Learning Forum

I am looking at the gravitational sag of an object held at 4 supports (visible in the picture below, which is a bottom view of the system). The supports are implemented as displacements with the y component (the direction of gravity) set to 0 and the other components set free. I noticed the following 2 issues:

1: If I apply this boundary condition to point-like supports (the 4 points at the centers of the holes in the picture) convergence with the mesh size is poor for some of the displacements I try to measure and the results don't always respect the symmetry of the problem (for instance there is one mirror plane with respect to which results should be symmetric and they are not). If I instead apply it to finite disks, convergence is better, but measured displacements in the y direction get bigger as the radius of the disks decreases and don't seem to converge to some limit as the disks become smaller (and below a certain radius I start running again into mesh convergence issues). I would appreciate any suggestions on how to improve these simulations in the small contact surface limit.

2: I want to measure the tilts on the inner surfaces of the two flat disks at the ends due to bending of the object under its own weight. I am implementing a remote point out of a few mesh points on a line parallel with the y-axis, as seen in the image below, and using the ROTX  APDL command to look at rotations around the x-axis. The measured tilts are inconsistent when I change the mesh size or make small changes in the support positions or even on multiple runs of the same simulation. If I look at the difference in tilts between the two sides, those results are consistent, though, which makes it look like maybe there is an offset added to the two tilts due to rigid body rotation. I expected some erroneous rigid body motion in the xz-plane due to the lack of constraints there (and I see it, but it's easy to subtract and not a problem for me), but did not expect this rotation, and I am not sure how to measure the actual deformation/bending when it's covered by it. What makes things tricky is that the material is anisotropic, so the two tilts are not expected to be symmetric/equal. Is there a way to eliminate this rotation from the results?

[Dave Looman]

It's expected that mesh convergence becomes problematic as the support approaches a singularity (zero area).  As soon as the support area becomes too small to prevent gross local deformation it is too small.  Your 4 UY constraints should have prevented ROTX and ROTY rigid body motion (assuming the support areas are large enough.)  Even though you have a way of dealing with the unconstrained lateral motion, it would be better to prevent it as having a zero stiffness can create numerical error.  

[peteroznewman]

Do these two disks have optical surfaces?  I assume that is why you want to track the tip/tilt of them. Are these optically flat mirrors or windows or does the surface have some curvature?

Optical parts are fastened to a barrel or some other mechanical part to support them. It is troubling to have rigid body motion in the xz plane because you haven't added sufficient constraints to support the optical parts. I suggest you do that before you try to measure tip/tilt.

Mechanical parts are supported on an optical bench, which you consider to be ground in this simulation. It is unusual to have four support areas on the mechanical part becuase that leads to problems when the four legs have any kind of variation or have different themal expansions when the temperature change is different on one leg than another. Three supports is a typical design for connecting the mechanical part to the optical bench.

Whether you have 3 or 4 supports, it is always best to have that support be a finite area. Whenever solid elements are used, avoid supporting individual nodes because that creates a theoretically infinite stress due to a node having zero area.

[ami2020]

The disks are indeed optical surfaces (mirrors). They have a large (10m) radius of curvature, which I ignored for now for simplicity.

Typically the whole thing sits on 4 symmetrically placed rubbery balls or on rounded pins on springs, which are meant to add a little bit of vibration isolation. It's not rigidly attached to the supports, though, it just sits on them, so I'm not sure what is the most realistic type of support to use that would constrain its xz motion. The contact surface is supposed to be just the very small areas at the center of those holes where the flat and rounded surfaces intersect.

I can see how supporting individual nodes is problematic and a finite area is the way to go. Maybe to get rid of the dependence on the surface area a better approach would be to redo the simulation with several different contact sizes and try to extrapolate to zero?

 

[peteroznewman]

A more accurate solution would include the four rubbery balls in the model. The bottom of each ball can be a Fixed Support. Use Frictional Contact between each ball and the flange on the barrel. Use a hyperelastic material for the balls to create a soft support. The part will settle down on the four balls as the gravity load ramps on during the solution. Friction will prevent rigid body motion in the xz plane.