Background Resumed: I have an ignorant but fundamental question that I hope somebody will take the time to answer. How does one compute (analytically, not via FEM) the bending in the glass beam from the geometry, forces, and torques shown in the above free-body diagram? (I don't mean to ask for a lesson on the bending of beams. I have simple equations for that, at least in the case of a thin beam where shear distortion is not important.)
Consider the following observations:
1) If the length of the support plates (in the y-direction in the first image above) and the weight of the glass bar are held constant, then the torque exerted by the right plate on the bar end, T1z, will remain approximately constant, independent of the height of the bar COM. (Assuming that the glass bar does not bend significantly compared to the much thinner plate, I can obtain this torque from beam Case 17 -- "S" bending -- in Machinery's Handbook.)
2) Varying delta -- the distance of the plate-bar bond above the COM of the bar in the free-body diagram -- which can be done without changing the length of the plates in (1) by varying the depth of the slots in the bar ends, moves the COM up or down relative to this bond, which is the location of application of T1z and the two components of F1. This varies the couple formed by -W and F1x (-W*delta) without changing T1z. (The couple, F2y and F1z, will likely also change.) Solidworks simulations show that varying delta also changes the degree of bending of the glass bar.
3) The bending of the bar can be reduced significantly by raising the height of this bond above the height of the bar COM, as shown in the figures. This suggests some sort of balancing between torques T1z and -W*delta that controls the moment in the right end of the bar. (The moment in the left end is essentially zero because of the slider below its support plate.)
4) The result in (4) is paradoxical in that, if the bar were supported directly by fixtures in the top of the slots, the minimum bending would occur when the top of these slots lies in the plane of the bar COM because the only applied couple, -W*delta, is zero then. The solution to this paradox is obviously that the bar bends primarily because of the torque, T1z, imposed by the "S" bending of the right plate.
To explore these issues, I created the quasi-2-D model described above, which is a highly simplified version of the real 3-D assembly on which I have been working. Here is an example of the bending that occurs in the glass bar and the right plate in this model:
The replacement of the glass bar with a beam was to see explicitly the bending moment in the bar so as to compare it with the torque and couples shown in the free-body diagram.
This is a long-winded buildup to the fundamental question that I cannot answer: If all the torques in the free-body diagram above already balance, how does one determine the moment applied to the right end of the glass bar? -- John Willett
This appears to be a solution to the problem explained in my second post. Since there is a flexible element in the free-body diagram above, the beam equations must be brought in to fully solve the problem analytically. Here's a way to do that:
1) Remove the flexible glass bar from the free-body diagram and replace it with forces and torques exerted by the beam on the two ends as in the diagram below. The external forces from the original free-body diagram still remain, although the weight of the bar is now explicitly transferred to the right end because the left end is anchored to a slider. Now there are effectively two separate free-body diagrams.
2) Use the beam equations to relate the forces and torques applied by the beam to the two free-body diagrams, one of the left end and one for the right end. The problem is once again closed, and the resulting equations are interesting:
M = T1z – W × ∆ = F2y × L
This tells me that M in the right end of the beam decreases linearly with increasing delta, explaining observation (3) in the previous post. It also shows that F2y (and of course F1y) varies linearly with M, hence with delta. I believe this answers my "ignorant but fundamental question."
I would appreciate any feedback as to whether I am finally understanding this problem correctly. -- John Willett
I still have my original question (even assuming that the answer proposed in my third post to the second question is correct, of which I'm still not sure). Having played around with the model with solids and beams, I can sharpen it up a bit:
First I build and study the results of the all-solid model. They seem to make sense. Then I replace the glass (blue) bar with a beam (treat as beam in the parts listing for the study). This seems to bring over all the cross-section and material characteristics of the bar correctly. Finally I look at the torque on the face of the right end piece that is bonded to the beam (simulation/results tools/list free body force), using a center point on that face as the vertex for moment. (There seems to be no direct way to get the overall beam moment vs. length from the beam itself.)
The case with the beam exerts a z-torque on the end piece that is less than 1/2 that in the case with all solids. This even though the same torque component at the bond between end piece and support plate is the same (larger) value in both cases. The x-normal stresses in the solid and beam also seem about the same, as do many other aspects of the solutions. Why this large difference?
I understand (I think) that the beam-solid bond becomes essentially rigid, and this might explain the approximately doubled value of von Mises stress at the bond between end piece and support plate, but the end piece is already nearly rigid, so why should this matter so much.
Again, am I doing something obviously wrong? -- John Willett
In the absence of any comment, I'm forced to conclude that the bond between a beam and a solid simply does not give the correct value of torque on the solid face, even though this may not significantly affect other aspects of the FEM solution. Anybody agree or disagree? -- John Willett
Dave Bear wrote:
I'm sorry you didn't get an outcome on this. I was interested to see what help/suggestions would arise.
My curse is that I'm just smart enough to know how dumb I am.
Post's like this one illustrate that very clearly.
FYI, in case anyone is still interested, I went through my VAR with this model and got the following useful input from SW:
1) I had not realized that one can get the forces and toques in the beam itself by right-clicking Results and selecting List Beam Forces. These results appear to be correct and agree with those from the all-solid model.
2) The SW Tech agrees there is something wrong with the free-body forces on the face of the end piece due to the beam. It appears to have something to do with Global Contact, which I left set to Bonded, in spite of having made individual contact sets on all contact pairs. "It almost seems like the automatic bonding is causing the end of the beam to be bonded to an additional face made from the Cut-Extrude1 feature of the end components. If I run a test where I exclude the stud plates (and modify fixtures), probing the Free Body Force on the faces that were part of the cut shows the missing portion of the Free Body Force. It only seems to happen with some geometries where there's a second face facing the beam behind the face that it actually should bond to."
More later from SW:
"I’ve confirmed that this issue occurs with automatic beam bonding (from global bonded contact) in cases where the solid body has both a coincident face, and another behind it whose normal also points towards the beam end joint and is located a close distance away. I have filed:
"SPR 1063499 – 'Automatic bonding (via component contact) causes beam end joint to be connected to both the solid face it is coincident with, as well as another nearby face behind it.'
"...The only workaround I’ve found for such geometries is to rely on local bonded contact sets, rather than the global condition. Having global condition switched to Allow Penetration, and defining bonded contact sets where needed avoids the issue."
This work-around is fraught with problems, however, as Contact Verification then shows the faces between beam and end pieces are No-Penetration instead of Bonded as they should be, and it forces a Direct Sparse solution requiring much more memory and time to solve the resulting contact constraints. Without the Global Bonded setting, it is also no longer possible to get compatible mesh even across the still-bonded faces between stud plates and end pieces. I also tried completely deleting the global contacts, which eliminates the former problem but still suffers from the latter.
More than enough said! Best Regards to All -- John Willett