7 Replies Latest reply on Mar 25, 2017 3:51 PM by John Willett

# Violation of Small-Angle Assumption?

I'm running SW Premium 2017 SP2.0, so it's linear static simulations only.  (This post has now been edited multiple times as I learn more.)  I guess there are really three questions:

1) Engineering: Am I getting wrong answers by using linear static on this problem?

2) Solidworks: Is there a way to get the Large-Displacement option to work with this model, as SW Help implies that it should?

2a) Combined: If not, can anyone think of a work-around to get the same boundary conditions without using a shell?

The problem is shearing a right-circular cylinder between rigid, parallel planes.  The bottom plane is represented by a fixture.  The top plane is displaced parallel to itself (X direction in image below) and must be allowed to move perpendicular to itself (Y direction) but not to tilt.  The only way I found to do this was to use a very stiff shell for the top plane and to constrain the edges perpendicular to that displacement so that they could not rotate around themselves (Z direction) like this:

(The dimensions of the cylinder are 3/8" X 1/8".)  Linear static simulations with small X displacement give near-zero Y displacement of the shell.  Large-displacement solutions give essentially the same until I make the prescribed X displacement 8X larger than the .001" shown here.  Then they fail during "Equilibrium iterations" within a single load step.  I've tried many combinations of settings in Study Properties to no avail.  If I make the X displacement significantly larger (say .02"), LD will set up more than one load step, but it still fails the same way.  Converting the problem to applied force instead of displacement doesn't appear to help either, although I can get it to go much further into the first load step before reporting, "Equilibrium satisfaction is not achieved."

I expect near-zero perpendicular displacements for very small parallel displacements (cosines of small angles).  I believe the planes must be pulled closer together, however, as the shear becomes large because the material begins to be stretched in tension (the volume is not changed, of course, under "simple shear," I think it's called), but I'm guessing it takes fairly large shear for this to show up.  Is my intuition wrong, or is my linear static solution just letting me down? -- John Willett

• ###### Re: Violation of Small-Angle Assumption?

Hi John,

I've looked through your setups and the description you have typed up but I am still left wondering what it is that you are trying to measure here and what real life system you are replicating.  What is supposed to be happening here that is not?

Is your concern with the non-zero Y-displacements on the front/back?

• ###### Re: Violation of Small-Angle Assumption?

>>...I am still left wondering what it is that you are trying to measure here and what real life system you are replicating.  What is supposed to be happening here that is not?<<

Ryan -- I'm sorry I wasn't clear.  The real-life system is a telescope mirror with its back face glued with silicone-rubber pads to a "rigid" substrate when the mirror is pointed horizontally wrt gravity.  This idealization considers only a single pad.  The mirror cannot tilt wrt the substrate because the other pads prevent that (ideally -- torque due to the offset COG of the mirror is ignored for the moment but in any case would cause minor tilt because of the other pads).  This might be a case of "simple shear" (no thickness change) except that there is nothing to prevent the pads from all changing thickness together.

What I'm trying to find out is whether and how much the pad thickness changes.  In linear static solutions it changes infinitesimally, but without a large-displacement solution I cannot be sure that this "second-order" change is correct.  Tests that I've done replacing the pad with a thin, steel rod (for which LD works) show appreciable shortening of the gap between faces, roughly as cosine(theta), as the transverse displacement (or theta) is increased.

Now I've also tried increasing the mesh resolution, but LD still fails.  I hope this clarifies the situation. -- John Willett

• ###### Re: Violation of Small-Angle Assumption?

Okay, that make more sense.  I think I'm on-board with your now.

You mention that for prescribed displacement values above 0.008" the Large Displacement solver fails on the model.  I just confirmed that on my end too.  In the linear static solver there are no settings to massage how Large Displacement works to help it solve in cases like this.  It either works or does not work.  If you are looking to get results for displacement values above 0.008" then you would need to move this setup over to the nonlinear solver.  I ran your setup in the nonlinear solver with 0.008" and it completed with just the default settings.  If you don't have nonlinear though I don't think you will be able to move forward with the linear static solver.

• ###### Re: Violation of Small-Angle Assumption?

Ryan -- I really appreciate your worrying at this.  It sounds as though you didn't spot any tricks I had missed to get the LD solver to work.

It's frustrating that this seems hit or miss and that I have no clue what might be preventing LD from running when it appears it should.  One thing I haven't tried yet that might be worthwhile is decreasing Youngs' modulus of the shell, which is pretty extreme compared to the elastomer, and/or decreasing Poisson's ratio of the elastomer, which is basically as high as I could push it without crashing the solver.  I'll also see if I can get anything useful out of my VAR and report if successful...

Thanks again! -- John Willett

• ###### Re: Violation of Small-Angle Assumption?

>>If you don't have nonlinear though I don't think you will be able to move forward with the linear static solver.<<

Ryan -- VAR tech support essentially agreed with you, but they did suggest a work-around to avoid the shell part:  Use Remote Displacement/Direct Transfer to apply the transverse displacement to the upper face of the pad.  This produces essentially the same result as the very stiff shell because the rigid-bar connections keep that face flat and (if the appropriate rotation is zeroed) prevent tilt while still allowing vertical (Y-directed) motion.  I can get LD to solve for much larger displacements this way than with the shell.

Other ways I've found to deal with this problem are to decrease Poisson's ratio somewhat -- say from 0.4997 to 0.4900 -- and/or to use two pads sandwiched symmetrically beside one another beneath an upper solid plate that is displaced only in the X direction but not restrained in Y.  The symmetrical assembly prevents essentially all of the tilt without using a restraint.  All of these approaches will solve for larger displacements that the one with the shell.  The shell version also is not improved much by smaller Poisson's ratio, so it appears to have been most of my problem.

I discovered another useful thing about the LD option in linear static:  Sometimes it will report, "Solver failed.  Do you want to restart?"  Knowledge Base tells me, "When the user clicks on 'Yes', the solver will adjust the loading increment (for contact, some other adjustment might also be triggered.) and restart from the previously successful loading step."  This does help to complete the solution in some cases by adding more, smaller load steps, more or less as could be done manually in a non-linear study I suppose.

The bottom line is, as Chris advised, "If at first you don't succeed, try different things."  Thank you both for your assistance.  It's always a learning experience to interact with other helpful members on this site. -- John Willett

• ###### Re: Violation of Small-Angle Assumption?

John, I can't speak to your specific problem, but nonlinear may shed some light on this.  I'm assuming you don't have it, though?

One has to be careful with the software.  It is marketed to anybody who isn't colorblind (RED: BAD, BLUE: GOOD, I think is their sales pitch).  I would prefer it be marketed to engineering professionals that at least know what Von Mises stress is and have at least once seen a Mhor's Circle.

That being said, I ran across a problem with buckling analysis on non-Euler columns in linear.  Totally false results, but the fact that results were given gives the operator a sense of assurance.  Fortunately, old-school codes illuminated the problem, and the crisis was averted.  This was only on a multi-billion dollar project, so no big deal, right?

I have a buddy that's an elastomer guru.  He presented at SWX world one year.  When asked what he thought of SWX simulation (even nonlinear) he said NO-GO when it comes to elastomers.

If this problem is even possible in linear simulation (maybe not) perhaps try some different setups.  Simulation works good in some instances and not in others.  For instance, why that shell on top and not a big, thick block?  Perhaps a different material instead of steel will give a higher stiffness.  Molybdnum under "other metals" is about 50 percent higher elastic modulus than what you're using.  Don't know if it will help, but maybe.

If at first you don't succeed, try different things.  That's what I've found out.  Often your constraints aren't doing what you thought.

Do you have proper material properties of your RTV?

Do you have any way to do some hand calc verifications or real-life experiments so you'll have a better idea what you're looking for?

• ###### Re: Violation of Small-Angle Assumption?

Chris -- Thanks for taking the trouble to write such a thoughtful reply.

>>For instance, why that shell on top and not a big, thick block?  Perhaps a different material instead of steel will give a higher stiffness...<<

The shell is there because of the boundary conditions I want (prevent tilt without constraint on vertical motion, which I don't know how to do with a solid).  Last night I thought of a possible way around this, however, using two identical glue pads side by side with a single steel block on top of both that is unconstrained and forced to the right.  That should eliminate tilt while still allowing vertical motion and avoiding the shell.  (It actually seems as though there's a kind of symmetry operating there.  Imagine cutting the block with a vertical plane half way between the pads.  The pads are identical except that they are displaced in the same direction wrt the "symmetry" plane, not mirror images.  I haven't figured out a way to set this up in SW yet...)

About the steel, it's already had its Young's modulus increased 1000X over the library material to get it essentially rigid.  (I have had no success and been warned off of "make rigid," and anyhow it doesn't work with shells.)  In fact the vast difference between that and the elastomer (or setting Poisson's ratio of the elastomer so close to 1/2) could be part of the problem.  I can play with both of those.

>>If at first you don't succeed, try different things.  That's what I've found out.  Often your constraints aren't doing what you thought.<<

That seems to be a place many people make mistakes.  As I said, that's what drove me to the shell in the first place.

>>Do you have proper material properties of your RTV?<<

I'm actually being generous by increasing Young's modulus by a factor of 3 over the measured value and "shading" Poisson's ratio slightly below 1/2.  As mentioned above, the latter might be a problem and needs to be varied...

>>Do you have any way to do some hand calc verifications or real-life experiments so you'll have a better idea what you're looking for?<<

Well, there is a perfectly good (and simple) formula for the stiffness of this kind of bonded pad in simple shear.  This problem is conceptually simple enough that there might be an analytic solution for the thinning of the pad with unconstrained shear, but I have not found one.  Any ideas? -- John Willett