference is indeed due to the local constraint conditions at the wall when using the brick element.

Your description of how you unlocked the constraints " ...except the ones at the midplane of the pipe wall thickness..." makes me wonder if you have pinned the nodes at mid thickness all around the middle circumference of the pipe.  If that is what you did, it is not what I intended.

See the image here. Only the nodes at mid-DEPTH of the pipe should be pinned at the wall.

 The pinned nodes(solid black circles) should have x,y,z restraint.  The remaining nodes should have just x restraint. Maybe you did do it as I intended, I just provided this picture to make sure I was being clear.  I think this should work.

If this does not work, then I can only say that perhaps the more precise continuum solution using the bricks is giving more precise local stress results.  Another thing to note is that it is sometimes difficult for problems using a 3d fem continuum solution to have restraints that mimic the simpler beam or hand calculations we often use from mechanics of materials.  Therefore, we might not expect them to match exactly.  (However, I thought if the restraints were correct the 3d fem solution would asymptotically approach the beam results as the mesh is refined.  Perhaps I'm wrong.)

 Another option would be to ask another person here at iMechanica.  Perhaps I'm missing something.

Good luck.

 Louie